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Home » Blog » A Writer's Relentless Journey, an Interview with Vanessa Martir
A Writer's Relentless Journey, an Interview with Vanessa Martir
One of the many reasons I am publishing these interviews is to give proper credit to those people in our communities who are doing amazing work and have impacted my life one way or another, the everyday hero who is not known by many. One of those people is Vanessa Martir. I first met Vanessa in the Spring of 2013 at my first reading with The New York City Latina Writers Group. She is someone who lets her presence be known when she walks into a room, especially as a writer. That day she shared her journey and the importance of respecting your craft and working relentlessly at it.
After that first encounter, I kept running into her in the writing scene and finally, in the Spring of 2017, I became one of her students at the Writing Our Lives workshop. Vanessa has helped me tremendously in my writing. By working with her I found my voice on the page and I let go of the shame others made me feel because of my accent, as she always reminds me "You carry Venezuela on your back and that's who you are, punto!". She also challenged me to read books I otherwise wouldn't pick up to read and to enjoy those books as a reader but also as a writer. After three workshops with her, my work has been published in numerous publications, I became a VONA alum in the Summer of 2017, created a book-writing club with a group of former members of her class (The Musa) and I have not stopped writing and submitting.
These series of interviews would not be complete without discussing with her the writer's journey, her own and the importance of documenting our stories.
– – – – – – – –
WA: Who is Vanessa Mártir, Where were you born?
VM: That's a big question. I'm many things: a queer woman, a mother, a writer, an educator, a sister, a daughter, a friend. I was born in NYC, raised in Bushwick, Brooklyn before gentrification, when the neighborhood was littered with abandoned buildings and rubble and garbage strewn lots, before and during the crack epidemic that destroyed so many of our people and communities. The foundation of my social activism was built there: in Bushwick.
I'm also a scholarship kid via the A Better Chance (ABC) Program that gave me the chance to attend a prestigious school in Wellesley, MA. I've also attended an Ivy League University. I am all these things too while holding on to and honoring my roots as an Afro-Indígena, Boricua-Hondureña, raised in the hood.
I'm a social activist. I am loud and quiet, an ambivert who loves community and fam, but also needs her solitude.
I'm a brooder, a creative. I love hard and bite back. Fierce and unfuckwithable, I am strong but not invincible. I contain multitudes.
WA: When did you claim yourself a writer? Why do you feel it takes time to claim it?
VM: It took me a long time to claim myself a writer, though I know now I became a writer in the plum tree of my backyard in Bushwick. It was up in those branches that I started telling myself stories. I left Bushwick at 13 to attend boarding school, and in eleventh grade, my professor gave me How the Garcia Girls Lost Their Accents by Julia Alvarez and my world has never been the same. This was the first book I'd read by a Latinx writer, and I could relate to her characters and their struggles in white America because I was living them. For the first time, I thought: "Maybe I can be a writer."
I started eating up books by Latinx writers and writers of color, hunting them down, however, I could. This was before the internet was really accessible so I asked teachers and dug into library shelves. When I went to college at Columbia University, I took every Latino literature and culture class I could, and in my junior year, I joined the fight for ethnic studies because I wanted to study the immigration experience. I wanted to know myself.
But that elite education coupled with the working class immigrant mindset instilled in me by my Honduran mother made me wary of pursuing the arts. How could I pursue a writing life? I needed a job, a salary, health insurance. So I did what was expected of me–I entered corporate America.
I was miserable for a long time. I wrote on my free time. I was published here and there, but I was still running away from the call. I was still referring myself a writer out of the side of my mouth.
It was when I was pregnant with daughter in 2004 that starting writing again in earnest. I filled five journals during those nine months. And I knew I couldn't go back to corporate America. I know what misery does to a family. There's a reason why I left everything I knew and loved at 13 to make my way out in the world… So, I set it up so I'd get fired (because my boss was Satan) and I wrote my first book, Woman's Cry. That's what it took to call myself a writer and believe it. I never looked back.
WA: Describe your writing process and what is your favorite place to write.
VM: This too is a huge question. I always think of Daniel José Older's essay "Writing Begins with Forgiveness" when I think about the writing process. I have made writing a part of my life. I write anywhere and everywhere, but I find there's something about writing on the train that opens something up for me. I also love writing in nature, in the woods, under a tree. I have a writing room now, so I love writing there, and on my deck, and on the corner of my couch. I've worked on training myself to write anywhere. Inspiration is great, but you have to grab the reins back and show up, so I do. Sometimes it works, sometimes it doesn't. I show up anyway.
WA: You are always talking about the importance of telling our stories, what is the responsibility of the writer? Do writers have a collective purpose?
VM: I think a writer's responsibility is to her work, to her stories, her authentic voice. As for a purpose, I think that's very individual, but I've found that when I ask writers why they write, their answer usually sums up to this: they write to take their power back. I know I do.
WA: What role identity plays in a writer's life, how important it is in your opinion
VM: I can't speak for anyone but myself here. I know that for me, identifying as a woman of color, as Afro-Indígena, as a woman from the hood, daughter of immigrants, has helped me in writing my stories. It's helped me determine how I approach the story; for whom I'm writing the story, that is, who is my intended audience. It's also helped me examine why I write the stories I write, what's important to me culturally, what do I want to honor as a writer of color, as a woman, as a second generation Latinx woman. There are so many layers to our identities and knowing what they are can help a writer understand themselves and their work better.
WA: What is the most daring thing you've ever put into words?
VM: I am really vulnerable in my work. I work to break silences that no longer serve or protect me if they ever did in the first place. I think the most daring thing I've written is about being unmothered, what happened to my mother that she couldn't and still can't mother me.
I have an essay coming out in Roxane Gay's anthology Not that Bad that is probably the most vulnerable thing I've ever written, which says a lot because if you know my work, you know I do a lot of shadow work. This essay is about my own experiences with incest and sexual assault, and ties into what I know about my mother's story. It took me seven years to write that essay, and I'm still terrified to have it out in the world, but it was time, and I'm honored that it found a home in that anthology.
WA: Writers often times have dealt with censorship, how you deal with it? Is it acceptable?
VM: This is a timely question. I just had to pull an essay from a magazine in Australia because the edits the editor in chief made felt like silencing. The magazine reached out to me to write for them. They follow my work and wanted my voice, my stories. So I submitted an essay about how my mother rejected my relationship with my butch partner. I included some of my mother's story because it's necessary to understanding why I am unmothered and why I had to (and could) walk away from her. The editor in chief determined that for legal reasons, much of what I'd written about abuse and rape, could not be published. I've worked so long to dismantle and reject a silence around these very issues, both in my family and society as a whole, so I couldn't in good conscience accept these edits. It was an extremely triggering situation, but I know withdrawing the essay was the right decision. This is about my integrity, and that's something I'm not willing to compromise.
In other words, you have to determine what you will accept when it comes to censorship, and it's important to understand and come to terms with your motivations. Only you can make this decision.
WA: In this age of social media frenzy, Where is the line between observation and surveillance?
VM: Observation as I understand it is the act of observing and being observed while surveillance is a close observation of a person or group with suspicion at its core and/or motivation.
I'm wary of social media though I am in all up in it, as a writer and documenter of my life. I've found a lot of love and solidarity online but have also found some real ugliness. People who watch you to wish for your failure, to harass you, to come for you at every chance they get. The internet has given the biggest cowards cojones the size of a bull's. It can be disillusioning and upsetting. I try to take breaks, to protect myself as best I can from those kinds of people, but as someone who writes online, it's hard to escape it.
I talked to a friend recently who has gotten some really ugly shit thrown at her via social media. It's hard to deal with that and remind yourself that you are loved, your work is important and necessary. When I'm feeling most distraught by it, I turn to folks who love and care for me. They hold up a mirror I believe in and trust. They keep me accountable and on my toes. I know they will be loving and tender with me. I know they will remind me of what and who is important.
WA: A lot of times being a writer is often discouraged by those around us, how you deal with this and your advice to those emerging writers experiencing this.
VM: It's hard when people you know and trust turn their backs on you because they don't like something you wrote or they can't handle your shine, or feel somehow challenged or insecure around you. This has happened to me a few times. I've had people in my family turn on me. That shit is hard. It's important to honor your feelings. Sweeping them under the rug or pretending that you are unfazed won't help you heal. It will show up somewhere else–how you show up for people you love, your relationships, your ability to trust, etc.
While I encourage you to let yourself grieve and feel the disappointment and loss, I also encourage you to remind yourself of why you are a writer and what made you start writing. Remind yourself of why periodically. Why you started and why you continue to write. This will give you courage and strength when it gets hard.
As Anne Lamott wrote: "You own everything that happened to you. Tell your stories. If people wanted you to write warmly about them, they should have behaved better."
I try not to write out of a place of resentment, though I know sometimes I have to write through it to really get to the story. That's where revision comes in. I'm not trying to vilify anyone in my work. I'm trying to make sense of the things that I've experienced and endured, and how it is I became this woman who writes to break down silences. So, while Anne Lamott's words are true, it's not easy. Not one bit.
WA: Which writers have influenced your work?
VM: There are so many but I'll give you a few: reading Julia Alvarez when I was a teenager made me believe for the first time that maybe I could be a writer too. Since then, I've been influenced by Roxane Gay, Jaquira Díaz, Junot Díaz, Chris Abani, Cherrie Moraga, Gloria Anzaldúa, Sandra Cisneros, Cheryl Strayed, Lidia Yuknavitch, Elmaz Abinader, Sofia Quintero, Linda Nieves Powell, Mat Johnson, Lizz Huerta, Glendaliz Camacho, Bell hooks, Toni Morrison, Alice Walker, and the list goes on and on and on…
WA: When did you discover you were also an educator?
VM: I discovered this after I wrote my first book. I started working with children doing literacy work and I really enjoyed it. Later I was asked to facilitate a fiction writing workshop with emerging writers and that solidified it for me: I wanted to teach and I was also good at it. I still am.
WA: You are the creator of Writing Our Lives which has helped many writers to propel their craft, how did you come up with the concept?
VM: I created a video recently to answer this very question. You can find it here.
In 2009, I attended my first VONA/Voices workshop. I walked out of there knowing I wanted to help bring our stories in the world. Stories by marginalized writers like me who didn't see themselves in the American canon, in the books they read in school or the ones that made bestseller and must-read lists. Writing Our Lives is my way of helping to bring our stories into the world.
There was so much going on in the country and in my life when I created the class. I quit my full-time editing job and threw myself heart first into writing and teaching. The climate of the country was contentious, to say the least—Prop 8 had just been ratified, anti-immigration legislation was sweeping the nation and the Texas Textbook wars were gathering steam.
The present climate continues to fuel my belief that it's time we write our stories, that we write them in our voices and that we do so unapologetically. The massacre in Orlando, the Black Lives Matter Movement, the murder of so many young black and brown women and men by police, the reality that Trump is in the White House…all this has served to convince me even more that: we need, the world needs our stories.
I've been enamored with all things autobiographical since I was a kid. I ate up the Laura Ingall's Wilder Little House on the Prairie books (which I know now are very problematic but was too young to know that then), reading the series at least three or four times, but it was reading St. Augustine's Confessions in my first year at Columbia that really grabbed me up and didn't let go. Known as the first memoir in history (which is questionable but that's a conversation for a later time), that book started this personal writing obsession that has made me search out and read thousands of memoirs and essays, that I've used to create this class: the Writing Our Lives Workshop, which I've reinvented several dozen times, and built upon on the journey.
My homegirl and fellow Bushwick veteran asked me recently what's different about my approach to this work. My response is relevant here: While I do teach craft, technique, and structure, etc., I think what stands in the way of most writers I've encountered in my teaching, is not technique but shame, and the emotional willingness and ability to navigate all that this kind of excavation will bring up. Much of this requires that we unlearn what we've been told about ourselves.
We've been told both directly and subliminally that our stories don't matter. We're taught this when the bulk of the authors we read in school are white men, and the history we learn is white and Western. It takes deliberate work to unlearn this.
I'm not afraid to walk with them on this journey, to help them navigate it, to share what has helped me, and to encourage them to keep digging while also taking intentional steps in caring for themselves while they're doing this work. As Roxane Gay once said: "Writing can't be everything." It's a part of the work we do to grow and heal, but it's not the entirety of the journey. It can't be.
WA: When did you launch it?
VM: I launched it in the spring of 2011.
WA: Why is it important to you personally to do this?
VM: Because I believe with my entire heart and body that our stories matter, and it's time we write them. I also know it's not easy to excavate your life for stories. I think it's my calling to help writers in their journey to do so.
WA: How does it feels to help so many writers find their voice?
VM: It's a responsibility that I take very seriously, and I am honored that so many writers have trusted me in their journey. I confess that I have some issues accepting praise, and that is rooted in my own upbringing and trauma. I'm working on opening myself up to this and receiving it with humility and pride.
WA: Writers read, you constantly encourage your students to read. What are you currently reading?
VM: I read essays daily. Personal, memoir and craft essays. I have a subscription The Sun which I am always digging into, along with Poets & Writers. I just bought the 2017 Best American Essays and am digging into that while also reading Jesmyn Ward's Men We Reaped, Alice Anderson's Some Bright Morning, I'll Fly Away, Roxane Gay's Difficult Women, and Carmen Maria Machado's Her Body and Other Parties. I also have Dr. Clarissa Pinkola Estes Women who Run with the Wolves at my bedside and on my desk, and I pick it up periodically to read excerpts whenever it calls to me. I've been doing this for years. That book is like a bible to me.
WA: Do you consider writing a healing process? Why?
VM: Writing for me has been an enormous part of my healing journey. I write to take back my power and try to make sense of and reconcile the things I've been through. I also stress that it is only part of healing, which I consider a journey, not a destination. Therapy has also been an enormous part of my journey as has been self-care like hikes in nature, working out, brooding, etc.
WA: How would you like to be remembered?
VM: That's a heavy question…I guess I'd like to be remembered as someone who loves her daughter immensely and mothers her in resistance to how I was mothered. A woman who is relentless in her work and approach to life, who loved with her entire self, who doesn't take shit, is unfuckwithable and strong, willing to check herself and learn. A woman who did what she could to help writers write their own stories. A woman who broke cycles.
WA: What's next for Vanessa?
VM: I'm bringing Writing Our Lives online starting in November. I have two classes coming up: Writing Fiction from Real Life, a three-part generative class, starting on November 8th; and Reclaiming Your Voice, also a three-part generative class, starting December 6th.
I'm also in the midst of creating a multi-genre class called "Writing the Mother Wound", as so much of my journey has been to write about my own mother wound and seek out the work of writers who have done the same, through various genres. I've been working towards creating this class for some time now. I'll be offering it in the spring in person in NYC and online. More information will be posted on my website in December.
I'm also expanding my teaching by teaching with reputable organizations like Sackett Street Writers in Brooklyn, and in the spring I'm joining the Grub Street faculty in Boston.
I'm in the midst of completing my memoir A Dim Capacity for Wings while also working on editing an anthology by and for unmothered women, and an anthology of writing by folks who've taken my Writing Our Lives classes. All this while I continue to submit and publish essays and short stories. I am relentless after all. 🙂
Vanessa Mártir is a NYC based writer, educator, and mama. She is currently completing her memoir, A Dim Capacity for Wings, and chronicles the journey at vanessamartir.blog. A five-time VONA/Voices and two-time Tin House fellow, Vanessa's work has appeared in The Butter, SmokeLong Quarterly, Kweli Journal, As/Us Journal and the VONA/Voices Anthology, Dismantle, among others. She has essays forthcoming in Not That Bad, edited by Roxane Gay, and Connections: An Integrated Reader and Rhetoric for College Writing, edited by Kerry Beckford and Donald Jones. Vanessa is the founder of the #52essays2017 challenge, and creator of the Writing Our Lives Workshop, which she teaches in NYC and online. You can find out more about Vanessa on her website at vanessamartir.com, on her author page on Facebook, and on Twitter @Vanessa_LaLoba.
wendyang
About wendyang
Wendy Angulo is a New York City born Latina, raised in Caracas, Venezuela. Wendy is a mother, writer, lawyer and the founder of Wendy Angulo Productions, an organization whose goal is to support, encourage, and promote poetry and visual arts in the borough of Queens. Wendy, re-discovered her love for writing in the summer of 2011 after attending a spoken word event in Queens. She then joined the New York City Latina Writers Group where she has been an active member and has taken on the role as the organization's Program Director. Wendy is an essayist who is currently working on her Memoir. She has read her work at several venues throughout New York City, including Nuyorican's Poets Cafe, East Harlem Cafe, Sankofa Sisterhood, Camaradas and has been published in the online journal Mom Egg Review; she is a 2016 VONA alum and the sole creator/curator and producer of Canvas of Words, an art and poetry showcase that birthed of Wendy's desire to bring the arts back to her beloved borough of Queens. Wendy continues to scout for new talent and build new connections to perpetuate the arts and strengthen the literary community.
Previous: Storytelling v. Gentrification, an Interview with Bridget Bartolini
Next: A Woman by Choice, an Interview with Andromeda Raheem
Canvas of Words is back ! December 16, 2021
Yes, You Actually do Know by Jose Luis Vilson October 25, 2019
After the Dust Settled… Unlearning and Breaking Cycles by Anthony Otero October 11, 2019
advocate of wordz art artist artists arts author BlackLivesMatter book reviews brooklyn canvas of words creatives documentary dreamers entrepreneurs Essays Featured Artists generational trauma graffiti Hip Hop lifting the burden of shame lifting the burden of shame2 masculinity Meriam Rodriguez Peggy Robles-Alvarado personal essay poet poetry poetry artists poets preserving our roots publisher queens shame storytelling summer of wordz testimonials theater Thomas Fucaloro trailblazers video wendy angulo wendy angulo productions womanhood women writers of color writers of color


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The Czech Women's Volleyball Cup  is organized by the Czech Volleyball Federation ( Český volejbalový svaz , ČVS). It was created in 1993 and it is the second most important Women's Volleyball club competition after the Czech Women's Volleyball Extraliga in the Czech Republic.

Competition history

Winners list

Honours by Club

References

External links
 www.cvf.cz in (Czech)

Volleyball in the Czech Republic

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Discussion in 'other firewalls' started by ratchet, Aug 5, 2008.
PC Tools FWP is up to version 4.0.0.44. It's not showing up yet via Smart Update. It's not clear from the forum announcement what if anything is different from 4.0.0.40.
I installed it my XP SP3 machine, somehow after mandatory installation reboot the PCT FW+ disappeared !!
I see the process running in task manager, but no icon is sys.tray !! I un-installed and jumped ship back to OA.
Guess, there are still some grey areas .... !!
When you ran the installer, did you choose the "Expert" user mode option? I had the same problem you did. I uninstalled and reinstalled and chose the "Normal" user mode and it installed and ran without a problem. The "Expert" mode can be enabled in the settings menu later. Been running for a few days without issue now.
I had the same problem with PCTFW and just did an uninstall.reinstall and everything is fine (running in Normal Mode).
I was running 4.0.0.40 and having a problem where permissions were not being remember. 4.0.0.44 does fix this so it's a worthwhile update. As of yesterday it was still not available via "smart update" so I downloaded the full installer and did an upgrade over 4.0.0.40.
We are happy to announce the release of PC Tools Firewall v4.0.0.45.
**Please note that the first login after the installation might take some time because the firewall is in learning mode and needs to check every Windows application that attempts to perform suspicious operations.
Where to download PC Tools Firewall v4.0.0.45?
You can download the product by clicking here.
Please note: If you currently have PCTFW v4.0.0.44, you may Smart Update to the latest version. Users' are able to reinstall over current versions.
It is FAILING the normal Leak Test app! Why would that be? It penetrates the firewall and permissions are listed as undetermined.
I've tried for the second time to use this Firewall. Upon installation my Nod icon had disappeared and the system froze, so had to reboot. Is it just me who's pc doesn't like PC tools?!
Piecan, have you gone into the applications tab, and selected 'give full access' to all of Nod's services. And not only give it full connection access, double click on each of Nod's services and enable 'allow' rather than the default 'prompt for permissions'.
The firewall has made a big jump, from single figures to now achieving a 74% rating at Matousec's site. Still a light firewall as well.
Been trying this new version out, and didn't realise it now had application control.
Tried using a portable file explorer to delete some files off the local drive and firewall plus gave the option to permit/deny/always-trust the action.
Those interested in just a pure firewall will probably now prefer rising, but those interested in a firewall with the ability to pass leak tests might now like this one (matousec report at this link).
Hmmm.. something might be wrong with how it's installing on my computer, because other apps besides LeakTest went straight out to the internet. Anyone have that problem, and could you solve it?
@ MVDU: I'm not sure, normally asked me to allow applications, but the new version has the feature to automatically create rules for known programs on it's list, so it might be that (for example, it didn't ask me for programs such as IE or utorrent, automatically allowed them). That can be unchecked if needed in the settings.
Besides, I had to uninstall it since it seems to have some bugs on Vista. While using utorrent, my system just froze and I had to restart. After that it didn't start with windows and I lost my patience and uninstalled it . Now everything runs smoothly again. It's a shame, couse i actually kinda liked this FW, it's very light on resources and neat to use.
Ah well......back to Vista FW for now, if anyone knows what might be the problem I experienced, please let me know.
Enhanced Security Verification ... Was Your Problem!
PC Tools only added Enhanced Security Verification to Version 4 of the firewall.
Enhanced Security Verification - Is turned ON By Default.
Version 3 - Code Injection Protection .... Was - NOT turned on by default.
http://forum.avast.com/index.php?topic=37991.0 Sorry but Symantec is going to destroy PCTools sooner or later with this move.
I have Enhanced Security Verification (off) as well. Other than that no problems.
I have everything turned on and haven't experienced any problems.
This was mentioned before, but make sure the install is set to 'normal user' rather than 'expert user'. Uninstall and reinstall if you haven't done so.
Expert user can be turned on later, but if installed to be the default, it seems to use more resources (and maybe have more conflicts).
Otherwise, from my experience so far, this firewall seems to be improving.
Thanx for the advice, might just try it out when I get home (I'm at work now, readin' forums 'n' stuff ).
By the way, I had a thought-maybe it happened becouse of peerguardian. Does PG have known problems with PCtools FW?
I Did... Install my PC Tools Firewall Plus as a Normal User.
The problem with Enhanced Security Verification seems to affect - approx 80% - of installations.
Why the other - approx 20% - get away with this problem... Is a mystery!
2/ Not everyone notices there is a problem with the firewall.
It may depend on certain circumstances... As to whether a person notices there's a problem.
* If they have Vista - With CPU gadgets in their Sidebar .... They are Far more likely to notice the problem.
** Someone that uses software a lot ( e.g Games ) - Is far more likely to notice... Than someone that just surfs the web.
I unchecked the "automatically allow," and still everything is getting through, even though I click block. Not sure what the problem is, as other firewalls work fine on my computer.
I have v4.0.0.40, smart update doesn't find anything to update.
Can I install v4.0.0.45 over v4.0.0.40 or just over v4.0.0.44?
How will this new version handle the Zemana tests Here?


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FLEET MANAGEMENT +
GTHA +
JOBS & HIRING
SAVINGS & TIPS
SMART TRUCKER
SMART TRUCKER 2016
Truckers Say Michigan Voters Got It Right on New Windsor-Detroit Bridge
The vote by the people of Michigan to defeat a ballot proposition that would have held up construction of the long-awaited second bridge at Windsor-Detroit, is "terrific news and shows that the people of Michigan reject the self-interest and cronyism that so many of the state's legislators have fallen victim to in recent years," says David Bradley, president of the Ontario Trucking Association.
Voters soundly rejected Proposal 6, the proposed constitutional amendment supported by the owners of the private Ambassador Bridge to delay or block the planned New International Trade Crossing (NITC) bridge between Detroit and Windsor.
The voters' defeat of Prop 6 helps clear the path for Gov. Rick Snyder and Canadian officials to proceed with the NITC project unimpeded.
Bradley, who has been an ardent supporter of a new, publicly-owned bridge for many years credits the efforts of Governor Rick Snyder, and the hard work of a dedicated group private citizens and business groups "in overcoming a campaign against the new bridge which has been founded more on financial might than what is right." He also commended the Government of Canada and its officials in the Canadian Consulate in Detroit for its leadership.
Denis Lebel, Federal Minister of Transport, Infrastructure and Communities has also welcomed the result of Proposition 6 on the Michigan ballot.
"The defeat of Proposition 6 clears the way for the construction of the new bridge across the Detroit River. This is good news for travellers, workers and industry on both sides of the border, who will benefit from the new publicly-owned bridge. The new bridge will attract new investments and business opportunities to boost our local and national economies and will result in much needed jobs for Ontario and Michigan communities."
"The new crossing will also increase border capacity to handle future trade and travel growth, and will be built with the security of both our countries in mind," said Lebel.
Community TV Shows
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Fleets save more than $895 million by adopting fuel-saving technologies
Auditor General report blasts MTO over truck inspections
Truxpo 2020 to be held on May 29-30 in Abbotsford, BC
Hyundai showcases hydrogen fuel cell concept truck at the NACV Show
dynaCERT establishes strategic alliance with MOSOLF Group of Europe
Cargo thieves give fleet-tracking market a boost
Stolen Dump Truck Crashes into Residence in Caledon
Kriska, Turbo Images and Turbo Studio celebrate tennis star Bianca Andreescu
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\section{Introduction}
Anomaly detection is an essential task with various applications, such as detecting abnormal patterns or actions in credit-card fraud, medical diagnosis, sudden natural disasters \citep{aggarwal2017introduction}, etc. In some directions of anomaly detection, the training set only contains normal data and is used to train a model that can distinguish unusual patterns from abnormal ones \citep{pang2021deep, seliya2021literature}. Anomaly detection on tabular data and images has been extensively studied recently \citep{ruff2018deep,Goyal2020drocc,chen2022deep,Liznerski2021explainable,Sohn2021learning}. In contrast, there is relatively little work on graph-level data despite the fact that graph anomaly detection is very useful in various problems, such as identifying abnormal communities in social networks or detecting unusual protein structures in biology experiments. Compared with other types of data, graph data is inherently complicated and rich in structural and relational information. The complexity of graph structure facilitates us to learn graph-level representations with discriminative patterns in many supervised tasks (e.g. graph classification). As for graph-level anomaly detection, however, the intricate graph structure brings many obstacles to unsupervised learning.

Graph anomaly detection usually composes four families: anomalous edge \citep{ouyang2020unified,xu2020icane}, node \citep{zhu2020mixedad,bojchevski2018bayesian}, sub-graph \citep{wang2018deep,zheng2018fraudne}, and graph-level detections \citep{zheng2019one,chalapathy2018group}. Herein, the target of the graph-level algorithms is to explore a regular group pattern and distinguish the abnormal manifestations of the group. Group abnormal behaviors usually foreshadow some unusual events and thus play an important role in practical applications. In the past decades, few approaches have focused on graph-level anomaly detection because of the difficulty of representing graphs into feature vectors without any label information. Considering that graph kernel can measure the similarity between graphs and regard the result as a representation non-strictly or implicitly, graph anomaly detection task associated with it usually performs as two-stage, which cannot maintain the quality of representation learning while learning normal data patterns. We also find that One-Class Support Vector Machine (OCSVM) \citep{bernhard1999support} with graph kernels sometimes yields unsatisfying performances since graph kernels may not be effective enough to quantify the similarity between graphs (see Section \ref{experiment}). So there is a large room for improvement regarding graph anomaly detection to our best knowledge. Concerning end-to-end models, \citet{ma2022deep} proposed a global and local knowledge distillation method for graph-level anomaly detection, which learns rich global and local normal pattern information by random joint distillation of graph and node representations. However, the method needs to train two graph convolutional networks jointly at a high time cost.
\citet{zhao2021using} combined the Deep Support Vector Data Description (Deep SVDD) objective function and graph isomorphism network to learn a hypersphere of normal samples.
\citet{qiu2022raising} also sought a hypersphere decision boundary and optimized the representations learned by $k$ Graph Neural Networks (GNN) close to the reference GNN while maximizing the differences between $k$ GNNs, but did not consider the relationship between the graph-level representation and node features.
Collecting all approaches based on the hypersphere assumption in graph anomaly detection, we find that the practical decision region may be an ellipsoid, thus causing the error when the standard hypersphere evaluation is employed. Besides, our experiment and the empirical exploration \cite{vershynin2018high} further confirm that the high-dimensional data sometimes may be more likely to locate in a bi-hypersphere region (also known as \textit{soap-bubble} phenonmenon).

\begin{figure*}[h!]
	\centering
	\includegraphics[width=\textwidth]{ Architecture_v5.pdf}\\
	\caption{Architecture of the proposed models \textit{(right top: DOHSC; right bottom: DO2HSC)}.}
	\label{architecture}
\end{figure*}

In order to effectively explore a better representation without label information and obtain a more suitable decision boundary with high efficiency, in this paper, we propose a one-class deep graph-level anomaly detection method and its improved version. The first proposed model, \textbf{\underline{D}}eep \textbf{\underline{O}}rthogonal \textbf{\underline{H}}yper\textbf{\underline{s}}phere \textbf{\underline{C}}ontraction (DOHSC), uses the mutual information of local feature maps and the global representation to learn a high-quality representation and simultaneously optimizes it to distribute in a hypersphere area. An orthogonal projection layer then renders the decision region more hyperspherical and compact to decrease evaluation errors. With regard to \textit{soap-bubble} phenomenon, an improved graph-level \textbf{\underline{D}}eep \textbf{\underline{O}}rthogonal \textbf{\underline{Bi}}-\textbf{\underline{H}}yper\textbf{\underline{s}}phere \textbf{\underline{C}}ompression (DO2HSC) for anomaly detection architecture is proposed. From a cross-sectional point of view, DO2HSC limits the decision area (of normal data) to an interval enclosed by two co-centered hyperspheres and learns the orthogonality-projected representation similarly. The framework of the methods mentioned above is shown in Figure \ref{architecture} correspondingly.
Furthermore, we define a new evaluation way according to DO2HSC, and comprehensive experimental results verify the effectiveness of all proposed methods. In summary, our main contributions are listed as follows.
\begin{itemize}
    \item First, we present a new graph-level hypersphere contraction algorithm for anomaly detection tasks, which is jointly trained via mutual information loss between local and global representations and hypersphere decision loss.
	\item Second, we impose an orthogonal projection layer on the proposed model to promote training data distribution close to the standard hypersphere, thus avoiding errors arising from inconsistencies between assessment criteria and actual conditions.
	\item Third, we propose the graph-level deep orthogonal bi-hypersphere compression model to further explore a decision region enclosed by two co-centered hyperspheres, which can effectively prevent anomalous data from falling close to the hyperspherical center and surpass baselines significantly in the experiments.
 \item Finally, the proposed methods are also applicable to and very effective on non-graph data (e.g. image).

\end{itemize}

\section{Proposed Approach}
\label{proposed_approach}
In this section, we first introduce a joint learning architecture in detail, named graph-level Deep Orthogonal Hypersphere Compression. Then an improved algorithm is proposed to compensate for deficiency of the underlying assumption.

\subsection{Graph-Level Deep
Orthogonal Hypersphere Contraction}
\subsubsection{Vallina Model}
Given a set of graphs $\mathbb{G}=\{G_1,...,G_N\}$ with $N$ samples, the proposed model aims to learn a $k$-dimensional representation and then set a soft-boundary according to it. In this paper, the Graph Isomorphism Network (GIN) \citep{xu2018powerful} is employed to obtain the graph representation in three stages: first, input the graph data and integrate neighbors of the current node (AGGREGATE); second, combine neighbor and current node features (CONCAT); finally, integrate all node information (READOUT) into one global representation.
Mathematically, the $i$-th node features of $l$-th layer and the global features of its affiliated $j$-th graph would be denoted as
\begin{equation}
    \begin{aligned}
\mathbf{z}_{\Phi}^{i}&=\text{CONCAT}(\{\mathbf{z}_i^{(l)}\}_{l=1}^{L}),\\
        \mathbf{Z}_{\Phi}(G_j)&=\text{READOUT}(\{\mathbf{z}_{\Phi}^i\}_{i=1}^{|G_j|}),
    \end{aligned}
\end{equation}
where $\mathbf{z}_{\Phi}^{i}\in\mathbb{R}^{1 \times k}$ and $\mathbf{Z}_{\Phi}(G_j)\in \mathbb{R}^{1 \times k}$.
To integrate the contained information and enhance the differentiation between node-level and global-level representations, we append additional fully connected layers denoted as the forms $M_{\Upsilon}(\cdot)$ and $T_{\Psi}(\cdot)$, respectively, where $\Upsilon$ and $\Psi$ are the parameters of the added layers. So the integrated node-level and graph-level representations are obtained via
\begin{equation}
\label{fully_layers}
    \begin{aligned}
        \mathbf{h}_{\Phi, \Upsilon}^{i}:=M_{\Upsilon}(\mathbf{z}_{\Phi}^{i});~~\mathbf{H}_{\Phi,\Psi}(G_j):=T_{\Psi}(\mathbf{Z}_{\Phi}(G_j)),
    \end{aligned}
\end{equation}

To better capture the local information, we utilize the batch optimization property of neural networks to maximize the mutual information (MI) between local and global representations in each batch $\mathbf{G}\subseteq\mathbb{G}$,
which is defined by \cite{sun2019infograph} as the following term:
\begin{equation}\label{mi}
\begin{aligned}
\hat{\Phi},\hat{\Psi}, \hat{\Upsilon} = \argmax_{\Phi,\Psi,\Upsilon} I_{\Phi,\Psi,\Upsilon}\left(\mathbf{h}_{\Phi,\Upsilon},\mathbf{H}_{\Phi,\Psi}(\mathbf{G})\right).
\end{aligned}
\end{equation}
Specifically, the mutual information estimator $I_{\Phi,\Psi,\Upsilon}$ follows Jensen-Shannon MI estimator \citep{NIPS2016_cedebb6e} with a positive-negative sampling method as below,
\begin{equation}
\label{mi_loss}
\begin{aligned}
&I_{\Phi,\Psi,\Upsilon}\left(\mathbf{h}_{\Phi,\Upsilon},\mathbf{H}_{\Phi,\Psi}(\mathbf{G})\right) \\
:&=  \sum_{G_j\in \mathbf{G}}\frac{1}{|G_j|}\sum_{u\in G_j} I_{\Phi,\Psi,\Upsilon}\left(\mathbf{h}^u_{\Phi,\Upsilon}(G_j),\mathbf{H}_{\Phi,\Psi}(\mathbf{G})\right)\\
&=\sum_{G_j\in \mathbf{G}}\frac{1}{|G_j|}\sum_{u\in G_j}\Bigr[\mathbb{E}\bigl(-\sigma \left(-\mathbf{h}_{\Phi,\Upsilon}^u (\mathbf{x}^{+})\times \mathbf{H}_{\Phi,\Psi}(\mathbf{x})\right)\bigl) -\mathbb{E}\bigl(\sigma\left(\mathbf{h}_{\Phi,\Upsilon}^u (\mathbf{x}^{-})\times \mathbf{H}_{\Phi,\Psi}(\mathbf{x})\right)\bigl)\Bigr],
\end{aligned}
\end{equation}
where a softplus function $\sigma(z) = \log (1+e^z)$ is activated after vector multiplication between node and graph representations. For $\mathbf{x}$ as an input sample graph, we calculate the expected mutual information with its positive samples $\mathbf{x}^+$ and negative samples $\mathbf{x}^-$, which are generated from distribution across all graphs in a subset. Given each $G=(\mathcal{V}_{G},\mathcal{E}_{G})$ and node set $\mathcal{V}_{G}=\{v_i\}_{i=1}^{|G|}$, the positive and negative samples are divided in this way:
\begin{equation}
\label{pos_neg}
\begin{aligned}
\mathbf{x}^+ = \left\{\begin{matrix}
\mathbf{x}_{ij}, & ~~\text{if}~~ v_{i}\in G_{j}, \\
0, & \text{otherwise. }
\end{matrix}\right.
\end{aligned}
\end{equation}
And $\mathbf{x}^-$ produces the opposite result in each of the conditions above.
In the next step, a data-enclosing decision boundary is required for our anomaly detection task. According to the assumption that most normal data can locate in a hypersphere, the center of this decision boundary should be initialized through
\begin{equation}
\label{initial_center}
\begin{aligned}
\mathbf{c}=\frac{1}{N}\sum_{i=1}^{N} \mathbf{H}_{\Phi,\Psi}(G_{i}).
\end{aligned}
\end{equation}
With this center, we expect to optimize the learned representation of normal data to be distributed as close to it as possible, so that the unexpected anomalous data falling out of this hypersphere would be detected. Besides, the regularization term is adopted to avoid over-fitting problems. Collectively denote the weight parameters of $\Phi$, $\Psi$ and $\Upsilon$ as $\mathcal{Q}:=\Phi\cup\Psi\cup\Upsilon$, we formulate the training loss with two joint objectives -- Hypersphere Contraction and MI:
\begin{equation}
\label{initialobjectivefunction}
\begin{aligned}
\min_{\Phi,\Psi,\Upsilon} & \frac{1}{|\mathbf{G}|}\sum_{i=1}^{|\mathbf{G}|} \|\mathbf{H}_{\Phi,\Psi}(G_{i})-\mathbf{c}\|^2+ \lambda I_{\Phi,\Psi,\Upsilon}\left(\mathbf{h}_{\Phi,\Upsilon},\mathbf{H}_{\Phi,\Psi}(\mathbf{G})\right)+ \frac{\mu}{2}\sum_{\mathbf{Q}\in\mathcal{Q}}\|\mathbf{Q}\|_{F}^2,
\end{aligned}
\end{equation}
where $|\mathbf{G}|$ denotes the number of graphs in batch $\mathbf{G}$ and $\lambda$ is a trade-off factor, the third term is a network weight decay regularizer with the hyperparameter $\mu$.

\subsubsection{Orthogonal Projection Layer} \label{section_orthogonal_projection_layer}
\begin{figure}[h!]
	\centering
	\includegraphics[width=0.7\linewidth]{ Orthogonal_projection.pdf}\\
	\caption{Illustration of decision boundaries with and without the orthogonal projection layer. In the left subfigure, the real decision region where training data are distributed may be an ellipsoid (dark grey). This contradicts with the hypersphere decision boundary (light grey) set by Equation \ref{initialobjectivefunction}. After orthogonal projection, the ellipsoid is expected to be transformed into a standard hypersphere, which avoids the evaluation error. \textit{Note: Data is simulated.}}
	\label{Orthogonal_projection}
\end{figure}
However, an empirical study shows that a hyperellipsoid is commonly observed during deep representation learning. This phenomenon would lead to inaccuracies in the final test because the evaluation results are based on the hypersphere decision region.
The objective (\ref{initialobjectivefunction}) obviously cannot guarantee the soft-boundary of learned representation to be a standard hypersphere like Figure \ref{Orthogonal_projection}.
Accordingly, we append an orthogonal projection layer after obtaining the global representation.
Note that we pursue orthogonal features of latent representation rather than computing the projection onto the column or row space of $\mathbf{H}_{\Phi,\Psi}$. This method is equivalent to performing Principal Component Analysis (PCA) \citep{wold1987principal} and using the standardized principal components.
Our experiments also justify the necessity of this projection step and standardization process, which will be discussed further in Section \ref{ablation_study} and Appendix \ref{supplementary_ablation_study}. Specifically, the projection layer can be formulated as
\begin{equation}
 \label{orthogonal}
 \begin{aligned}
\mathbf{\tilde{H}}_{\Phi,\Psi,\Theta}(G)=\text{Proj}_{\Theta}(\mathbf{H}_{\Phi,\Psi}(G))=\mathbf{H}_{\Phi,\Psi}\mathbf{W},
 ~~\text{subject to} ~~ \mathbf{\tilde{H}}_{\Phi,\Psi,\Theta}^\top\mathbf{\tilde{H}}_{\Phi,\Psi,\Theta}=\mathbf{I}_{k'}
 \end{aligned}
\end{equation}
where $\Theta:=\{\mathbf{W}\in \mathbb{R}^{k\times k'}\}$ are the projection parameters, $\mathbf{I}_{k'}$ denotes an identity matrix, and $k'$ is the projected dimension. Note that to achieve (\ref{orthogonal}), one may consider adding a regularization term $\tfrac{\alpha}{2}\Vert\mathbf{\tilde{H}}_{\Phi,\Psi,\Theta}^\top\mathbf{\tilde{H}}_{\Phi,\Psi,\Theta}-\mathbf{I}_{k'}\Vert_F^2$ with large enough $\alpha$ to the objective, which is not very effective and will lead to one more tuning hyperparameter. Instead, we propose to achieve (\ref{orthogonal}) via singular value decomposition, i.e.
\begin{equation}
\label{orthogonal_weight}
\begin{aligned}
\mathbf{U}\mathbf{\Lambda}\mathbf{V}^\top =\mathbf{H}_{\Phi,\Psi},~~\mathbf{W}: = \mathbf{V}_{k'} \mathbf{\Lambda}_{k'}^{-1}
\end{aligned}
\end{equation}
where $\mathbf{\Lambda}=\text{diag}(\rho_1,\rho_2,...,\rho_{|\mathbf{G}|})$ and $\mathbf{V}$ are the diagonal matrix with sigular values and right-singular matrix of $\mathbf{H}_{\Phi,\Psi}$, respectively. It needs to be emphasized that $\mathbf{V}_{k'}:=[\mathbf{v}_{1},...,\mathbf{v}_{k'}]$ denotes the first $k'$ right-singular vectors and $\mathbf{\Lambda}_{k'}:=\text{diag}(\rho_1,...,\rho_{k'})$.
In each forward propagation epoch, the original weight parameter is substituted to a new matrix $\mathbf{W}$ in subsequent loss computations.
\subsubsection{Anomaly Detection}
\label{section_anomaly_detection_DOHSC}
Attaching with an orthogonal projection layer, the improved initialization of the center is rewritten in the following form
\begin{equation}
\label{centers}
\begin{aligned}
\mathbf{\tilde{c}}=\frac{1}{N}\sum_{i=1}^{N} \mathbf{\tilde{H}}_{\Phi,\Psi,\Theta}(G_{i})
\end{aligned}
\end{equation}
and the final objective function for anomaly detection tasks in a mini-batch would become
\begin{equation}
\label{objectivefunction_1}
\begin{aligned}
\min_{\Theta,\Phi,\Psi,\Upsilon} & \frac{1}{|\mathbf{G}|}\sum_{i=1}^{|\mathbf{G}|} \|\tilde{\mathbf{H}}_{\Phi,\Psi,\Theta}(G_{i})-\mathbf{\tilde{c}}\|^2 +  \lambda \sum_{\mathbf{G}\in\mathbb{G}} I_{\Phi,\Psi,\Upsilon}\left(\mathbf{h}_{\Phi,\Upsilon},\tilde{\mathbf{H}}_{\Phi,\Psi,\Theta}(\mathbf{G})\right) + \frac{\mu}{2}\sum_{\mathbf{Q}\in\mathcal{Q}}\|\mathbf{Q}\|_{F}^2. \\
\end{aligned}
\end{equation}

After the training stage, a decision boundary $\hat{r}$ will be fixed, which is calculated based on the $1-\nu$ percentile of the training data distance distribution:
\begin{equation}
\label{compute_r}
    \begin{aligned}
        \hat{r} = \argmin_{r} \mathcal{P}(\mathbf{D}\le r)\geq \nu
    \end{aligned}
\end{equation}
where $\mathbf{D}:=\{d_i\}_{i=1}^N$ follows a sampled distribution $\mathcal{P}$, and $d_i=\|\tilde{\mathbf{H}}_{\Phi,\Phi,\Theta}(G_{i})-\tilde{\mathbf{c}}\|$. Accordingly, the anomalous score of $i$-th instance is defined as follows:
\begin{equation}
\label{anomalous_score_1}
    \begin{aligned}
        {s}_i=d_{i}^2-\hat{r}^2
    \end{aligned}
\end{equation}
where $\mathbf{s}=(s_1,s_2,\ldots,s_N)$.
It is evident that when the score is positive, the instance is identified as abnormal, and the opposite is considered normal.

The detailed procedures of algorithm are summarized into Algorithm \ref{algorithm_1} (see Appendix \ref{Supplementary_Algorithm}).
It starts with graph representation learning and promotes the training data to approximate the center of a hypersphere while adding an orthogonal projection layer. Unfortunately, it can be observed from Figures \ref{improved_motivation} and \ref{fig:visualizations_er_md_distance} that the anomalous data would appear in partial regions of the learned decision hypersphere, which are not filled by the training data, especially the region close to the center.
To explore this particular phenomenon and handle it, an improved graph-level anomaly detection approach, termed as graph-level Deep Orthogonal Bi-Hypersphere Compression (DO2HSC), is designed in the next section.

\begin{figure}[t]
	\centering
	\includegraphics[width=\linewidth]{ improved_motivation_v2.pdf}\\
	\caption{Illustration of inevitable flaws in DOHSC on both the training and testing data of COX2. Left: the $\ell_2$-norm distribution of 4-dimensional distances learned from the real dataset; Right: the pseudo-layout in two-dimensional space sketched by reference to the empirical distribution.
 }
	\label{improved_motivation}
\end{figure}

\subsection{Graph-Level Deep Orthogonal Bi-Hypersphere Compression}
\subsubsection{Motivation and Theoretical Analysis}
As aforementioned, we found that the learned distribution of training data sometimes does not conform the hypersphere assumption.
Let the anomaly score be determined by $\ell_2$ norm $\Vert\mathbf{z}-\mathbf{c}\Vert$ where $\mathbf{c}$ denotes the centroid, the original evaluation of anomaly detection is to compare the score with a threshold $\hat{r}$ determined by a certain quantile (e.g. 0.95). Specifically, if $\Vert\mathbf{z}-\mathbf{c}\Vert \ge \hat{r}$ then $\mathbf{z}$ is abnormal.
So it is natural to expect most samples to locate near the origin. However, the empirical exploration found that in a high dimensional space, most samples are far away from the origin. Taking Gaussian distributions as an example, the distributions
would look like a \textit{soap-bubble}\footnote{\href{https://www.inference.vc/high-dimensional-gaussian-distributions-are-soap-bubble/}{https://www.inference.vc/high-dimensional-gaussian-distributions-are-soap-bubble/}}, which means the high-dimensional normal data are more likely to locate in a bi-hypersphere instead of a simple hypersphere \citep{vershynin2018high}. To be more specific, referred to \citep{vershynin2018high}, the typical set, where data has information closest to the expected entropy of the population, of a Gaussian is the thin shell within a distance from the origin, just like the circumstances showed in Figure \ref{fig:high_dimension_distance_distribution}. The higher the dimensionality of the data, the further the sampled instance is from the center instead.

\begin{figure}[h]
    \centering
\includegraphics[width=0.8\linewidth,height=!]{ high_dimension_distance_distribution.pdf}\\
    \caption{Histogram of distances (Euclidean norm) from the center of 10,000 random samples under (univariate or) high-dimensional Gaussian distributions $\mathcal{N}(\mathbf{0}, \mathbf{I})$.}
    \label{fig:high_dimension_distance_distribution}
\end{figure}

To sum up, we formally formulate the following proposition and it can be easily derived from Lemma 1 of \citep{laurent2000adaptive}.
\begin{prop}\label{proposition_lower_bound}
Suppose $\mathbf{z}_1, \mathbf{z}_2,\cdots, \mathbf{z}_n$ are sampled from $\mathcal{N}(\mathbf{0},  \mathbf{I}_d)$ independently. Then for any $\mathbf{z}_i$ and all $t \ge 0$, the following inequality holds:
$$\mathbb{P}\left[\Vert \mathbf{z}_i\Vert \geq \sqrt{d-2\sqrt{dt}}\right] \geq 1-e^{-t}.$$
\end{prop}

The proposition proves that when the dimension is high, each $\mathbf{z}_i$ is outside of a hypersphere of radius $r':=\sqrt{d-2\sqrt{dt}}$, with probability at least $1-e^{-t}$. When $r'$ is closer to $\hat{r}$ (refer to \eqref{compute_r}), normal data are more likely away from the center (also can be seen in Figure \ref{fig:high_dimension_distance_distribution}).

It should be pointed out that in anomaly detection, $\mathbf{z}_i$ (e.g. $\mathbf{z}_i=\tilde{\mathbf{H}}_{\Phi,\Phi,\Theta}(G_{i})$ in Section \ref{section_anomaly_detection_DOHSC}) are not necessarily isotropic Gaussian. However, we have the following result.
\begin{prop}\label{proposition_lower_bound_ng}
Let $\mathbf{z}_i=\tilde{\mathbf{H}}_{\Phi,\Phi,\Theta}(G_{i})$, $i=1,\ldots,N$ and let $f:\mathbb{R}^k\rightarrow\mathbb{R}^k$ be an $\eta$-Lipschitz function such that $\mathbf{s}=f(\mathbf{z})$ are isotropic Gaussian $\mathcal{N}(\bar{\mathbf{c}},\mathbf{I}_k)$. Let $\mathbf{c}$ be a predefined center of $\{\mathbf{z}_i\}_{i=1}^N$ and suppose $\|\bar{\mathbf{c}}-f(\mathbf{c})\|\leq \epsilon$. Then for any $\mathbf{z}_i$ and all $t \ge 0$, the following inequality holds:
$$\mathbb{P}\left[\Vert \mathbf{z}_i-\mathbf{c}\Vert \geq \eta^{-1}\left(\sqrt{k-2\sqrt{kt}}-\epsilon\right)\right] \geq 1-e^{-t}.$$
\end{prop}
The proposition (proved in Appendix \ref{sec_appendix_prop2}) shows that most data ($N'$) satisfy $\Vert\mathbf{z}-\mathbf{c}\Vert \ge r':=\eta^{-1}\left(\sqrt{k-2\sqrt{kt}}-\epsilon\right)$ (with probability around $\binom{N}{N'}(1-e^{-t})^{N'}e^{-t(N-N')}$) where $r'$ is close to $\hat{r}$, which means the normality could not be supported by the training data within the range $[0, r']$. Therefore, it is justified that hypersphere anomaly detection tasks should be improved as the bi-hypersphere version.

\subsubsection{Architecture of DO2HSC}
\label{section_anomaly_detection_DO2HSC}
Since DOHSC cannot detect anomalies close to the center, we propose an improved approach, DO2HSC, which sets the decision boundary as an interval region between two co-centered hyperspheres. This can narrow the decision area's scope so as to induce normal data to fill the entire interval area as much as possible. Also, it can better handle \textit{soap-bubble} problems than DOHSC.

After the same graph representation learning stage, we firstly utilize the DOHSC model for a few epochs to initialize the large radius $r_{\text{max}}$ and the small radius $r_{\text{min}}$ of the interval area according to the $1-\nu$ percentile and $\nu$ of the sample distances distribution, respectively. The aforementioned descriptions can be denoted mathematically as below.
\begin{equation}
\label{initialize_r1r2}
    \begin{aligned}
        r_{\text{max}}&=\argmin_{r} \mathcal{P}(\mathbf{D}\le r)\geq \nu, \\
        r_{\text{min}}&=\argmin_{r} \mathcal{P}(\mathbf{D}\le r)\geq 1-\nu.
    \end{aligned}
\end{equation}
After fixing the decision boundaries $r_{\text{max}}$ and $r_{\text{min}}$, the training loss is also set with a trade-off factor $\lambda$, which implicitly controls the importance of the max-min term:
\begin{equation}
\label{objectivefunction_2}

    \begin{aligned}
    \min_{\Theta,\Phi,\Psi,\Upsilon}& \frac{1}{|\mathbf{G}|}\sum_{i=1}^{|\mathbf{G}|} \left(\max\{d_i, r_{\text{max}}\}-\min \{d_i, r_{\text{min}}\} \right)+ \lambda \sum_{\mathbf{G}\in\mathbb{G}} I_{\Phi,\Psi,\Upsilon}\left(\mathbf{h}_{\Phi,\Upsilon},\tilde{\mathbf{H}}_{\Phi,\Psi,\Theta}(\mathbf{G})\right)+\frac{\mu}{2}\sum_{\mathbf{Q}\in\mathcal{Q}}\|\mathbf{Q}\|_{F}^2.

    \end{aligned}

\end{equation}
This decision loss has the lowest bound $r_{\text{max}}-r_{\text{min}}$ and can be jointly minimized with mutual information effectively.
Besides, the evaluation standard of test data is also needed to change based on this interval structure. More specifically, all instances located in the inner hypersphere and out of the outer hypersphere should be identified as anomalous graphs; only those located in the interval area should be regarded as normal data.
Compared with \eqref{anomalous_score_1}, we reset a new score function to award the positive samples beyond $[r_{\text{min}}, r_{\text{max}}]$ and meanwhile punishing the negative samples within the range. Accordingly, the distinctive scores are calculated by
\begin{equation}
\label{anomalous_score_2}
    \begin{aligned}
        {s}_i=(d_i-r_{\text{max}})\cdot(d_i-r_{\text{min}}),
    \end{aligned}
\end{equation}
where $i\in\{1,...,N\}$. This way, we can also effectively identify a sample's abnormality by its score.
In general, the improved deep graph-level anomaly detection algorithm changes the decision boundary and effectively makes the normal area more compact. Correspondingly, the new practical evaluation is raised to adapt to the improved detection way.
Eventually, we summarize the detailed procedures of the optimization into Algorithm \ref{algorithm_2} (please see Appendix \ref{Supplementary_Algorithm}).
\section{Connections with Previous Work}
As one of the classic one-class anomaly detection algorithm, Deep SVDD \cite{bernhard1999support} assumes that the specific shape of decision regions is a hypersphere. Considered that it is difficult to guarantee that the learned embedding representation's distribution perfectly fits the hypersphere hypothesis, we design the orthogonal projection layer to obtain an embedding representation that conforms as closely as possible to the standard assumption.
This point also differs the proposed graph-level representation learning stage from infoGraph method \cite{sun2019infograph}, which promotes the learned graph representation to better meet theoretical requirements.
Due to the similar network architectures, we also clarify the differences between \cite{zhao2021using} and ours. \citet{zhao2021using} optimized one-class model based on Deep SVDD as the anomaly measure, which directly utilized the readout result of GIN for Deep SVDD module. Whereas, the involved mutual information loss in the proposed models can obtain the graph representation incorporating local and global information, and avoid trivial solutions when solving anomaly detection problems.
Besides, like we mentioned above, we imposed an orthogonal projection layer to maintain consistency between the learned decision boundary and normal data distributions.
Last but not least, a new method is presented to construct a more suitable decision region learned as a bi-hypersphere, between which normal data are accommodated and hence yield more space for anomalies.
Bi-hypersphere assumption has not been studied in the anomaly detection field to our best knowledge. It is the first exploration and provides a new perspective for future detection works.
More related works are summarized in Appendix \ref{Related_Work_on_Graph_Kernel}.
\section{Generalization to Other Data Types}
The methods above can also be generalized to non-graph types of data, such as tabular or image data. To tackle these datasets, the graph representation learning module is replaced by a common representation learning module. We still keep the proposed orthogonal projection layer but remove mutual information loss. Then the objective functions of DOHSC and DO2HSC will become the following forms:
\begin{equation}
    \begin{aligned}
        \min_{\mathcal{W},\Theta} \frac{1}{n}\sum_{i=1}^{n} &\|\text{Proj}_{\Theta}(f_{\text{enc}}(\mathbf{x}_i,\mathcal{W}))-\tilde{\mathbf{c}}\|^2+\frac{\lambda}{2}\sum_{l=1}^{L}\|\mathbf{W}^l\|_{F}^2,
    \end{aligned}
\end{equation}
\begin{equation}

   \begin{aligned}
       \min_{\mathcal{W},\Theta} \frac{1}{n}\sum_{i=1}^{n}(\max\{d_i,r_{\text{max}}\}-\min(\{d_i,r_{\text{min}}\})
       +\frac{\lambda}{2}\sum_{l=1}^{L}\|\mathbf{W}^l\|_{F}^2
   \end{aligned}

\end{equation}
where $f_{enc}$ means the representation learning module (just like an encoder architecture) with the parameter set $\mathcal{W}=\{\mathbf{W}\}_{l=1}^L$ and $d_i=\|\text{Proj}_{\Theta}(f_{\text{enc}}(\mathbf{x}_i,\mathcal{W}))-\tilde{\mathbf{c}}\|$.
After the representation learning stage, the subsequent anomaly detection evaluation procedures are implemented according to Section \ref{section_anomaly_detection_DOHSC} and Section \ref{section_anomaly_detection_DO2HSC}.

\section{Experiments on Graph Data}
\label{experiment}
\subsection{Experiment Setting}
\textbf{Datasets:} We evalutate our models on six real-world graph datasets\footnote{\href{https://ls11-www.cs.tu-dortmund.de/staff/morris/graphkerneldatasets}{https://ls11-www.cs.tu-dortmund.de/staff/morris/graphkerneldatasets}} (COLLAB, COX2, ER\_MD, MUTAG, DD and IMDB-Binary), which are converted from graph classification benchmarks for GAD tasks. We follow the standard one-class experimental settings and data-split method in previous work \citep{zhao2021using, qiu2022raising}. The details of datasets are shown in Appendix \ref{app_exp_con}.

\textbf{Baselines:} We compare our methods with the following unsupervised graph-level anomaly detection methods, including four graph kernels combined with OCSVM and four state-of-the-art baselines: Random Walk (RW) \citep{gartner2003graph, kashima2003marginalized}, Shortest Path Kernel (SP) \citep{borgwardt2005shortest}, Weisfeiler-Lehman Sub-tree Kernel (WL) \citep{shervashidze2011weisfeiler} and Neighborhood Hash Kernel (NH)
 \citep{hido2009linear}, Deep One Class Model with GIN network (OCGIN)
 \citep{zhao2021using}, Graph-level embedding Learning via Mutual Information Maximization+Deep SVDD (infoGraph+Deep SVDD)
 \citep{sun2019infograph,ruff2018deep}, Global and Local Knowledge Distillation for Graph-level Anomaly Detection (GLocalKD)
 \citep{ma2022deep} and One-Class Graph Transformation Learning (OCGTL) \citep{qiu2022raising}.

\subsection{Results}
In this section, the averages and standard deviations of the Area Under Operating Characteristic Curve (AUC) are used to support the comparable experiments by repeating each algorithm ten times.
Tables \ref{result-1} and \ref{result-2} report the mean AUC and its standard deviations. It can be seen that the proposed methods basically achieve the best AUC values compared to other algorithms on all datasets. Both approaches outperform other state-of-the-art baselines, and DO2HSC obtains superior performance and get $5\%$ higher performance than other algorithms on many datasets, such as MUTAG, COLLAB Class 1, and ER$\_$MD Class 0, IMDB-Binary Class 1, etc. It is woth mentioning that we defeat infoGraph$+$Deep SVDD with a large improvement, which is a degraded version of the proposed models, thus showing that promoting representation learning towards the anomaly detection goal is meaningful and well targeted. Besides, it can be seen that there exists a large improvement (exceeding 20\%) on Class 1 of ER\_MD between DOHSC and DO2HSC. An distance distribution visualization is given to prove their differences (see Figure \ref{fig:visualizations_er_md_distance}).
\begin{figure}[h!]
	\centering
	\includegraphics[height=!,width=0.65\linewidth]{ ER_MD_distance_comparison.pdf}
	\caption{Distance distribution visualizations of DOHSC and DO2HSC on ER$\_$MD dataset.}
	\label{fig:visualizations_er_md_distance}
\end{figure}

\begin{table*}[h!]

	\centering
	\caption{Average AUCs with standard deviation (10 trials) of different graph-level anomaly detection algorithms. We assess models by regarding every data class as normal data, respectively. The best results are highlighted in \textbf{bold} and '--' means out of memory.}
     \resizebox{\textwidth}{!}{
	\begin{tabular}{l|lll|ll|ll}
		\toprule

		& \multicolumn{3}{c|}{COLLAB}       & \multicolumn{2}{c|}{COX2}
    & \multicolumn{2}{c}{ER\_MD}
  \\

  \cline{2-8}
& \multicolumn{1}{c|}{0}& \multicolumn{1}{c|}{1}&\multicolumn{1}{c|}{2}
& \multicolumn{1}{c|}{0}& \multicolumn{1}{c|}{1}
& \multicolumn{1}{c|}{0}& \multicolumn{1}{c}{1}
\\ \hline
SP+OCSVM& \multicolumn{1}{l|}{0.5910  $\pm$ 0.0000}& \multicolumn{1}{l|}{0.8397 $\pm$ 0.0000} & 0.7902 $\pm$ 0.0000 & \multicolumn{1}{l|}{0.5408 $\pm$ 0.0000 }& 0.5760 $\pm$ 0.0000
& \multicolumn{1}{l|}{0.4092 $\pm$ 0.0000 }  & 0.3824 $\pm$ 0.0000
\\

WL+OCSVM (optimal)                & \multicolumn{1}{l|}{0.5122 $\pm$ 0.0000 } & \multicolumn{1}{l|}{0.8054 $\pm$ 0.0000 }   & \textbf{0.7996 $\pm$ 0.0000}  & \multicolumn{1}{l|}{0.5990 $\pm$ 0.0000 }   & 0.5057  $\pm$ 0.0000
& \multicolumn{1}{l|}{0.4571  $\pm$ 0.0000 }         & 0.3262 $\pm$ 0.0000
\\

NH+OCSVM & \multicolumn{1}{l|}{0.5976 $\pm$ 0.0000 } & \multicolumn{1}{l|}{0.8054 $\pm$ 0.0000 }  & 0.6414  $\pm$ 0.0000  & \multicolumn{1}{l|}{0.4841 $\pm$ 0.0000 } & 0.4717 $\pm$ 0.0000
 & \multicolumn{1}{l|}{0.5155 $\pm$ 0.0200}  & 0.3648 $\pm$ 0.0000
\\

RW+OCSVM & \multicolumn{1}{c|}{--} & \multicolumn{1}{c|}{--}                   & \multicolumn{1}{c|}{--}                     & \multicolumn{1}{l|}{0.5243 $\pm$ 0.0000}         & 0.6553 $\pm$ 0.0000
 & \multicolumn{1}{l|}{0.4820 $\pm$ 0.0000}   & 0.3484  $\pm$ 0.0000
\\ \midrule
OCGIN & \multicolumn{1}{l|}{0.4217  $\pm$ 0.0606 }        & \multicolumn{1}{l|}{0.7565  $\pm$ 0.2035 }               & 0.1906  $\pm$ 0.0857                             & \multicolumn{1}{l|}{0.5964  $\pm$ 0.0578 }          & 0.5683  $\pm$ 0.0768
 & \multicolumn{1}{l|}{0.5645 $\pm$ 0.0323}& 0.4358 $\pm$ 0.0538
\\

infoGraph+Deep SVDD                  & \multicolumn{1}{l|}{0.5662 $\pm$ 0.0597}          & \multicolumn{1}{l|}{0.7926 $\pm$ 0.0986}& 0.4062  $\pm$ 0.0978                             & \multicolumn{1}{l|}{0.4825  $\pm$ 0.0624 }          & 0.5029 $\pm$ 0.0700
 & \multicolumn{1}{l|}{0.5312 $\pm$ 0.1545}& 0.5682 $\pm$ 0.0704
\\

		GLocalKD                            & \multicolumn{1}{l|}{0.4638  $\pm$ 0.0003 }                                             & \multicolumn{1}{l|}{0.4330  $\pm$ 0.0016 }& 0.4792  $\pm$ 0.0004        & \multicolumn{1}{l|}{0.3861  $\pm$ 0.0131 }          & 0.3143  $\pm$ 0.0383
 &   \multicolumn{1}{l|}{0.5781  $\pm$ 0.1790}& 0.7154 $\pm$ 0.0000
  \\

        OCGTL  & \multicolumn{1}{l|}{0.6504 $\pm$ 0.0433}                                             & \multicolumn{1}{l|}{0.8908 $\pm$ 0.0239}& 0.4029 $\pm$ 0.0541  & \multicolumn{1}{l|}{0.5541 $\pm$ 0.032}  &0.4862 $\pm$ 0.0224
 &   \multicolumn{1}{c|}{0.2755 $\pm$ 0.0317}&0.6915 $\pm$ 0.0207
        \\ \midrule
		DOHSC (Ours)  & \multicolumn{1}{l|}{\textbf{0.9185 $\pm$ 0.0455}}       & \multicolumn{1}{l|}{\textbf{0.9755 $\pm$ 0.0030}}              & 0.5450   $\pm$ 0.0469                               & \multicolumn{1}{l|}{0.6263 $\pm$ 0.0333}& \textbf{0.6805 $\pm$ 0.0168 }
& \multicolumn{1}{l|}{0.6620   $\pm$ 0.0308}         & 0.5184 $\pm$ 0.0793
  \\

		DO2HSC (Ours)        & \multicolumn{1}{l|}{0.6718 $\pm$ 0.0353}       &  \multicolumn{1}{l|}{0.9153 $\pm$ 0.0070}       & 0.7188 $\pm$ 0.0260    & \multicolumn{1}{l}{\textbf{0.6329 $\pm$ 0.0292}}    & 0.6518 $\pm$ 0.0481
& \multicolumn{1}{l|}{\textbf{0.6867 $\pm$ 0.0226}} & \textbf{0.7351 $\pm$ 0.0159}
  \\

	\bottomrule
	\end{tabular}}
\label{result-1}
\end{table*}

\begin{table*}[h!]

	\centering
 \caption{Average AUCs with standard deviation (10 trials) of different graph-level anomaly detection algorithms. We assess models by regarding every data class as normal data, respectively. The best results are highlighted in \textbf{bold} and '--' means out of memory.}
	\resizebox{0.95\textwidth}{!}{

	\begin{tabular}{l|ll|ll|ll}
		\toprule

	&	\multicolumn{2}{c|}{MUTAG}  &	\multicolumn{2}{c|}{DD}                      & \multicolumn{2}{c}{IMDB-Binary}     \\

  \cline{2-7}
& \multicolumn{1}{c|}{0}  & \multicolumn{1}{c|}{1}
 & \multicolumn{1}{c|}{0}  & \multicolumn{1}{c|}{1}        & \multicolumn{1}{c|}{0}  & \multicolumn{1}{c}{1} \\ \hline
		SP+OCSVM
  & \multicolumn{1}{l|}{0.5917 $\pm$ 0.0000 } & 0.2608 $\pm$ 0.0000
  & \multicolumn{1}{l|}{0.6856 $\pm$ 0.0000 }  & 0.4474 $\pm$ 0.0000  & \multicolumn{1}{l|}{0.4592$\pm$ 0.0000 } & 0.4716 $\pm$ 0.0000  \\

		WL+OCSVM (optimal)
  & \multicolumn{1}{l|}{0.6509 $\pm$ 0.0000 }    & 0.2960   $\pm$ 0.0000
  & \multicolumn{1}{l|}{0.7397 $\pm$ 0.0000 } & 0.4946 $\pm$ 0.0000 & \multicolumn{1}{l|}{0.5157  $\pm$ 0.0000 }   & 0.4607 $\pm$ 0.0000                \\

		NH+OCSVM
& \multicolumn{1}{l|}{0.7959 $\pm$ 0.0274}         & 0.1679 $\pm$ 0.0062
  & \multicolumn{1}{l|}{\textbf{0.7424 $\pm$ 0.0000}}  & 0.3684 $\pm$ 0.0000    & \multicolumn{1}{l|}{0.5321 $\pm$ 0.0000}      & 0.4652 $\pm$ 0.0000\\

		RW+OCSVM
   & \multicolumn{1}{l|}{0.8698  $\pm$ 0.0000}  & 0.1504  $\pm$ 0.0000
  & \multicolumn{1}{c|}{--}  & \multicolumn{1}{c|}{--}                        & \multicolumn{1}{l|}{0.4951 $\pm$ 0.0000}                   & 0.5311 $\pm$ 0.0000\\ \midrule
		OCGIN
 & \multicolumn{1}{l|}{0.8491 $\pm$ 0.0424}   & 0.4933 $\pm$ 0.1525
  & \multicolumn{1}{l|}{0.6659 $\pm$ 0.0444}      & 0.6003 $\pm$ 0.0534   & \multicolumn{1}{l|}{0.4047 $\pm$ 0.1083}& 0.3332 $\pm$ 0.0649\\

		infoGraph+Deep SVDD
 & \multicolumn{1}{l|}{0.8805 $\pm$ 0.0448}& 0.6166 $\pm$ 0.2052
  & \multicolumn{1}{l|}{0.3942 $\pm$ 0.0436}          & 0.6484 $\pm$ 0.0236  & \multicolumn{1}{l|}{0.6353 $\pm$ 0.0277}& 0.5836 $\pm$ 0.0995\\

		GLocalKD
& \multicolumn{1}{l|}{0.3952 $\pm$ 0.2258}& 0.2965 $\pm$ 0.2641
  &  \multicolumn{1}{l|}{0.1952 $\pm$ 0.0000} & 0.2203  $\pm$ 0.0001 & \multicolumn{1}{l|}{0.5383 $\pm$ 0.0124}& 0.4812 $\pm$ 0.0101 \\

        OCGTL
& \multicolumn{1}{l}{0.6570 $\pm$ 0.0210} & 0.7579 $\pm$ 0.2212
        &   \multicolumn{1}{c|}{0.6990 $\pm$ 0.0260 } & 0.6767 $\pm$ 0.0280
        & \multicolumn{1}{c|}{0.6510 $\pm$ 0.0180} & 0.6412 $\pm$ 0.0127 \\ \midrule
DOHSC (Ours)
  & \multicolumn{1}{l|}{0.8822 $\pm$ 0.0432} & 0.8115 $\pm$ 0.0279
& \multicolumn{1}{l|}{0.7083  $\pm$ 0.0188}                           & 0.7579  $\pm$ 0.0154                      &

  \multicolumn{1}{l|}{\textbf{0.7160 $\pm$ 0.0600}}
  & \textbf{0.7705 $\pm$ 0.0045} \\

		DO2HSC (Ours)
 & \multicolumn{1}{l|}{\textbf{0.9089 $\pm$ 0.0609}} & \textbf{0.8250 $\pm$ 0.0790}
  & \multicolumn{1}{l|}{0.7320 $\pm$  0.0194} & \textbf{0.7651 $\pm$ 0.0317} & \multicolumn{1}{l|}{0.6406 $\pm$ 0.0642} & 0.7101 $\pm$ 0.0429\\

		\bottomrule
	\end{tabular}}
\label{result-2}
\end{table*}

The anomaly detection visualization results of DO2HSC are displayed in Figure \ref{anomalydetection_visualization} and those of DOHSC are also shown in Appendix \ref{supplementary_visualization}. We draw them by setting the projection dimension to three directly. Results of different perspectives are given to avoid blind spots in the field of vision, demonstrating excellent performance.
Hence, it can be concluded that the effect of the improved model is in line with our motivation and shows much potential.
\begin{figure}[h!]
	\centering
	\includegraphics[width=\linewidth]{ improved_ours_v2.pdf}\\
	\caption{3D Visualization results of the DO2HSC on MUTAG Class 0 from different perspectives.}
\label{anomalydetection_visualization}
\end{figure}

\subsection{Ablation Study}
\label{ablation_study}

\begin{table}[h!]
\small
\begin{center}
 \caption{Ablation study of the orthogonal projection layer (OPL). We test models by regarding every data class as normal data, respectively. The best performance is highlighted in \textbf{bold}.
\label{ablation}

 }

			\begin{tabular}{c||c|c|c|c|c}
				\toprule
				 & OPL  & Class    & MUTAG  & COX2 & IMDB-Binary \\
				\midrule\midrule
				\multirow{4}{*}{DOHSC}
				&\multirow{2}{*}{$\times$}
				& 0    & 0.8521   & 0.5817 & 0.5880\\
				& & 1  & 0.8912   & 0.5737 & 0.6082\\
				&\multirow{2}{*}{$\checkmark$}
				& 0    & \textbf{0.8639}   & \textbf{0.6433} & \textbf{0.6192}\\
				& & 1  & \textbf{0.9088}   & \textbf{0.6077} & \textbf{0.6830}\\\midrule
				\multirow{4}{*}{DO2HSC}
				&\multirow{2}{*}{$\times$}
				& 0    & 0.8934& 0.6281 & 0.6252 \\
				& & 1  & 0.7504& 0.6178 & 0.6541\\
				&\multirow{2}{*}{$\checkmark$}
				& 0   & \textbf{0.9467} & \textbf{0.7158} & \textbf{0.6933}\\
				& & 1 & \textbf{0.9184} & \textbf{0.7074} & \textbf{0.6700}\\
				\bottomrule
		\end{tabular}

	\end{center}
\end{table}
In this section, we display the ablation study of the orthogonal projection layer on three datasets. From quantitive comparisons in Table \ref{ablation}, we concluded that orthogonality positively influences all performance to some extent. It also well supports our assumption discussed in Section \ref{section_orthogonal_projection_layer}.
Except for the aforementioned contents, please see the detailed experiment configurations, parameter sensitivity and robustness of the proposed models, supplemented visualizations of distance distributions for anomaly detection and visualization comparison between proposed models with orthogonal projection layer and without orthogonal projection layer in Appendix \ref{supplementary_ablation_study}, which can also strongly support our theory and validate the effectiveness.

\section{Experiments on non-graph data}
\subsection{Experiment Setting}
\textbf{Datasets:} One image dataset (Fashion-MNIST) and two tabular datasets (Thyroid, Arrhythmia) are tested to verify the effectiveness of the proposed extension on non-graph data. Herein, we follow the data split settings in \cite{zong2018deepautoencoding} for both tabular datasets.

\textbf{Baselines:}
We follow the work of \citep{ruff2018deep} and utilize the AUCs of three state-of-the-art anomaly detection algorithms Deep SVDD \cite{ruff2018deep}, deep robust one-class classification (DROCC) \cite{Goyal2020drocc}, and fully convolutional data description for explainable deep one-class classification (FCDD) \cite{Liznerski2021explainable}) on the image dataset, and the F1-scores of several compared methods OCSVM \cite{bernhard1999support}, classification-based anomaly detection for general data (GOAD) \cite{classification2020liron}, DROCC, local outlier factor for anomaly detection (LOF) \cite{markus2000lof}, Deep SVDD and perturbation learning based anomaly detection (PLAD) \cite{cai2022perturbation}). Herein, some performance on tabular data is reported directly according to the following papers \cite{Goyal2020drocc,cai2022perturbation,classification2020liron}. Other compared methods are reproduced by their official codes.
Note that the network architecture of Deep SVDD is set the same as ours so as to keep fairness.

\subsection{Results}
\begin{table}[h!]
\centering
\caption{Average F1-scores with the standard deviation in one-class anomaly detection on two tabular datasets. The best two results are marked in \textbf{bold}.}
\label{experiment_tabular}
\begin{tabular}{c|c|c}
\toprule
   & Thyroid         & Arrhythmia      \\\midrule\midrule
OCSVM \cite{bernhard1999support}   & 0.56 $\pm$ 0.01 & 0.64 $\pm$ 0.01 \\
Deep SVDD \cite{ruff2018deep} & 0.73 $\pm$ 0.00 & 0.54 $\pm$ 0.01 \\
LOF \cite{markus2000lof}      & 0.54 $\pm$ 0.01 & 0.51 $\pm$ 0.01 \\
GOAD \cite{classification2020liron}     & 0.75 $\pm$ 0.01 & 0.52 $\pm$ 0.02 \\
DROCC \cite{Goyal2020drocc}    & 0.78 $\pm$ 0.03 & 0.69 $\pm$ 0.02 \\
PLAD \cite{cai2022perturbation}    & 0.77 $\pm$ 0.01 & \textbf{0.71 $\pm$ 0.02} \\ \midrule
DOHSC    & \textbf{0.92 $\pm$ 0.01} & 0.70 $\pm$ 0.03 \\
DO2HSC   & \textbf{0.88 $\pm$ 0.03} & \textbf{0.74 $\pm$ 0.02}               \\\bottomrule
\end{tabular}
\end{table}
\begin{table}[h!]
\caption{Average AUCs in one-class anomaly detection on Fashion-MNIST. The best performance is highlighted in \textbf{bold}.}
\label{experiment_fashionmnist}
\centering
\begin{tabular}{c|c|c|c|c|c}
\toprule
Normal Class      & Deep SVDD           & DROCC    & FCDD                & DOHSC               & DO2HSC                               \\\midrule
T-shirt    & 0.8263 & 0.8931 & 0.8143   & 0.9153 & \textbf{0.9196}                        \\
Trouser    & 0.9632  & 0.9835  & \textbf{0.9855}  & 0.9817& 0.9839                        \\
Pullover   & 0.7885 & 0.8656 & 0.8423  & 0.8007 & \textbf{0.8768}                        \\
Dress      & 0.8607 & 0.8776 & 0.9143   & \textbf{0.9178} & 0.9171 \\
Coat       & 0.8417 & 0.8453 & 0.8607   & 0.8805 & \textbf{0.9038}                        \\
Sandal     & 0.8902 & \textbf{0.9336}& 0.9089  & 0.8932 & 0.9308                        \\
Shirt      & 0.7507 & 0.7789 & 0.7750   & \textbf{0.8177} & 0.8022                  \\
Sneaker    & 0.9676 & 0.9624 & \textbf{0.9874}  & 0.9678 & 0.9677                        \\
Bag        & 0.9039 & 0.7797 & 0.8584  & \textbf{0.9122}  & 0.9090                        \\
Ankle Boot & 0.9488 & 0.9589 & 0.9432 & 0.9756 & \textbf{0.9785}   \\
\bottomrule
\end{tabular}
\end{table}
Non-graph experimental results are reported in Tables \ref{experiment_tabular} and  \ref{experiment_fashionmnist}.
First, Table \ref{experiment_tabular} summarizes the F1-scores of all competitive methods on Thyroid and Arrhythmia datasets. It can be seen a significant margin between the baselines and ours, especially the 92\% performance of DOHSC on the Thyroid. Even if there exists the difficulty of a small sample size on Arrhythmia data, DO2HSC still surpasses 2\% compared to PLAD.
On Fashion-MNIST dataset, DOHSC and DO2HSC obtained seven best AUCs out of ten in total. And in the remaining three classes, the proposed models still achieved comparable performance with gaps of less than $2\%$. The complete results on Fashion-MNIST (with standard deviation) can be referred in Appendix \ref{supplementary_image_result}.
Second, Deep SVDD plays an important baseline role relative to DOHSC. But DOHSC defeats it by a large margin in all classes on non-graph datasets. It further verifies that the proposed orthogonal projection is constructive.
Besides, bi-hypersphere learning also performs sufficiently, which fully demonstrates our applicability on non-graph data.

\section{Conclusion}
This paper has proposed two novel end-to-end graph-level AD methods, DOHSC and DO2HSC, which combined the effectiveness of mutual information between node-level and global features to learn graph representation and the power of hypersphere compression. DOHSC and DO2HSC mitigate the possible shortcomings of hypersphere boundary learning by applying an orthogonal projection for global representation. Furthermore, DO2HSC projects normal data between the interval area of two co-centered hyperspheres to significantly alleviate the \textit{soap-bubble} issue. We also extended DOHSC and DO2HSC to other data types, i.e. image data and tabular data. Comprehensive experimental results strongly demonstrate the superiority of DOHSC and DO2HSC on multifarious datasets. In the future, an interesting direction could be inspecting the reason behind serious \textit{soap-bubble} issue in GAD tasks.

\nocite{langley00}

redpajama_set_name: RedPajamaArXiv


text:
Mario Merz (né à Milan le  - mort à Turin, ), est un artiste contemporain italien représentant du courant de l'Arte Povera.

Biographie

Mario Merz grandit à Turin, il fréquente deux ans la faculté de l'armée de l'Université de Turin. Pendant la Seconde Guerre mondiale, il entre dans le groupe antifasciste Justice et Liberté et en 1945 il est arrêté et emprisonné, pour avoir distribué des tracts. En prison, il dessine sur tout et rien, du matin au soir, sans lever la main du support choisi. Et dès sa libération il va retrouver les collines turinoises où l'herbe, le soleil, les parfums et les bruits seront enregistrés comme par un sismographe à la pointe du crayon qui trace des circonvolutions. C'est une sorte d'écriture du sensible dans un cycle sans fin. Il cherche un langage qui va donner forme au monde.   Après la Libération, encouragé par le critique Luciano Pistoi, il se consacre à plein temps à la peinture, en commençant par la peinture à l'huile. Il commence avec une peinture de style expressionniste-abstrait, pour ensuite passer à un traitement informel de la peinture (subvertir les codes de la création plutôt que d'en tenter le dépassement). En 1954, à la Galerie La Bussola à Turin, a lieu sa première exposition personnelle. Au milieu des années soixante, il abandonne la peinture pour expérimenter des matériaux comme les tubes au néon, avec lesquels il troue la superficie des toiles pour symboliser une infusion d'énergie, et à expérimenter les premiers assemblages tridimensionnels, les « peintures volumétriques ».

Il est présent dès les premières expositions d'Arte Povera avec les artistes qui ont participé à l'exposition collective organisée par Germano Celant à la Galerie la Bertesca de Gênes (1967) et Merz, Michelangelo Pistoletto, Giuseppe Penone, Luciano Fabro, Alighero Boetti et d'autres se réunissent à la Galerie turinoise de Gian Enzo Sperone. Il devient vite un élément de référence du groupe.

Le climat de 68 et l'idée d'un renouvellement politique et social se retrouvent dans ses œuvres : Merz reproduit avec des néons les slogans de protestation du mouvement étudiant.

À partir de 1968 il commence à réaliser des structures archétypiques comme l'igloo, réalisés avec les matériaux les plus disparates (verre, terre, plomb...), qui deviendront caractéristiques de sa production et que représentent le dépassement définitif, de la part de l'artiste, du cadre et du plan bidimensionnel. En 1970, il introduit dans ses œuvres la suite de Fibonacci comme symbole de l'énergie inhérente de la matière et de la croissance organique, en plaçant les chiffres réalisés au néon soit sur ses œuvres soit dans des lieux d'exposition, comme, en 1971 le long de la spirale du Musée Solomon R. Guggenheim, en 1984 sur le Mole Antonelliana de Turin et en 1990 sur la Manica Lunga du Castello di Rivoli.

En 1976, il introduit la figure symbolique de la spirale qui fut successivement associée à celle de la table, sur la surface desquelles il disposait des fruits ou des légumes de sorte que, laissés à leur destin naturel, ils introduisent dans l'œuvre la dimension du temps réel.

À la fin des années 1970, Merz retourne à l'art figuratif, en dessinant de grandes images d'animaux archaïques, qu'il définit comme préhistoriques, sur des toiles de grandes dimensions non encadrées.

La renommée

Au cours des années de très nombreuses expositions ont été consacrées à Merz dans les plus importants musées du monde. Parmi ceux-ci,  on peut citer le Walker Art Center de Minneapolis en 1972, la Kunsthalle de Bâle en 1981, le Moderna Museet de Stockholm en 1983, le Musée d'art contemporain de Los Angeles et le Musée Solomon R. Guggenheim de New York en 1989, la Fundation Antoni Tàpies de Barcelone en 1993, le Château de Rivoli près de Turin et le Centre Luigi Pecci pour l'art contemporaon de Prato en 1990, la Galerie civile d'art contemporain de Trente en 1995, la Fundation de Serralves de Porto (Portugal) en 1999, le Carré d'Art de Nîmes en 2000, la Fundation Proa de Buenos Aires en 2002. Merz a également participé aux expositions collectives les plus prestigieuses parmi lesquelles la Documenta de Kassel en 1972, 1982 et 1992, la Biennale de Paris en 1971, la Biennale de Venise en 1976, 1997. En 2003, il lui a été attribué le Praemium Imperiale au Japon.

Œuvres

1968 : Igloo di Giap, au Musée national d'Art moderne, à Paris.
1982 : Igloo di pietra
1983 : Cinque dita au musée de Grenoble.
1987 : Tournons en rond dans les maisons ou les maisons tournent-elles en rond autour de nous?; Installation.

Voir aussi
 Arte Povera

Mario Merz's exhibition at Fundació Antoni Tàpies 30/3/1993 - 6/6/1993

Sources

Liens externes

 Mario Merz sur ART ZOO

Naissance à Milan
Artiste contemporain italien
Plasticien italien contemporain
Arte povera
Lauréat du Praemium Imperiale
Antifasciste italien
Giustizia e Libertà
Résistant italien
Naissance en janvier 1925
Décès en novembre 2003
Décès à Turin
Décès à 78 ans


Many people think that the Patriots will probably not draft a wide receiver in the first round, but giving Tom Brady a vertical wide receiver in the last couple years of his career would be a huge help. Tom Brady has not had a vertical threat quite like the ability of Dorial Green-Beckham since Randy Moss. Lets take a more in depth look at Green-Beckham and see if he is an actual option for the defending World Champs.
In short, this kid is an absolute freak. Green-Beckham is an outstanding physical specimen. Green-Beckham stands at 6'5 and weighs 237 pounds. Wow. Although he is absolutely massive, it does not seem to effect his speed. In the NFL Combine this week, Green-Beckham dazzled NFL scouts with an impressive 4.49 40 yard dash, 33.5 inch vertical, and 119 inch broad jump. Again, wow. Green-Beckham has the unique ability to "put it into second gear" and blow by defensive backs with his long strides. Green-Beckham also has the abilities to bring down those "wow catches." He has soft hands and can contort his body in the air to catch balls that are not necessarily thrown perfectly.
However, Green-Beckham does have some weakness. His routes are more "rounded" than hard cuts to create separation from the defense. But to a more pressing matter, his work ethic and "problem child" mentality has come into issue. At Missouri, Green-Beckham was suspended and arrested twice for marijuana-related incidents. After an alleged burglary incident, Green-Beckham was not able to play for the entire 2014 season. There was also suspicion that he was involved in an incident at Missouri for pushing a woman down a flight of stairs, yet charges were never filed.
NFL executives seem to think that he is an exceptional athlete, yet would be surprised if he is drafted before the third day. There is no question that he is a phenomenal athlete. If he is able to keep his head on straight, he could be a very special player in the NFL. After everything that has happened in the past year with Josh Gordon and Ray Rice, I think teams may be more cautious than they have been in the past.
However, that should not turn the Patriots off from drafting the athletic wide receiver. Bill Belichik has a very well known reputation for taking in troubled players and setting them straight. The Patriots have the structure in the locker room to keep him in line, while also having the depth at the position to gamble on a potential superstar. If it was up to me, I would draft Green-Beckham. I would have to think about drafting him in the first round, but if he is sitting there when the Patriots have their late first round pick, I would probably pull the trigger.


The purpose of this Council is to provide a venue to help wealth advisor firms think about strategic objectives for their companies by means of peer insights, investigation of the drivers of success for integrated wealth management, and articulation of the needs of the ultra-high-net-worth target market.
The next meeting will be held at the FOX office in downtown Chicago.
For information about joining this Council, contact us by email or call 312-327-1247.
Mindy Earley, an experienced family learning officer, will present the key components of a successful family education program, offering a range of experiences available for family members. She will share lessons learned from her work creating learning programs for rising gen family members and leave you with practical tips to incorporate learning into your daily practices.
FOX will present the latest trends that are impacting those who are in the business of serving families of wealth. We will share highlights from our recently completed wealth advisor survey and our insights on what these trends mean to wealth advisors and discuss in our peer exchange.
Hiring the right person for the job in a family office is as much about "fit" as it is technical qualifications and skills. In this session, Linda will outline what you need to know before your next interview – from paying attention to non-verbal cues and asking open-ended questions that help you to assess for the service gene.


I did some private image swaps on Swap-Bot to help get some of them started with ratings so they can play in most any swap then without issue. This was one of the images I received in the swap - I like how the train is coming head on at you. I added some Crystal Lacquer to the light on the front other than that I only drug my ink pad around and across it some to "muck" it up LOL! The happy birthday is a rub on and the rest is just torn paper that I edged with the ink pad. Pretty easy card - hoping it will be a good "guy" birthday card.
that is awesome love the colors and i feel it coming towards me.
The gold inking on the train image really makes it pop!! :) Cute!


text:
ABBYY USA's Vice President of Sales Joe Budelli Elected AIIM North American Chairman
ABBYY®, a leading provider of document recognition, data capture and linguistic software, today announced that Joe Budelli, the company's vice president of sales, has been selected by members of the AIIM (Association for Information and Image Management) Advisory Trade Member program as the group's next North American Chairman. Mr. Budelli will take over as the North American chairman on January 1, 2010 and will also serve on AIIM's International Board of Directors for two years.
"For over 60 years, AIIM has joined the industry's leading companies together to serve as a neutral, unbiased source of information for the enterprise content management (ECM) market worldwide," said John Mancini, AIIM president "Joe's involvement as the North American chairman and member of the International Board of Directors will enable our organization to continue to serve as a trusted resource and drive the market to new levels."
AIIM is a leading international organization focused on helping users, suppliers and the channel to understand the challenges associated with managing documents, content, records and business processes. Serving the needs of its members, AIIM performs various functions including: market education to assist users specify, select and deploy ECM solutions to solve organizational problems; industry professional development services through certificate training programs and courses; peer networking opportunities; and industry advocacy by interfacing with standards organizations, the media, and government decision-makers.
"No facet of the industry can grow independently of the rest. Growth depends on the full spectrum of hardware and software manufacturers' working with customers on what inevitably helps everyone," said Joe Budelli. "With a strong AIIM, manufacturers and customers have a forum within which they can build consensus and understanding for what will benefit the industry as a whole. I am looking forward to working with AIIM's other Board members and member organizations to develop further understanding and future direction for the enterprise content management industry."
For more information about ABBYY, please visit: http://www.abbyyusa.com. Additionally, for more information on AIIM, please visit: http://www.aiim.org.


text:
"One of These Things Is Not Like the Others": Linguistic Representations of Yao Ming in NBA Game Commentary
in International Journal of Sport Communication
Katherine L. Lavelle 1
1 University of Northern Iowa, USA
https://doi.org/10.1123/ijsc.4.1.50
Chinese identity; National Basketball Association; sports; rhetoric; model minority
The re/production of Chinese cultural identity is often fraught with contradictions. When China's Yao Ming was drafted Number 1 in the National Basketball Association (NBA) draft, he was supposed to reinforce and transcend Chinese/ Asian identity. Yao's entrance into the NBA signaled a new understanding of Asian identity in the United States. To study this phenomenon, the author examined commentary from television broadcasts of U.S. NBA games featuring a prominent Asian athlete (Yao Ming) using critical discourse analysis. Analysis of 13 games from Yao Ming's 2nd and 3rd seasons revealed that Yao is linguistically constructed as a panethnic Asian/Chinese person. In addition, the analysis upholds the stereotypes that Asian people are a "model minority" and unfit to play professional sports. Given the dearth of Asian players in the NBA, how do linguistic representations of Yao Ming in game commentary reinforce Asian and Chinese cultural stereotypes or create a new identity of China?
* The author is with the Dept. of Communication Studies, University of Northern Iowa, Cedar Falls, IA.
International Journal of Sport Communication
Katherine L. Lavelle


Phil Proctor is principal trumpet with the Maui Chamber Orchestra, having joined the group in Fall 2015. Phil has nearly twenty years' experience as a performer, conductor and music educator. Currently, Phil also is the Dean of Students and music teacher for Kīhei Charter Middle School.


Biovax® Bamboo & Avocado oil is a complex, intensely regenerating range of cosmetics, it provides multidimensional hair care of dry, weak and lacking density. The treatment created in purpose to increase hair thickness, their density and strengthens. It provides professional hair care from roots to the hair ends. Biovax recipe is based on natural and safe active ingredients.
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Mask recipe contains a complex 3D Bamboo Protect, rebuilding and thickening hair structure, stimulates them to grow and restores whole length of hair. During application it reaches to the most damaged hair places and repairs them. As a result, hair gain new healthy glow, vitality and resilience. New hair roots are nourished and hair regrow healthy, thick and dense.
•extract from bamboo root - the richest natural source of organic silicon which help with hair strengthening, thickening and density.
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•Oil from young bamboo shoots - thanks to high concentration of vitamins and minerals strengthens core of hair and gives to hair additional protective shield.
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3D Bamboo Protect was formed from high quality natural active ingredients which were carefully selected to gives and provides full regeneration on totally hair structure: hair roots, hair stem and hair core.
Biovax guarantees healthy hair and safe ingredients. Product friendly for allergy sufferers.
•parabens •SLS (Sodium Lauryl Sulfate) •SLES (Sodium Laureth Sulfate) •silicones, paraffin.These substances can cause skin irritation and even inflammation. They contribute to a formation of dandruff, itching and dryness of scalp.
•Termocap - cap supporting the maintenance of heat, so that the active ingredients penetrate more easily into the interior of the hair.
Direction for use: At washed, towel-dried hair distribute right amount. Gently massage into hair and scalp. For more intensive effect put thermocap and leave mask for 15 minutes or longer. In addition wrap your hair with towel to keep right temprature of heat. Rinse with lukewarm water. Repeat every 3-5 days.
Ingredients: AQUA PURIFICATA* • CETEARYL ALCOHOL • CETEARETH-20 • PERSEA GRATISSIMA (AVOCADO) OIL* • BEHENTRIMONIUM CHLORIDE • BAMBUSA ARUNDINACEA ROOT EXTRACT* • BAMBUSA VULGARIS (LEAF/STEM) EXTRACT* • BAMBUSA VULGARIS SHOOT EXTRACT* • SILICA • HELIANTHUS ANNUUS (SUNFLOWER) SEED OIL* • HYDROXYPROPYL STARCH PHOSPHATE • PROPYLENE GLYCOL DICAPRYLATE/DICAPRATE • BIS-(ISOSTEAROYL/OLEOYL ISOPROPYL) DIMONIUM METHOSULFATE • LACTIC ACID • PARFUM • BENZYL ALCOHOL • BHT • METHYLCHLOROISOTHIAZOLINONE • METHYLISOTHIAZOLINONE • ISOPROPYL ALCOHOL • C.I. 42090 • C.I. 19140.


Lodge at the Presidio sits in the historic heart of the Presidio of San Francisco, a former U.S. Army post founded in 1776 that today is a vibrant national park. It is the closest hotel in San Francisco to the iconic Golden Gate Bridge.
The lodge is located within the red brick Montgomery Street Barracks, built between 1895-1897 to house six artillery companies, a cavalry troop, and two infantry companies. The structure has been lovingly rehabilitated to preserve its original character while making it a contemporary launching pad for national park adventures.
The Presidio's rich Native American Ohlone and military history is showcased throughout the Lodge with memorabilia and original art, found objects, and historic photographs. Large photographic murals "bring the outdoors in" by reflecting the beauty of the Presidio's national park setting, including its forest and bay views. Gathering spaces include a fire pit and courtyard garden overlooking the bridge, an expansive front porch with rocking chairs, and a large dining lounge with a fireplace.
Guest amenities include complimentary breakfast, an evening wine and cheese reception, free WiFi, complimentary usage of bikes for exploring the national park, and more.
The Lodge is steps away from the Presidio Visitor Center, 25 miles of hiking and biking trails, beaches, the 18-hole Presidio Golf Course, the Walt Disney Family Museum, renowned restaurants, and so much more. From spring to fall, the Presidio also hosts picnics on Sundays which feature international food trucks and family activities. A free shuttle invites guests to explore San Francisco.
The Lodge at the Presidio, a member of Historic Hotels of America since 2018, dates back to the 1894.
Battery F of the Third Artillery Regiment was the first Army unit to occupy the north side of the building that now houses the Lodge at the Presidio.
Hotel/Resort Fees & Taxes: There is a 14% Park Fee for all accommodations.
Parking: On-site parking is available for $8.00 per night.
Learn more about the History of The Lodge at the Presidio .