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Paper title:
Weakly Supervised Clustering by Exploiting Unique Class Count

Paper body:
A weakly supervised learning based clustering framework is proposed in this paper . As the core of this framework , we introduce a novel multiple instance learning task based on a bag level label called unique class count ( ucc ) , which is the number of unique classes among all instances inside the bag . In this task , no annotations on individual instances inside the bag are needed during training of the models . We mathematically prove that with a perfect ucc classifier , perfect clustering of individual instances inside the bags is possible even when no annotations on individual instances are given during training . We have constructed a neural network based ucc classifier and experimentally shown that the clustering performance of our framework with our weakly supervised ucc classifier is comparable to that of fully supervised learning models where labels for all instances are known . Furthermore , we have tested the applicability of our framework to a real world task of semantic segmentation of breast cancer metastases in histological lymph node sections and shown that the performance of our weakly supervised framework is comparable to the performance of a fully supervised Unet model . 1 INTRODUCTION . In machine learning , there are two main learning tasks on two ends of scale bar : unsupervised learning and supervised learning . Generally , performance of supervised models is better than that of unsupervised models since the mapping between data and associated labels is provided explicitly in supervised learning . This performance advantage of supervised learning requires a lot of labelled data , which is expensive . Any other learning tasks reside in between these two tasks , so are their performances . Weakly supervised learning is an example of such tasks . There are three types of supervision in weakly supervised learning : incomplete , inexact and inaccurate supervision . Multiple instance learning ( MIL ) is a special type of weakly supervised learning and a typical example of inexact supervision ( Zhou , 2017 ) . In MIL , data consists of bags of instances and their corresponding bag level labels . Although the labels are somehow related to instances inside the bags , the instances are not explicitly labeled . In traditional MIL , given the bags and corresponding bag level labels , task is to learn the mapping between bags and labels while the goal is to predict labels of unseen bags ( Dietterich et al. , 1997 ; Foulds & Frank , 2010 ) . In this paper , we explore the feasibility of finding out labels of individual instances inside the bags only given the bag level labels , i.e . there is no individual instance level labels . One important application of this task is semantic segmentation of breast cancer metastases in histological lymph node sections , which is a crucial step in staging of breast cancer ( Brierley et al. , 2016 ) . In this task , each pathology image of a lymph node section is a bag and each pixel inside that image is an instance . Then , given the bag level label that whether the image contains metastases or not , the task is to label each pixel as either metastases or normal . This task can be achieved by asking experts to exhaustively annotate each metastases region in each image . However , this exhaustive annotation process is tedious , time consuming and more importantly not a part of clinical workflow . In many complex systems , such as in many types of cancers , measurements can only be obtained at coarse level ( bag level ) , but information at fine level ( individual instance level ) is of paramount importance . To achieve this , we propose a weakly supervised learning based clustering framework . Given a dataset consisting of instances with unknown labels , our ultimate objective is to cluster the instances in this dataset . To achieve this objective , we introduce a novel MIL task based on a new kind of bag level label called unique class count ( ucc ) , which is the number of unique classes or the number of clusters among all the instances inside the bag . We organize the dataset into non-empty bags , where each bag is a subset of individual instances from this dataset . Each bag is associated with a bag level ucc label . Then , our MIL task is to learn mapping between the bags and their associated bag level ucc labels and then to predict the ucc labels of unseen bags . We mathematically show that a ucc classifier trained on this task can be used to perform unsupervised clustering on individual instances in the dataset . Intuitively , for a ucc classifier to count the number of unique classes in a bag , it has to first learn discriminant features for underlying classes . Then , it can group the features obtained from the bag and count the number of groups , so the number of unique classes . Our weakly supervised clustering framework is illustrated in Figure 1 . It consists of a neural network based ucc classifier , which is called as Unique Class Count ( UCC ) model , and an unsupervised clustering branch . The UCC model accepts any bag of instances as input and uses ucc labels for supervised training . Then , the trained UCC model is used as a feature extractor and unsupervised clustering is performed on the extracted features of individual instances inside the bags in the clustering branch . One application of our framework is the semantic segmentation of breast cancer metastases in lymph node sections ( see Figure 4 ) . The problem can be formulated as follows . The input is a set of images . Each image ( bag ) has a label of ucc1 ( image is fully normal or fully metastases ) or ucc2 ( image is a mixture of normal and metastases ) . Our aim is to segment the pixels ( instances ) in the image into normal and metastases . A UCC model can be trained to predict ucc labels of individual images in a fully supervised manner ; and the trained model can be used to extract features of pixels ( intances ) inside the images ( bags ) . Then , semantic segmentation masks can be obtained by unsupervised clustering of the pixels ( each is represented by the extracted features ) into two clusters ( metastases or normal ) . Note that ucc does not directly provide an exact label for each individual instance . Therefore , our framework is a weakly supervised clustering framework . Finally , we have constructed ucc classifiers and experimentally shown that clustering performance of our framework with our ucc classifiers is better than the performance of unsupervised models and comparable to performance of fully supervised learning models . We have also tested the performance of our model on the real world task of semantic segmentation of breast cancer metastases in lymph node sections . We have compared the performance of our model with the performance of popular medical image segmentation architecture of Unet ( Ronneberger et al. , 2015 ) and shown that our weakly supervised model approximates the performance of fully supervised Unet model1 . Hence , there are three main contributions of this paper : 1 . We have defined unique class count as a bag level label in MIL setup and mathematically proved that a perfect ucc classifier , in principle , can be used to perfectly cluster the individual instances inside the bags . 1Code and trained models : http : //bit.ly/uniqueclasscount 2 . We have constructed a neural network based ucc classifier by incorporating kernel density estimation ( KDE ) ( Parzen , 1962 ) as a layer into our model architecture , which provided us with end-to-end training capability . 3 . We have experimentally shown that clustering performance of our framework is better than the performance of unsupervised models and comparable to performance of fully supervised learning models . The rest of the paper is organized such that related work is in Section 2 , details of our weakly supervised clustering framework are in Section 3 , results of the experiments on MNIST , CIFAR10 and CIFAR100 datasets are in Section 4 , results of the experiments in semantic segmentation of breast cancer metastases are in Section 5 , and Section 6 concludes the paper . 2 RELATED WORK . This work is partly related to MIL which was first introduced in ( Dietterich et al. , 1997 ) for drug activity prediction . Different types of MIL were derived with different assumptions ( Gärtner et al. , 2002 ; Zhang & Goldman , 2002 ; Chen et al. , 2006 ; Foulds , 2008 ; Zhang & Zhou , 2009 ; Zhou et al. , 2009 ) , which are reviewed in detail in ( Foulds & Frank , 2010 ) , and they were used for many different applications such as , image annotation/categorization/retrieval ( Chen & Wang , 2004 ; Zhang et al. , 2002 ; Tang et al. , 2010 ) , text categorization ( Andrews et al. , 2003 ; Settles et al. , 2008 ) , spam detection ( Jorgensen et al. , 2008 ) , medical diagnosis ( Dundar et al. , 2007 ) , face/object detection ( Zhang et al. , 2006 ; Felzenszwalb et al. , 2010 ) and object tracking ( Babenko et al. , 2011 ) . In MIL , different types of pooling layers are used to combine extracted features of instances inside the bags , such as max-pooling and log-sum-exp pooling ( Ramon & De Raedt , 2000 ; Zhou & Zhang , 2002 ; Wu et al. , 2015 ; Wang et al. , 2018 ) . On the other hand , our UCC model uses KDE layer in order to estimate the distribution of extracted features . The advantage of KDE over pooling layers is that it embeds the instance level features into distribution space rather than summarizing them . There are also methods modeling cardinality and set distributions ( Liu et al. , 2015 ; Brukhim & Globerson , 2018 ; Kipf et al. , 2018 ) . However , cardinality of a set and ucc are completely different from each other . It is also important to state that ucc is obviously different from object/crowd counting ( Idrees et al. , 2013 ; Arteta et al. , 2014 ; Zhang et al. , 2015 ; 2016 ) since the task in object/crowd counting is to count the instances of the same type of object or people . Lastly , we compare clustering accuracies of our models with clustering accuracies of unsupervised baseline models : K-means ( Wang et al. , 2015 ) and Spectral Clustering ( Zelnik-Manor & Perona , 2005 ) ; state of the art unsupervised models : JULE ( Yang et al. , 2016 ) , GMVAE ( Dilokthanakul et al. , 2016 ) , DAC ( Chang et al. , 2017 ) , DEPICT ( Ghasedi Dizaji et al. , 2017 ) and DEC ( Xie et al. , 2016 ) ; and state of the art semi-supervised models : AAE ( Makhzani et al. , 2015 ) , CatGAN ( Springenberg , 2015 ) , LN ( Rasmus et al. , 2015 ) and ADGM ( Maaløe et al. , 2016 ) . 3 WEAKLY SUPERVISED CLUSTERING FRAMEWORK . In this section , we state our machine learning objective and formally define our novel MIL task , which is the core of our weakly supervised clustering framework . Finally , we explain details of the two main components of our framework , namely UCC model and unsupervised clustering branch . Objective : Let X = { x1 , x2 , · · · , xn } be a dataset such that each instance xi ∈ X belongs to a class , but its label is unknown . In this paper , we assume that total number of classes K is known . Hence , each instance xi is endowed with an underlying , but unkown , label L ( xi ) = li ∈ { 1 , 2 , · · · , K } . Further assume that for each class k ∈ { 1 , 2 , · · ·K } , there exist at least one element xi ∈ X such that L ( xi ) = li = k. Our eventual objective is to derive a predicted class label l̂i for each instance xi that tends towards underlying truth class li , i.e . l̂i → L ( xi ) = li .

5-sentence paper summary:
This paper proposes a MIL clustering method. The proposed MIL setup is called "unique class count (ucc)", this is, for a bag os samples ucc is the number of clusters in the bag. The method learns the features of the samples using two losses: an autoender loss and the ucc loss. Once trained on a dataset the method can perform clustering on classes (classify) better than a fully unsupervised clustering algorithm and worse than a fully supervised model. The method is evaluated on MNIST, CIFAR10, CIFAR100  and on binary breast cancer segmentation.