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an embedding is a map from input data to points in euclidean space .
machine learning researchers and developers often need to explore the properties of a specific embedding to understand the behavior of their model . an engineer who creates an embedding of songs for a recommendation system might want to verify that the nearest neighbors of `` stairway to heaven '' include `` whole lotta love '' and not `` let it go '' from frozen .
meanwhile , a researcher may be interested in global geometric properties , such as linear relationships between meaningful subsets of embedded points . for both sets of users , gaining
an understanding of embedding geometry is a key step in interpreting a machine learning model .
an appealing approach to analyzing embeddings is to visualize them .
since embeddings often exist in a space of hundreds of dimensions , an essential step is `` dimensionality reduction '' which projects points to a more approachable two or three dimensions .
many tools exist to perform various types of dimensionality reduction , but they are largely non - interactive ( e.g. , matplotlib [ 3 ] , or the code released in [ 5 ] ) .
unfortunately , these static views are generally inadequate for exploring high - dimensional data  although an important first step in the process , users then typically want to switch quickly between many views , zooming and filtering , and then closely inspecting details .
indeed , there have been many toolkits created with the express purpose of exploring high - dimensional data ( e.g. , [ 2 ] , [ 8 ] ) , and a key lesson has been that rich interactivity coupled with multiple linked views is extremely helpful .    at the same time , the embeddings that arise in machine learning differ from the kind of data sets seen in conventional `` high - dimensional '' visualization .
most notably , traditional systems often assume the underlying dimensions have a particular meaning ( the expression level of a given gene , or the age of a person ) . on the other hand ,
the basis vectors in a typical embedding are typically not meaningful  in fact , discovering semantically significant directions can be a goal in itself .    in this paper , we present the embedding projector , a system for interactive visualization and analysis of high - dimensional data . although designed to be a general - purpose tool , it is optimized for the use cases that arise in machine learning and includes special features to explore meaningful directions in a data set .
we held informal interviews with engineers and researchers within our organization to learn how they worked ( or wanted to work ) with embeddings .
we also looked at usage of existing internal tools .
three themes arose consistently .
[ [ task-1.-exploring - local - neighborhoods ] ] task 1 . exploring local neighborhoods + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +    many users wanted to inspect the nearest neighbors of a given point .
confirming that nearby points are semantically related represented an important step in establishing trust in an algorithm .
[ [ task-2.-viewing - global - geometry - and - finding - clusters ] ] task 2 .
viewing global geometry and finding clusters + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +    several users were interested in finding large clusters of related points , as well as seeing the global geometry of the embeddings .    [ [ task-3.-finding - meaningful - directions ] ] task 3 . finding meaningful `` directions '' + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +    researchers have found that embedding spaces sometimes contain semantically significant directions .
for example [ 6 ] discovered that the vector defined by subtracting the point for `` man '' from the point for `` woman '' represented a kind of `` female '' direction in space .
users we talked with considered the discovery of such directions interesting and worthwhile .
we know of no current tools that help with this use case .
the embedding projector is a web application , available as both a standalone tool and integrated into the tensorflow platform [ 1 ] .
users may either upload arbitrary high - dimensional data , in a simple text format , or ( in tensorflow ) take advantage of the model checkpoint system that makes it easy to visualize any tensors as an embedding .    .
]    fig .
[ fig - main ] shows the main view of the web app with ( a ) _ data _ panel on the left , where users can choose data columns to color and label points , ( b ) the _ projected _ view in the center , and ( c ) the _ inspector _ panel on the right side , where users can search for particular points and see a list of nearest neighbors .
the embedding projector offers three methods of reducing the dimensionality of a data set : two linear and one nonlinear .
each method can be used to create either a two- or three - dimensional view .
[ [ principal - component - analysis ] ] principal component analysis + + + + + + + + + + + + + + + + + + + + + + + + + + + +    a straightforward technique for reducing dimensions is principal component analysis ( pca ) .
the embedding projector computes the top 10 principal components .
menus let the user project those components onto any combination of two or three .
pca is often effective at supporting task 2 , examining global geometry .
[ [ t - sne ] ] t - sne + + + + +    a popular non - linear dimensionality reduction technique is t - sne [ 5 ] .
the embedding projector offers both two- and three - dimensional t - sne views .
layout is performed client - side .
because t - sne often preserves some local structure , in practice it supports both task 1 and task 2 .
[ [ custom ] ] custom + + + + + +    users can construct specialized linear projections based on text searches , supporting task 3 , finding meaningful directions in space . to define a projection axis ,
the user enters two search strings or regular expressions .
the program computes the centroids of the sets of points whose labels match these searches , and uses the difference vector between centroids as a projection axis .
for example , in the smart reply data [ 4 ] , this view uncovered a surprisingly regular relationship between phrases ending in periods versus exclamation points .      to explore a data set
, users can navigate the views in either a 2d or a 3d mode , zooming , rotating , and panning using natural click - and - drag gestures . to help interpretation of the 3d mode ,
the projector uses multiple redundant depth cues : changing the size of points based on distance to camera ; adding fog to fade out more distant points ; and initializing the view with an animated `` lazy susan '' motion .
both modes exploit webgl to provide smooth , fluid interaction , which encourages exploration of the underlying space , supporting both task 1 and task 2 .
to support task 1 , clicking on a point causes the right pane to show an explicit textual list of nearest neighbors , along with distances to the current point .
the nearest - neighbor points themselves are highlighted on the projection .
users sometimes wish to focus on a subset of points  an interesting cluster , or perhaps the set of nearest neighbors of a given point .
zooming into the cluster gives some information , but it is sometimes more helpful to restrict the view to a subset of points and perform t - sne or pca only on those points .
to do so , the user can select points in multiple ways : after clicking on a point , its nearest neighbors are selected ; after a search , the points matching the query are selected ; right - clicking and dragging defines a selection sphere . after selecting a set of points ,
the user can isolate those points for further analysis on their own with the `` isolate points '' button in the inspector pane on the right hand side .    in 3d mode , labels can appear as `` billboards ''  flat images that always face the user . fig .
[ 3d - labels ] depicts this view .
when there is an image associated with a data point , we can simply use the actual image as the `` label '' .
a nice example is an embedding of mnist images shown in fig .
[ mnist - colorized ] where each image has a background color according to its true label .
[ [ collaborative - features ] ] collaborative features + + + + + + + + + + + + + + + + + + + + + +    early in the development process we saw that users of the embedding projector wanted to share specific views of their data .
indeed , previous work in visualization has shown the benefits of allowing users to share the state of a visualization [ 7 ] .    to allow easy collaboration
, the embedding projector lets users save the current state ( including computed coordinates of t - sne embeddings ) as a small file . the projector can then be pointed to a set of one or more of these files , producing the panel seen in the bottom right of fig .
[ fig - main ] .
other users can then walk through a sequence of bookmarks .
the embedding projector is a new visualization tool that helps users interpret machine learning models that rely on embeddings . unlike other high - dimensional visualization systems ,
it is customized for the kinds of tasks faced by machine learning developers and researchers : exploring local neighborhoods for individual points , analyzing global geometry , and investigating semantically meaningful vectors in embedding space .
the projector is part of the tensorflow platform , and seamlessly allows analysis and interpretation of tensorflow models .
there are a number of directions for future work on the visualization .
for example , when developing multiple versions of a model , or inspecting how a model changes over time , it could be useful to visually compare two embeddings .
doing so would require nontrivial additions to the current visualizations .
a second direction for future research is to make it easier for users to discover meaningful directions in the data .
while the current interface makes it easy to explore various hypotheses , there may be ways for the computer to generate and test hypotheses automatically .
thanks to shan carter for invaluable design contributions , and to our colleagues who provided thoughtful feedback .
[ 1 ] m.  abadi , a.  agarwal , p.  barham , e.  brevdo , z.  chen , c.  citro , g.  s. corrado , a.  davis , j.  dean , m.  devin , et  al .
tensorflow : large - scale machine learning on heterogeneous distributed systems . , 2016 .
[ 2 ] c.  ahlberg and b.  shneiderman .
visual information seeking : tight coupling of dynamic query filters with starfield displays . in _ proceedings of the sigchi conference on human factors in computing systems _ , pages 313317 .
acm , 1994 .
embeddings are ubiquitous in machine learning , appearing in recommender systems , nlp , and many other applications . 
 researchers and developers often need to explore the properties of a specific embedding , and one way to analyze embeddings is to visualize them . 
 we present the embedding projector , a tool for interactive visualization and interpretation of embeddings .