Visualizing NIPS Cooperations using Multiple Maps t-SNE

Our demonstration shows visualizations of NIPS co-authorships that were constructed by the multiple maps version of $t$-SNE. We gathered a dataset of the co-authorships in all NIPS papers (volume 1-20). The co-authorships are represented in a square matrix in which each row (and column) corresponds to a single author. The element ($i$, $j$) in the matrix represents the number of papers that author $i$ and author $j$ wrote together. After normalization, this matrix may form the input into a multidimensional scaling technique, such as $t$-SNE (L.J.P. van der Maaten and G.E. Hinton. {\em Visualizing Data using $t$-SNE}. Journal of Machine Learning Research, 2008), to construct a two-dimensional map that visualizes the pairwise similarities between the authors. Unfortunately, it is impossible for multidimensional scaling techniques to construct an appropriate visualization of the similarity data, because of the following fundamental problem: if author A wrote papers together with author B and author B wrote papers together with author C, but author C never wrote papers with author A, the similarity relations cannot be modeled in a two-dimensional metric map due to the triangle inequality: in the map, author A is then modeled close to author B, and author B is modeled close to author C, as a result of which A is close to C as well, which is wrong. In order to alleviate this problem, we developed a multiple maps version of $t$-SNE that creates a collection of multiple maps (based on ideas proposed in J.A. Cook, I. Sutskever, A. Mnih, and G.E. Hinton. {\em Visualizing similarity data with a mixture of maps}. Proceedings of AI*STATS-07, 2007). Each author has a copy in each of the maps, and each copy is weighted by a mixing proportion (the mixing proportions for a single author over all maps sum up to 1). The multiple maps version of $t$-SNE can perfectly model the example above, and as a result, it is very good at visualizing NIPS co-authorship data. We ran the multiple maps version of $t$-SNE on the NIPS dataset, and constructed a visualization tool that shows the resulting maps in a visually appealing way. The visualization clearly shows the research clusters within the NIPS community, and reveals cooperations between these clusters (or people that have moved from one research cluster to another during their career). The visualization tool allows the user to quickly switch between maps, zoom and scroll in maps, search for authors, find out if authors are modeled in other maps as well, lay over a cooperation graph over the maps, etc.