The second MITACS seminar of the fall will be on Thursday, October 16th, 15:00 at UdeM.
Title: Visualizing high-dimensional data using t-SNE Speaker: Geoffrey Hinton Date: Thursday Oct 16th, 2008, 15:00 Place: Room 3195 (pav. André-Aisenstadt)
Abstract: Over the last decade, many new methods have been developed for visualizing high-dimensional data by giving each data-point a location in a two-dimensional map. The goal is to represent the separations of pairs of data-points by the separations of their corresponding map-points, with an emphasis on representing the small separations accurately. I will describe a new method, called t-SNE, that is based on two ideas. The first idea is to convert the set of pairwise distances between data-points into a set of probabilities of selecting pairs of data-points. The selection probability of a pair of points is proportional to a Gaussian function of their separation. If the distances between map-points are converted into pairwise probabilities in the same way, any given arrangement of map-points can be evaluated by measuring the divergence between the probability distributions obtained from the data-points and the map-points. A good arrangement of map-points is then found by performing gradient descent in this divergence.
Unfortunately, if the probabilities of pairs of map-points are computed using a Gaussian function of their separation, the difference between the distributions of pairwise distances in high-dimensional and low-dimensional spaces causes the map-points to be crowded together in the center of the map. This problem can be largely overcome by using a heavy-tailed t-distribution when computing the selection probabilities of pairs of map-points. This leads to maps that look much better than those produced by other recent methods. In particular, t-SNE is very good at preserving clusters in the data at many different scales simultaneously.
The talk describes joint work with Laurens van der Maaten that will appear in the Journal of Machine Learning Research.
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Geoffrey Hinton's talk on t-SNE will finally be at 15:30, and in room AA-6214, because it is now part of DIRO's seminars http://www.iro.umontreal.ca/~csuros/ColloquesDIRO/.
Here are the updated informations:
Title: Visualizing high-dimensional data using t-SNE Speaker: Geoffrey Hinton Date: Thursday Oct 16th, 2008, 15:30 Place: Room 6214 (pav. André-Aisenstadt)
Abstract: Over the last decade, many new methods have been developed for visualizing high-dimensional data by giving each data-point a location in a two-dimensional map. The goal is to represent the separations of pairs of data-points by the separations of their corresponding map-points, with an emphasis on representing the small separations accurately. I will describe a new method, called t-SNE, that is based on two ideas. The first idea is to convert the set of pairwise distances between data-points into a set of probabilities of selecting pairs of data-points. The selection probability of a pair of points is proportional to a Gaussian function of their separation. If the distances between map-points are converted into pairwise probabilities in the same way, any given arrangement of map-points can be evaluated by measuring the divergence between the probability distributions obtained from the data-points and the map-points. A good arrangement of map-points is then found by performing gradient descent in this divergence.
Unfortunately, if the probabilities of pairs of map-points are computed using a Gaussian function of their separation, the difference between the distributions of pairwise distances in high-dimensional and low-dimensional spaces causes the map-points to be crowded together in the center of the map. This problem can be largely overcome by using a heavy-tailed t-distribution when computing the selection probabilities of pairs of map-points. This leads to maps that look much better than those produced by other recent methods. In particular, t-SNE is very good at preserving clusters in the data at many different scales simultaneously.
The talk describes joint work with Laurens van der Maaten that will appear in the Journal of Machine Learning Research.
lisa_seminaires@iro.umontreal.ca
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Pascal Lamblin