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A Probabilistic Approach to Data Visualization
Geoffrey E Hinton

Thu Dec 09 03:00 PM -- 03:30 PM (PST) @

Dimensionality reduction methods allow us to visualize the structure of large, high-dimensional datasets by giving each data-point a location in a two-dimensional map. Sam Roweis was involved in the development of several different methods for producing maps that preserve local similarity by displaying very similar data-points at nearby locations in the map without worrying too much about the map distances between dissimilar data-points. One of these methods, called Stochastic Neighbor Embedding, converts the problem of finding a good map into the problem of matching two probability distributions. It uses the density under a high-dimensional Gaussian centered at each data-point to determine the probability of picking each of the other data-points as a neighbor. It then uses exactly the same method to determine neighbor probabilities using the two-dimensional locations of the corresponding map points. The aim is to move the map points so that the neighbor probabilities computed in the high-dimensional data-space are well-modeled by the neighbor probabilities computed in the low-dimensional map. This leads to very nice maps for a variety of datasets. I will describe some further developments of this method that lead to even better maps.

Author Information

Geoffrey E Hinton (Google & University of Toronto)

Geoffrey Hinton received his PhD in Artificial Intelligence from Edinburgh in 1978 and spent five years as a faculty member at Carnegie-Mellon where he pioneered back-propagation, Boltzmann machines and distributed representations of words. In 1987 he became a fellow of the Canadian Institute for Advanced Research and moved to the University of Toronto. In 1998 he founded the Gatsby Computational Neuroscience Unit at University College London, returning to the University of Toronto in 2001. His group at the University of Toronto then used deep learning to change the way speech recognition and object recognition are done. He currently splits his time between the University of Toronto and Google. In 2010 he received the NSERC Herzberg Gold Medal, Canada's top award in Science and Engineering.

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