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Learning the 2-D Topology of Images
Nicolas Le Roux · Yoshua Bengio · Pascal Lamblin · Marc Joliveau · Balázs Kégl

Wed Dec 05 10:30 AM -- 10:40 AM (PST) @

We study the following question: is the two-dimensional structure of images a very strong prior or is it something that can be learned with a few examples of natural images? If someone gave us a learning task involving images for which the two-dimensional topology of pixels was not known, could we discover it automatically and exploit it? For example suppose that the pixels had been permuted in a fixed but unknown way, could we recover the relative two-dimensional location of pixels on images? The surprising result presented here is that not only the answer is yes but that about as few as a thousand images are enough to approximately recover the relative locations of about a thousand pixels. This is achieved using a manifold learning algorithm applied to pixels associated with a measure of distributional similarity between pixel intensities. We compare different topology-extraction approaches and show how having the two-dimensional topology can be exploited.

Author Information

Nicolas Le Roux (Microsoft Research)
Yoshua Bengio (Mila / U. Montreal)

Yoshua Bengio (PhD'1991 in Computer Science, McGill University). After two post-doctoral years, one at MIT with Michael Jordan and one at AT&T Bell Laboratories with Yann LeCun, he became professor at the department of computer science and operations research at Université de Montréal. Author of two books (a third is in preparation) and more than 200 publications, he is among the most cited Canadian computer scientists and is or has been associate editor of the top journals in machine learning and neural networks. Since '2000 he holds a Canada Research Chair in Statistical Learning Algorithms, since '2006 an NSERC Chair, since '2005 his is a Senior Fellow of the Canadian Institute for Advanced Research and since 2014 he co-directs its program focused on deep learning. He is on the board of the NIPS foundation and has been program chair and general chair for NIPS. He has co-organized the Learning Workshop for 14 years and co-created the International Conference on Learning Representations. His interests are centered around a quest for AI through machine learning, and include fundamental questions on deep learning, representation learning, the geometry of generalization in high-dimensional spaces, manifold learning and biologically inspired learning algorithms.

Pascal Lamblin (Google Research – Brain Team)
Marc Joliveau (Ecole Centrale Paris)
Balázs Kégl (Huawei France)

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