Manifold Tangent Classifier

author: Yann Dauphin, Université de Montréal
published: Jan. 25, 2012,   recorded: December 2011,   views: 9133


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We combine three important ideas present in previous work for building classifiers: the semi-supervised hypothesis (the input distribution contains information about the classifier), the unsupervised manifold hypothesis (data density concentrates near low-dimensional manifolds), and the manifold hypothesis for classification (different classes correspond to disjoint manifolds separated by low density). We exploit a new algorithm for capturing manifold structure (high-order contractive autoencoders) and we show how it builds a topological atlas of charts, each chart being characterized by the principal singular vectors of the Jacobian of a representation mapping. This representation learning algorithm can be stacked to yield a deep architecture, and we combine it with a domain knowledge-free version of the TangentProp algorithm to encourage the classifier to be insensitive to local directions changes along the manifold. Record-breaking results are obtained and we find that the learned tangent directions are very meaningful.

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