The Manifold Tangent Classifier

We combine three important ideas present in previous work for building classifiers: thesemi-supervised hypothesis (the input distribution contains information about the classifier), the unsupervised manifold hypothesis (data density concentrates nearlow-dimensional manifolds), and the manifold hypothesis for classification (differentclasses correspond to disjoint manifolds separated by low density). We exploit a novel algorithm for capturing manifold structure (high-order contractive auto-encoders) 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 classification results are obtained.