Learning data manifolds with a cutting plane method

Sue Yeon Chung, Uri Cohen, Haim Sompolinsky, Daniel D. Lee

Research output: Contribution to journalArticlepeer-review


We consider the problem of classifying data manifolds where each manifold represents invariances that are parameterized by continuous degrees of freedom. Conventional data augmentation methods rely on sampling large numbers of training examples from these manifolds. Instead, we propose an iterative algorithm, MCP, based on a cutting plane approach that efficiently solves a quadratic semi-infinite programming problem to find the maximum margin solution. We provide a proof of convergence as well as a polynomial bound on the number of iterations required for a desired tolerance in the objective function. The efficiency and performance of MCP are demonstrated in high-dimensional simulations and on image manifolds generated from the ImageNet data set. Our results indicate that MCP is able to rapidly learn good classifiers and shows superior generalization performance compared with conventional maximum margin methods using data augmentation methods.

Original languageEnglish (US)
Pages (from-to)2593-2615
Number of pages23
JournalNeural computation
Issue number10
StatePublished - Oct 1 2018

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Cognitive Neuroscience


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