Learning Data Manifolds with a Cutting Plane Method

Author:

Chung SueYeon,Cohen Uri,Sompolinsky Haim1,Lee Daniel D.

Affiliation:

1. Center for Brain Science, Harvard University, Cambridge, MA 02138, U.S.A., and Edmond and Lily Safra Center for Brain Sciences, Hebrew University of Jerusalem, Jerusalem 9190401, Israel

Abstract

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, [Formula: see text], 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 [Formula: see text] are demonstrated in high-dimensional simulations and on image manifolds generated from the ImageNet data set. Our results indicate that [Formula: see text] is able to rapidly learn good classifiers and shows superior generalization performance compared with conventional maximum margin methods using data augmentation methods.

Publisher

MIT Press - Journals

Subject

Cognitive Neuroscience,Arts and Humanities (miscellaneous)

Cited by 8 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Representations and generalization in artificial and brain neural networks;Proceedings of the National Academy of Sciences;2024-06-24

2. Linear Classification of Neural Manifolds with Correlated Variability;Physical Review Letters;2023-07-12

3. Soft-margin classification of object manifolds;Physical Review E;2022-08-24

4. Attributed Graph Force Learning;IEEE Transactions on Neural Networks and Learning Systems;2022

5. Modeling the Influence of Data Structure on Learning in Neural Networks: The Hidden Manifold Model;Physical Review X;2020-12-03

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