On semi-supervised learning and sparsity

  • Authors:
  • Alexander Balinsky;Helen Balinsky

  • Affiliations:
  • Cardiff School of Mathematics, Cardiff University, Cardiff, United Kingdom;Hewlett Packard Labs, Bristol, United Kingdom

  • Venue:
  • SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
  • Year:
  • 2009

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Abstract

In this article we establish a connection between semi-supervised learning and compressive sampling. We show that sparsity and compressibility of the learning function can be obtained from heavy-tailed distributions of filter responses or coefficients in spectral decompositions. In many cases the NP-hard problems of finding sparsest solutions can be replaced by l1-problems from convex optimisation theory, which provide effective tools for semi-supervised learning. We present several conjectures and examples.