The Geometric Basis of Semi-Supervised Learning
Sindhwani Vikas, Belkin Misha, Partha Niyogi · The MIT Press eBooks · 2006
This chapter presents an algorithmic framework for semi-supervised inference based on geometric properties of probability distributions. This approach brings together Laplacian-based spectral techniques, regularization with kernel methods, and algorithms for manifold learning. This framework provides a natural semi-supervised extension for kernel methods and resolves the problem of out-of-sample inference in graph-based transduction. An interpretation is discussed here in terms of a family of globally defined data-dependent kernels and unsupervised learning within the same framework is also addressed. The algorithms in this chapter effectively exploit both manifold and cluster assumptions to demonstrate state-of-the-art performance on various classification tasks. This chapter also reviews other recent work on out-of-sample extension for transductive graph-based methods.