Overcoming the curse of dimensionality with Laplacian regularization in semi-supervised learning

As annotations of data can be scarce in large-scale practical problems,\nleveraging unlabelled examples is one of the most important aspects of machine\nlearning. This is the aim of semi-supervised learning. To benefit from the\naccess to unlabelled data, it is natural to diffuse smoothly knowledge of\nlabelled data to unlabelled one. This induces to the use of Laplacian\nregularization. Yet, current implementations of Laplacian regularization suffer\nfrom several drawbacks, notably the well-known curse of dimensionality. In this\npaper, we provide a statistical analysis to overcome those issues, and unveil a\nlarge body of spectral filtering methods that exhibit desirable behaviors. They\nare implemented through (reproducing) kernel methods, for which we provide\nrealistic computational guidelines in order to make our method usable with\nlarge amounts of data.\n