Overcoming the curse of dimensionality with Laplacian regularization in semi-supervised learning
It addresses a key bottleneck in semi-supervised learning for practitioners dealing with high-dimensional data, offering a more robust approach to leverage unlabeled examples.
The paper tackles the curse of dimensionality in Laplacian regularization for semi-supervised learning by providing a statistical analysis and introducing spectral filtering methods implemented via kernel techniques, with computational guidelines for large-scale data.
As annotations of data can be scarce in large-scale practical problems, leveraging unlabelled examples is one of the most important aspects of machine learning. This is the aim of semi-supervised learning. To benefit from the access to unlabelled data, it is natural to diffuse smoothly knowledge of labelled data to unlabelled one. This induces to the use of Laplacian regularization. Yet, current implementations of Laplacian regularization suffer from several drawbacks, notably the well-known curse of dimensionality. In this paper, we provide a statistical analysis to overcome those issues, and unveil a large body of spectral filtering methods that exhibit desirable behaviors. They are implemented through (reproducing) kernel methods, for which we provide realistic computational guidelines in order to make our method usable with large amounts of data.