Combining graph Laplacians for semi--supervised learning
Andreas Argyriou, Mark Herbster and Massimiliano Pontil
In: NIPS 2005, December, 2005, Vancouver, CA.

## Abstract

We build on recent methods for graph regularization in semi-supervised learning. A foundational problem for these methods is the construction of the underlying graph. We propose to use a method which can optimally combine a number of differently constructed graphs. For each of these graphs we associate a basic graph kernel. We then compute an optimal {\em combined} kernel. This kernel solves an extended regularization problem which requires a joint minimization over both the data and the set of graph kernels. We present encouraging results on a variety of OCR tasks where the optimal combined kernel is computed from graphs constructed with a variety of distance functions and the `$k$' in nearest neighbors.