University of Washington - Department of Statistics
Spectral segmentation is a technique used to group data based on pairwise similarities. A similarity matrix is used as input into a spectral clustering algorithm and a clustering over the data is output. The clustering criterion is such that similar points are put in the same cluster and dissimilar points are put in different clusters. Generally, this similarity matrix is assumed known, while in reality this matrix is usually constructed by hand, a very time consuming process. We propose a method which learns the similarity as a function of observed pairwise features; this can also be viewed as a variable weighting scheme. We propose an objective for learning involving cluster quality, the gap of a clustering, as well as a stability term, the eigengap. We first present this objective in the supervised case and then extend it to the unsupervised case by using an iterative algorithm.