Regularized spectral learning
Spectral clustering is a technique for finding groups in data consisting of similarities Sij between pairs of points. We approach the problem of learning the similarity as a function of other observed features, in order to optimize spectral clustering results on future data. This paper formulates a new objective for learning in spectral clustering, that balances a clustering accuracy term, the gap, and a stability term, the eigengap with the later in the role of a regularizer. We derive an algorithm to optimize this objective, and semiautomatic methods to chose the optimal regularization. Preliminary experiments confirm the validity of the approach. We start by introducing notation and some basic facts in section 2, we define the learning problem in section 3 and introduce the new objective in 4. Sections 5, 6 present respectively a gradient algorithm for optimizing the criterion and a method for selecting the anlount of regularization. Experimental results are in section 7 and 8 concludes the paper. 2 Spectral clustering notation and background In spectral clustering, the data is a set of similarities Sij, satisfying Sij = Sji '2.: 0, between pairs of points i, j in a set V, IVI = n, The matrix S [Sij]i,jEV is called the similarity matrix. We denote by D i ;;:::: Vol {i} (1)