Bernhard Schölkopf, Machine Learning and Perception Group, Microsoft Research Cambridge
John Platt, CCSP Group, Microsoft Research
John Shawe-Taylor, Department of Computer Science, Royal Holloway, University of London
Alex J. Smola, RSISE, Australian National University
Robert C. Williamson, RSISE, Australian National University
Neural Computation, v 13, no 7, pp. 1443-1472, (2001).
Suppose you are given some data set drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S equals some a priori specified value between 0 and 1.
We propose a method to approach this problem by trying to estimate a function f that is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also provide a theoretical analysis of the statistical performance of our algorithm.
The algorithm is a natural extension of the support vector algorithm to the case of unlabeled data.
The journal paper is only available on-line with a subscription to Neural Computation.
An earlier version of the paper is available as Microsoft Research Technical Report MSR-TR-99-87, (1999).
A conference version was Support Vector Method for Novelty Detection by B. Schölkopf, R. Williamson, A.J. Smola, J. Shawe-Taylor, J.C. Platt, Advances in Neural Information Processing Systems 12, pp. 582-588, (2000).