Estimating the Support of a High-Dimensional Distribution (1999) [251 citations — 23 self]
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author = {Bernhard Schölkopf and John C. Platt and John Shawe-taylor and Alex J. Smola and Robert C. Williamson},
title = {Estimating the Support of a High-Dimensional Distribution},
year = {1999}
}
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Abstract:
Suppose you are given some dataset 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 is bounded by some a priori specified between 0 and 1. We propose a method to approach this problem by trying to estimate a function f which 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 preliminary theoretical analysis of the statistical performance of our algorithm. The algorithm is a natural extension of the support vector algorithm to the case of unlabelled d...
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