27 November 1999; revised 18 September 2000 | Bernhard Schölkopf, John C. Platt, John Shawe-Taylor, Alex J. Smola, Robert C. Williamson
This paper proposes a method to estimate a "simple" subset of input space, such that the probability that a test point drawn from the underlying distribution lies outside this subset is specified. The method involves estimating a function \( f \) that is positive on the subset and negative elsewhere, using a kernel expansion in terms of a small subset of the training data. The function is regularized by controlling the length of the weight vector in an associated feature space, and the expansion coefficients are found by solving a quadratic programming problem through sequential optimization over pairs of input patterns. The paper also provides a theoretical analysis of the statistical performance of the algorithm, including a generalization error bound. The algorithm is an extension of the support vector algorithm to the case of unlabelled data, and it is shown to have tractable computational complexity even in high-dimensional cases. The paper includes experimental results on artificial and real-world data, demonstrating the effectiveness of the method in novelty detection and outlier identification.This paper proposes a method to estimate a "simple" subset of input space, such that the probability that a test point drawn from the underlying distribution lies outside this subset is specified. The method involves estimating a function \( f \) that is positive on the subset and negative elsewhere, using a kernel expansion in terms of a small subset of the training data. The function is regularized by controlling the length of the weight vector in an associated feature space, and the expansion coefficients are found by solving a quadratic programming problem through sequential optimization over pairs of input patterns. The paper also provides a theoretical analysis of the statistical performance of the algorithm, including a generalization error bound. The algorithm is an extension of the support vector algorithm to the case of unlabelled data, and it is shown to have tractable computational complexity even in high-dimensional cases. The paper includes experimental results on artificial and real-world data, demonstrating the effectiveness of the method in novelty detection and outlier identification.