# Estimating the Support of a High-Dimensional Distribution

Schölkopf, B., Platt, J.C., Shawe-Taylor, J.S., Smola, A.J. and Williamson, R.C.
(2001)
Estimating the Support of a High-Dimensional Distribution.
*Neural Computation*, 13, (7), 1443-1471.

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## Description/Abstract

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.

Item Type: | Article |
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ISSNs: | 0899-7667 |

Divisions: | Faculty of Physical Sciences and Engineering > Electronics and Computer Science |

ePrint ID: | 259789 |

Date Deposited: | 17 Aug 2004 |

Last Modified: | 27 Mar 2014 20:02 |

Further Information: | Google Scholar |

ISI Citation Count: | 663 |

URI: | http://eprints.soton.ac.uk/id/eprint/259789 |

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