Estimating the Support of a High-Dimensional Distribution

Article Properties
  • Language
    English
  • Publication Date
    2001/07/01
  • Indian UGC (Journal)
  • Refrences
    17
  • Citations
    1,966
  • Bernhard Schölkopf Microsoft Research Ltd, Cambridge CB2 3NH, U.K.
  • John C. Platt Microsoft Research, Redmond, WA 98052, U.S.A
  • John Shawe-Taylor Royal Holloway, University of London, Egham, Surrey TW20 OEX, U.K.
  • Alex J. Smola Department of Engineering, Australian National University, Canberra 0200, Australia
  • Robert C. Williamson Department of Engineering, Australian National University, Canberra 0200, Australia
Abstract
Cite
Schölkopf, Bernhard, et al. “Estimating the Support of a High-Dimensional Distribution”. Neural Computation, vol. 13, no. 7, 2001, pp. 1443-71, https://doi.org/10.1162/089976601750264965.
Schölkopf, B., Platt, J. C., Shawe-Taylor, J., Smola, A. J., & Williamson, R. C. (2001). Estimating the Support of a High-Dimensional Distribution. Neural Computation, 13(7), 1443-1471. https://doi.org/10.1162/089976601750264965
Schölkopf B, Platt JC, Shawe-Taylor J, Smola AJ, Williamson RC. Estimating the Support of a High-Dimensional Distribution. Neural Computation. 2001;13(7):1443-71.
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Description

How can we efficiently estimate the support of a high-dimensional probability distribution? This research introduces an algorithm for estimating a subset *S* of the input space that captures most of the probability mass of an underlying distribution *P*. The method estimates a function *f* that is positive on *S* and negative on the complement, using a kernel expansion based on a small subset of training data. A regularization technique controls the length of the weight vector in an associated feature space. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data. The expansion coefficients are determined by solving a quadratic programming problem, implemented via sequential optimization over pairs of input patterns. The authors provide a theoretical analysis of the algorithm’s statistical performance. Described as a natural extension of the support vector algorithm to unlabeled data, this approach addresses the challenge of dimensionality reduction and density estimation. This study provides a valuable tool for machine learning, pattern recognition, and data analysis, where understanding data support is crucial.

Being published in Neural Computation, this paper fits into the journal's focus on machine learning algorithms and neural network models. The journal explores methods of knowledge. This article directly addresses a problem related to machine learning and statistical performance. The references and citations likely connect it to other works in support vector machines and density estimation published in related journals.

Refrences
Citations
Citations Analysis
The first research to cite this article was titled 10.1162/15324430260185565 and was published in 2000. The most recent citation comes from a 2024 study titled 10.1162/15324430260185565 . This article reached its peak citation in 2021 , with 226 citations.It has been cited in 765 different journals, 18% of which are open access. Among related journals, the IEEE Access cited this research the most, with 60 citations. The chart below illustrates the annual citation trends for this article.
Citations used this article by year