A Computable Plug-In Estimator of Minimum Volume Sets for Novelty Detection

Authors:
Chiwoo Park;Jianhua Z. Huang;Yu Ding
Affiliations:
Department of Industrial and Systems Engineering, Texas A&M University, College Station, Texas 77843;Department of Statistics, Texas A&M University, College Station, Texas 77843;Department of Industrial and Systems Engineering, Texas A&M University, College Station, Texas 77843
Venue:
Operations Research
Year:
2010

Citing 7
Cited 0

Support vector domain description

Pattern Recognition Letters - Special issue on pattern recognition in practice VI
Novelty detection: a review—part 1: statistical approaches

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Novelty detection: a review—part 2: neural network based approaches

Signal Processing
Estimating the Support of a High-Dimensional Distribution

Neural Computation
Kernel estimation of density level sets

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Kernel PCA for novelty detection

Pattern Recognition
Learning Minimum Volume Sets

The Journal of Machine Learning Research

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Abstract

A minimum volume set of a probability density is a region of minimum size among the regions covering a given probability mass of the density. Effective methods for finding the minimum volume sets are very useful for detecting failures or anomalies in commercial and security applications---a problem known as novelty detection. One theoretical approach of estimating the minimum volume set is to use a density level set where a kernel density estimator is plugged into the optimization problem that yields the appropriate level. Such a plug-in estimator is not of practical use because solving the corresponding minimization problem is usually intractable. A modified plug-in estimator was proposed by Hyndman in 1996 to overcome the computation difficulty of the theoretical approach but is not well studied in the literature. In this paper, we provide theoretical support to this estimator by showing its asymptotic consistency. We also show that this estimator is very competitive to other existing novelty detection methods through an extensive empirical study.