Optimal Pooling of Covariance Matrix Estimates Across Multiple Classes

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Researchers

Research units

Abstract

The paper considers the problem of estimating the covariance matrices of multiple classes in a low sample support condition, where the data dimensionality is comparable to, or larger than, the sample sizes of the available data sets. In such conditions' a common approach is to shrink the class sample covariance matrices (SCMs) towards the pooled SCM. The success of this approach hinges upon the ability to choose the optimal regularization parameter. Typically, a common regularization level is shared among the classes and determined via a procedure based on cross-validation. We use class-specific regularization levels since this enables the derivation of the optimal regularization parameter for each class in terms of the minimum mean squared error (MMSE). The optimal parameters depend on the true unknown class population covariances. Consistent estimators of the parameters can, however, be easily constructed under the assumption that the class populations follow (unspecified) elliptically symmetric distributions. We demonstrate the performance of the proposed method via a simulation study as well as via an application to discriminant analysis using both synthetic and real data sets.

Details

Original languageEnglish
Title of host publication2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Proceedings
Publication statusPublished - 10 Sep 2018
MoE publication typeA4 Article in a conference publication
EventIEEE International Conference on Acoustics, Speech, and Signal Processing - Calgary, Canada
Duration: 15 Apr 201820 Apr 2018
https://2018.ieeeicassp.org/

Publication series

NameProceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing
ISSN (Electronic)2379-190X

Conference

ConferenceIEEE International Conference on Acoustics, Speech, and Signal Processing
Abbreviated titleICASSP
CountryCanada
CityCalgary
Period15/04/201820/04/2018
Internet address

    Research areas

  • Classification, Covariance matrix estimation, Elliptical distribution, Regularization

Download statistics

No data available

ID: 28748860