Cellwise robust regularized discriminant analysis

Stephanie Aerts*, Ines Wilms

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Web of Science)

Abstract

Quadratic and linear discriminant analysis (qda and lda) are the most often applied classification rules under normality. In qda, a separate covariance matrix is estimated for each group. If there are more variables than observations in the groups, the usual estimates are singular and cannot be used anymore. Assuming homoscedasticity, as in lda, reduces the number of parameters to estimate. This rather strong assumption is however rarely verified in practice. Regularized discriminant techniques that are computable in high dimension and cover the path between the 2 extremes qda and lda have been proposed in the literature. However, these procedures rely on sample covariance matrices. As such, they become inappropriate in the presence of cellwise outliers, a type of outliers that is very likely to occur in high-dimensional datasets. In this paper, we propose cellwise robust counterparts of these regularized discriminant techniques by inserting cellwise robust covariance matrices. Our methodology results in a family of discriminant methods that (1) are robust against outlying cells, (2) cover the gap between lda and qda, and (3) are computable in high dimension. The good performance of the new methods is illustrated through simulated and real data examples. As a by-product, visual tools are provided for the detection of outliers.
Original languageEnglish
Pages (from-to)436-447
Number of pages12
JournalStatistical Analysis and Data Mining
Volume10
Issue number6
DOIs
Publication statusPublished - Dec 2017
Externally publishedYes

Keywords

  • cellwise robust precision matrix
  • classification
  • discriminant analysis
  • penalized estimation
  • INVERSE COVARIANCE ESTIMATION
  • GRAPHICAL LASSO
  • MULTIVARIATE LOCATION
  • SCATTER

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