A Penalized Likelihood Method for Classification With Matrix-Valued Predictors

We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product decomposition. Our penalties encourage pairs of response category mean ma...

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Bibliographic Details
Published in:Journal of computational and graphical statistics Vol. 28; no. 1; pp. 11 - 22
Main Authors: Molstad, Aaron J., Rothman, Adam J.
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis 02.01.2019
American Statistical Association, the Institute of Mathematical Statistics, and the Interface Foundation of North America
Taylor & Francis Ltd
Subjects:
Algorithms
Alternating minimization algorithm
Classification
Discriminant analysis
Estimators
Mathematical models
Matrix methods
Optimization
Optimization with Penalization
Penalized likelihood
ISSN:1061-8600, 1537-2715
Online Access:Get full text
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Summary:We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product decomposition. Our penalties encourage pairs of response category mean matrix estimators to have equal entries and also encourage zeros in the precision matrix estimator. To compute our estimators, we use a blockwise coordinate descent algorithm. To update the optimization variables corresponding to response category mean matrices, we use an alternating minimization algorithm that takes advantage of the Kronecker structure of the precision matrix. We show that our method can outperform relevant competitors in classification, even when our modeling assumptions are violated. We analyze three real datasets to demonstrate our method's applicability. Supplementary materials, including an R package implementing our method, are available online.
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ISSN:1061-8600
1537-2715
DOI:10.1080/10618600.2018.1476249