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Shrinkage‐based Diagonal Discriminant Analysis and Its Applications in High‐Dimensional Data
Author(s) -
Pang Herbert,
Tong Tiejun,
Zhao Hongyu
Publication year - 2009
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2009.01200.x
Subject(s) - linear discriminant analysis , diagonal , shrinkage , discriminant , regularization (linguistics) , pattern recognition (psychology) , computer science , artificial intelligence , shrinkage estimator , clustering high dimensional data , mathematics , statistics , machine learning , cluster analysis , mean squared error , minimum variance unbiased estimator , bias of an estimator , geometry
Summary High‐dimensional data such as microarrays have brought us new statistical challenges. For example, using a large number of genes to classify samples based on a small number of microarrays remains a difficult problem. Diagonal discriminant analysis, support vector machines, and k ‐nearest neighbor have been suggested as among the best methods for small sample size situations, but none was found to be superior to others. In this article, we propose an improved diagonal discriminant approach through shrinkage and regularization of the variances. The performance of our new approach along with the existing methods is studied through simulations and applications to real data. These studies show that the proposed shrinkage‐based and regularization diagonal discriminant methods have lower misclassification rates than existing methods in many cases.