Influence functions for a linear subspace method

Kuniyoshi Hayashi

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A linear subspace method, which is one of discriminant methods, was proposed as a pattern recognition method and was studied. Because the method and its extensions do not encounter the situation of singular covariance matrix, we need not consider extensions such as generalized ridge discrimination, even when treating a high dimensional and sparse dataset. In addition, classifiers based on a multi-class discrimination method can function faster because of the simple decision procedure. Therefore, they have been widely used for face and speech recognition. However, it seems that sufficient studies have not been conducted about the statistical assessment of training data performance for classifier in terms of prediction accuracy. In statistics, influence functions for statistical discriminant analysis were derived and the assessments for analysis result were performed. These studies indicate that influence functions are useful for detecting large influential observations for analysis results by using discrimination methods and they contribute to enhancing the performance of a target classifier. In this paper, we propose the statistical diagnostics of a classifier on the basis of an influence function by using the linear subspace method. We first propose the discriminant score for the linear subspace method. Next, we derive the sample and empirical influence functions for the average of the discriminant scores to detect large influential observations for the misclassification rate. Finally, through a simulation study and a real data analysis, we detect the outliers in the training dataset using the derived influence function and develop a highly sophisticated classifier in the linear subspace method.

Original languageEnglish
Pages (from-to)2241-2254
Number of pages14
JournalPattern Recognition
Volume47
Issue number6
DOIs
Publication statusPublished - Jun 2014

Fingerprint

Classifiers
Discriminant analysis
Face recognition
Covariance matrix
Speech recognition
Pattern recognition
Statistics

Keywords

  • CLAFIC
  • Cross-validation
  • Perturbation analysis
  • Single-case diagnostics

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence
  • Computer Vision and Pattern Recognition
  • Signal Processing

Cite this

Influence functions for a linear subspace method. / Hayashi, Kuniyoshi.

In: Pattern Recognition, Vol. 47, No. 6, 06.2014, p. 2241-2254.

Research output: Contribution to journalArticle

Hayashi, Kuniyoshi. / Influence functions for a linear subspace method. In: Pattern Recognition. 2014 ; Vol. 47, No. 6. pp. 2241-2254.
@article{4d2a777820804671841811b50248d602,
title = "Influence functions for a linear subspace method",
abstract = "A linear subspace method, which is one of discriminant methods, was proposed as a pattern recognition method and was studied. Because the method and its extensions do not encounter the situation of singular covariance matrix, we need not consider extensions such as generalized ridge discrimination, even when treating a high dimensional and sparse dataset. In addition, classifiers based on a multi-class discrimination method can function faster because of the simple decision procedure. Therefore, they have been widely used for face and speech recognition. However, it seems that sufficient studies have not been conducted about the statistical assessment of training data performance for classifier in terms of prediction accuracy. In statistics, influence functions for statistical discriminant analysis were derived and the assessments for analysis result were performed. These studies indicate that influence functions are useful for detecting large influential observations for analysis results by using discrimination methods and they contribute to enhancing the performance of a target classifier. In this paper, we propose the statistical diagnostics of a classifier on the basis of an influence function by using the linear subspace method. We first propose the discriminant score for the linear subspace method. Next, we derive the sample and empirical influence functions for the average of the discriminant scores to detect large influential observations for the misclassification rate. Finally, through a simulation study and a real data analysis, we detect the outliers in the training dataset using the derived influence function and develop a highly sophisticated classifier in the linear subspace method.",
keywords = "CLAFIC, Cross-validation, Perturbation analysis, Single-case diagnostics",
author = "Kuniyoshi Hayashi",
year = "2014",
month = "6",
doi = "10.1016/j.patcog.2013.11.030",
language = "English",
volume = "47",
pages = "2241--2254",
journal = "Pattern Recognition",
issn = "0031-3203",
publisher = "Elsevier Limited",
number = "6",

}

TY - JOUR

T1 - Influence functions for a linear subspace method

AU - Hayashi, Kuniyoshi

PY - 2014/6

Y1 - 2014/6

N2 - A linear subspace method, which is one of discriminant methods, was proposed as a pattern recognition method and was studied. Because the method and its extensions do not encounter the situation of singular covariance matrix, we need not consider extensions such as generalized ridge discrimination, even when treating a high dimensional and sparse dataset. In addition, classifiers based on a multi-class discrimination method can function faster because of the simple decision procedure. Therefore, they have been widely used for face and speech recognition. However, it seems that sufficient studies have not been conducted about the statistical assessment of training data performance for classifier in terms of prediction accuracy. In statistics, influence functions for statistical discriminant analysis were derived and the assessments for analysis result were performed. These studies indicate that influence functions are useful for detecting large influential observations for analysis results by using discrimination methods and they contribute to enhancing the performance of a target classifier. In this paper, we propose the statistical diagnostics of a classifier on the basis of an influence function by using the linear subspace method. We first propose the discriminant score for the linear subspace method. Next, we derive the sample and empirical influence functions for the average of the discriminant scores to detect large influential observations for the misclassification rate. Finally, through a simulation study and a real data analysis, we detect the outliers in the training dataset using the derived influence function and develop a highly sophisticated classifier in the linear subspace method.

AB - A linear subspace method, which is one of discriminant methods, was proposed as a pattern recognition method and was studied. Because the method and its extensions do not encounter the situation of singular covariance matrix, we need not consider extensions such as generalized ridge discrimination, even when treating a high dimensional and sparse dataset. In addition, classifiers based on a multi-class discrimination method can function faster because of the simple decision procedure. Therefore, they have been widely used for face and speech recognition. However, it seems that sufficient studies have not been conducted about the statistical assessment of training data performance for classifier in terms of prediction accuracy. In statistics, influence functions for statistical discriminant analysis were derived and the assessments for analysis result were performed. These studies indicate that influence functions are useful for detecting large influential observations for analysis results by using discrimination methods and they contribute to enhancing the performance of a target classifier. In this paper, we propose the statistical diagnostics of a classifier on the basis of an influence function by using the linear subspace method. We first propose the discriminant score for the linear subspace method. Next, we derive the sample and empirical influence functions for the average of the discriminant scores to detect large influential observations for the misclassification rate. Finally, through a simulation study and a real data analysis, we detect the outliers in the training dataset using the derived influence function and develop a highly sophisticated classifier in the linear subspace method.

KW - CLAFIC

KW - Cross-validation

KW - Perturbation analysis

KW - Single-case diagnostics

UR - http://www.scopus.com/inward/record.url?scp=84894341697&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894341697&partnerID=8YFLogxK

U2 - 10.1016/j.patcog.2013.11.030

DO - 10.1016/j.patcog.2013.11.030

M3 - Article

AN - SCOPUS:84894341697

VL - 47

SP - 2241

EP - 2254

JO - Pattern Recognition

JF - Pattern Recognition

SN - 0031-3203

IS - 6

ER -