Distance-based classifier by data transformation for high-dimension, strongly spiked eigenvalue models

DOI10.1007/s10463-018-0655-zzbMath1420.62267arXiv1710.10768OpenAlexW2964119980MaRDI QIDQ2000734

Kazuyoshi Yata, Makoto Aoshima

Publication date: 28 June 2019

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.10768

zbMATH Keywords

asymptotic normalitydiscriminant analysisnoise-reduction methodologylarge \(p\) small \(n\)spiked modeldata transformation

Mathematics Subject Classification ID

Classification and discrimination; cluster analysis (statistical aspects) (62H30) Applications of statistics to biology and medical sciences; meta analysis (62P10)

Related Items (14)

A classifier under the strongly spiked eigenvalue model in high-dimension, low-sample-size context ⋮ Simultaneous testing of the mean vector and covariance matrix among k populations for high-dimensional data ⋮ Robust support vector machine for high-dimensional imbalanced data ⋮ Semiparametric estimation of the high-dimensional elliptical distribution ⋮ Unnamed Item ⋮ Bias-corrected support vector machine with Gaussian kernel in high-dimension, low-sample-size settings ⋮ Kick-one-out-based variable selection method for Euclidean distance-based classifier in high-dimensional settings ⋮ Consistent variable selection criteria in multivariate linear regression even when dimension exceeds sample size ⋮ Hypothesis tests for high-dimensional covariance structures ⋮ Clustering by principal component analysis with Gaussian kernel in high-dimension, low-sample-size settings ⋮ Geometric classifiers for high-dimensional noisy data ⋮ Asymptotic properties of distance-weighted discrimination and its bias correction for high-dimension, low-sample-size data ⋮ Double data piling leads to perfect classification ⋮ Inference on high-dimensional mean vectors under the strongly spiked eigenvalue model

Uses Software

• GitHub
• datamicroarray

Cites Work

• Distance-Weighted Discrimination
• PCA consistency for the power spiked model in high-dimensional settings
• Asymptotic properties of the misclassification rates for Euclidean distance discriminant rule in high-dimensional data
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• High-dimensional classification using features annealed independence rules
• Some theory for Fisher's linear discriminant function, `naive Bayes', and some alternatives when there are many more variables than observations
• Dependent central limit theorems and invariance principles
• A two-sample test for high-dimensional data with applications to gene-set testing
• Support vector machine and its bias correction in high-dimension, low-sample-size settings
• Two-Stage Procedures for High-Dimensional Data
• Geometric Classifier for Multiclass, High-Dimensional Data
• A Direct Estimation Approach to Sparse Linear Discriminant Analysis
• Sparse Quadratic Discriminant Analysis For High Dimensional Data
• Theoretical Measures of Relative Performance of Classifiers for High Dimensional Data with Small Sample Sizes
• Scale adjustments for classifiers in high-dimensional, low sample size settings
• Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data
• Two-sample tests for high-dimension, strongly spiked eigenvalue models
• The maximal data piling direction for discrimination
• Geometric Representation of High Dimension, Low Sample Size Data
• Unnamed Item

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