Intrinsic Dimensionality Estimation of High-Dimension, Low Sample Size Data withD-Asymptotics

DOI10.1080/03610920903121999zbMath1318.62204OpenAlexW2158027741MaRDI QIDQ3585254

Makoto Aoshima, Kazuyoshi Yata

Publication date: 19 August 2010

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610920903121999

zbMATH Keywords

effective dimensionHDLSSlarge \(p\) small \(n\)maximum eigenvaluedual covariance matrix

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Factor analysis and principal components; correspondence analysis (62H25)

Related Items (15)

Optimization of the maximum likelihood estimator for determining the intrinsic dimensionality of high-dimensional data ⋮ Statistical inference for high-dimension, low-sample-size data ⋮ Asymptotic distributions of some test criteria for the mean vector with fewer observations than the dimension ⋮ Asymptotics of hierarchical clustering for growing dimension ⋮ Inference on high-dimensional mean vectors with fewer observations than the dimension ⋮ Design of input assignment and feedback gain for re‐stabilizing undirected networks with High‐Dimension Low‐Sample‐Size data ⋮ Unnamed Item ⋮ A survey of high dimension low sample size asymptotics ⋮ Effective PCA for high-dimension, low-sample-size data with singular value decomposition of cross data matrix ⋮ Effective Two-Stage Estimation for a Linear Function of High-Dimensional Gaussian Means ⋮ Discussion on “Two-Stage Procedures for High-Dimensional Data” by Makoto Aoshima and Kazuyoshi Yata ⋮ Effective PCA for high-dimension, low-sample-size data with noise reduction via geometric representations ⋮ Two-Stage Procedures for High-Dimensional Data ⋮ Authors' Response ⋮ Solving the linear interval tolerance problem for weight initialization of neural networks

Uses Software

• multtest

Cites Work

• Measuring the strangeness of strange attractors
• No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices
• On the distribution of the largest eigenvalue in principal components analysis
• A scale-based approach to finding effective dimensionality in manifold learning
• Eigenvalues of large sample covariance matrices of spiked population models
• Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
• Geometric Representation of High Dimension, Low Sample Size Data
• Geodesic Entropic Graphs for Dimension and Entropy Estimation in Manifold Learning
• The high-dimension, low-sample-size geometric representation holds under mild conditions
• Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
• An Algorithm for Finding Intrinsic Dimensionality of Data

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