Tools for HDLSS data

We have published R code and manuals for an analytical method developed and proposed in our laboratory for High-Dimension, Low-Sample-Size (HDLSS) data. Please read the following notes on usage and use it only if you agree. For more details on the analytical method, please refer to the relevant paper.

Contents

• Installation from GitHub
• R tools for high-dimensional data
  • Principal Component Analysis
  • Correlation Test
• License
  • Copyright
  • Disclaimer and Prohibited Matters
  • Instructions for Using this Program
• Contact Information

Installation from GitHub

Use the following command in the terminal to install the package to a local folder.

git clone https://github.com/Aoshima-Lab/HDLSS-Tools.git

R tools for high-dimensional data

Principal Component Analysis

1. Noise Reduction Methodology (NRM.R)

   Eigenvalues, eigenvectors, and principal component scores for high-dimensional data are estimated using the "Noise Reduction Methodology (NRM)".

   Reference : "Effective PCA for High-Dimension, Low-Sample-Size Data with Noise Reduction via Geometric Representations"
   Journal of Multivariate Analysis, 105 (2012), 193-215
   DOI : 10.1016/j.jmva.2011.09.002

2. Cross-Data-Matrix Methodology (CDM.R)

   Eigenvalues, eigenvectors, and principal component scores for high-dimensional data are estimated using the "Cross-Data Matrix Methodology (CDM)".

   Reference : "Effective PCA for High-Dimension, Low-Sample-Size Data with Singular Value Decomposition of Cross Data Matrix"
   Journal of Multivariate Analysis, 101 (2010), 2060-2077
   DOI: 10.1016/j.jmva.2010.04.006

Correlation Test

1. Extended Cross-Data-Matrix Methodology (ECDM.R)

   The "Extended Cross-Data-Matrix Methodology (ECDM)" estimates tr(Σ^2) for a high-dimensional covariance matrix Σ and performs a high-dimensional correlation test.

   Reference : "High-Dimensional Inference on Covariance Structures via the Extended Cross-Data-Matrix Methodology"
   Journal of Multivariate Analysis, 151 (2016), 151-166
   DOI: 10.1016/j.jmva.2016.07.011

License

Copyright

1. The copyright of this R code belongs to the Aoshima Laboratory.
2. When publishing research results using this R code, please cite the relevant paper.

Disclaimer and Prohibited Matters

1. The Aoshima Laboratory bears no responsibility for any direct or indirect damages arising from the use of this R code and its results.
2. Modification, porting, or redistribution of this R code without the permission of the copyright holder is prohibited.

Instructions for Using this Program

1. Prior to using this R code, please install the statistical software "R." For installation of "R," please refer to this link.
2. In the "Public R Code" below, please click on each method name.

Contact Information

Aoshima Laboratory, Mathematical Science Area, Department of Mathematical and Physical Sciences, University of Tsukuba

Email: aoshima[at]math[dot]tsukuba[dot]ac[dot]jp