HIGH-DIMENSIONAL DATA ANALYSIS TOOLS

We are making available the R code and the Python code for the analytical methods developed and proposed in our laboratory for analyzing high-dimensional data. Please read the "LICENSE" and agree to them before using the code. For details on the analytical methods, please refer to the relevant papers.

For any questions or inquiries, please contact us at the address below.

Aoshima Laboratory, Institute of Mathematics, University of Tsukuba
E-mail: aoshima[at]math[dot]tsukuba[dot]ac[dot]jp

PUBLISHED CODE

(1) High-dimensional PCA
  1. Noise-Reduction Methodology (NRM)

    2. Relevant paper: "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)

    3. Relevant paper: "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

  3. Automatic Sparse PCA (A-SPCA)

    4. Relevant paper: "Automatic Sparse PCA for High-Dimensional Data"
    Statistica Sinica, 35 (2025), 1069-1090
    DOI: 10.5705/ss.202022.0319

(2) Testing for high-dimensional independence
  1. Extended Cross-Data-Matrix Methodology (ECDM)

    2. Relevant paper: "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

(3) High-dimensional discriminant analysis
  1. Distance-Based Discriminant Analysis (DBDA)

    2. Relevant paper: "A Distance-Based, Misclassification Rate Adjusted Classifier for Multiclass, High-Dimensional Data"
    Annals of the Institute of Statistical Mathematics, 66 (2014), 983-1010
    DOI: 10.1007/s10463-013-0435-8

  2. Geometrical Quadratic Discriminant Analysis (GQDA)

    3. Relevant paper: "Geometric Classifier for Multiclass, High-Dimensional Data"
    Sequential Analysis, Special Issue: Celebrating Seventy Years of Charles Stein's 1945 Seminal Paper on Two-Stage Sampling, 34 (2015), 279-294
    DOI: 10.1080/07474946.2015.1063256

  3. Feature Selected Diagonal Quadratic Discriminant Analysis (FS-DQDA)

    4. Relevant paper: "High-dimensional quadratic classifiers in non-sparse settings"
    Methodology and Computing in Applied Probability, 21 (2019), 663-682
    DOI: 10.1007/s11009-018-9646-z

  4. Bias-Corrected Support Vector Machine (BC-SVM)

    5. Relevant paper: "Support vector machine and its bias correction in high-dimension, low-sample-size settings"
    Journal of Statistical Planning and Inference, 191 (2017), 88-100
    DOI: 10.1016/j.jspi.2017.05.005

    Relevant paper: "Bias-Corrected Support Vector Machine with Gaussian Kernel in High-Dimension, Low-Sample-Size Settings"
    Annals of the Institute of Statistical Mathematics, 72 (2020), 1257-1286
    DOI: 10.1007/s10463-019-00727-1