An Analysis Toolbox for Hermitian Positive Definite Matrices

An implementation of data analysis tools for samples of symmetric or Hermitian positive definite matrices, such as collections of covariance matrices or spectral density matrices. The tools in this package can be used to perform: (i) intrinsic wavelet transforms for curves (1D) or surfaces (2D) of Hermitian positive definite matrices with applications to dimension reduction, denoising and clustering in the space of Hermitian positive definite matrices; and (ii) exploratory data analysis and inference for samples of positive definite matrices by means of intrinsic data depth functions and rank-based hypothesis tests in the space of Hermitian positive definite matrices.


The pdSpecEst (positive definite Spectral Estimation) package provides data analysis tools for samples of symmetric or Hermitian positive definite matrices, such as collections of positive definite covariance matrices or spectral density matrices.

The tools in this package can be used to perform:

  • Intrinsic wavelet transforms for curves (1D) or surfaces (2D) of Hermitian positive definite matrices, with applications to for instance: dimension reduction, denoising and clustering for curves or surfaces of Hermitian positive definite matrices such as (time-varying) Fourier spectral density matrices. These implementations are based in part on the papers (Chau and Sachs 2017) and (Chau and Sachs 2018) and Chapters 3 and 5 of (Chau 2018).

  • Exploratory data analysis and inference for samples of Hermitian positive definite matrices by means of intrinsic data depth functions and depth rank-based hypothesis tests. These implementations are based on the paper (Chau, Ombao, and Sachs 2017) and Chapter 4 of (Chau 2018).

For more details and examples on how to use the package see the accompanying vignettes in the vignettes folder.

An R-Shiny app to demonstrate and test the implemented functionality in the package is available here.

Author and maintainer: Joris Chau ([email protected]).

Installation

  • Stable CRAN version: install from within R

  • Current development version: install via devtools::install_github("JorisChau/pdSpecEst")

References

Chau, J. 2018. “Advances in Spectral Analysis for Multivariate, Nonstationary and Replicated Time Series.” PhD thesis, Universite catholique de Louvain.

Chau, J., H. Ombao, and R. von Sachs. 2017. “Intrinsic Data Depth for Hermitian Positive Definite Matrices.” ArXiv Preprint 1706.08289. https://arxiv.org/abs/1706.08289.

Chau, J., and R. von Sachs. 2017. “Intrinsic Wavelet Regression for Curves of Hermitian Positive Definite Matrices.” ArXiv Preprint 1701.03314. https://arxiv.org/abs/1701.03314.

Chau, J., and R. von Sachs. 2018. “Intrinsic Wavelet Regression for Surfaces of Hermitian Positive Definite Matrices.” ArXiv Preprint 1808.08764. https://arxiv.org/abs/1808.08764.

News

pdSpecEst 1.2.3

  • Fixed warning non-ASCII characters in references
  • Fixed note CRAN checks

pdSpecEst 1.2.2

  • New and updated features:
    • intrinsic k-means clustering with pdkMeans
    • new example simulated data in rExamples1D and rExamples2D
    • intrinsic median of HPD matrices with pdMedian
  • New and updated functions: pdSpecClust1D, pdSpecClust2D, pdDepth, pdSpecEst1D, pdSpecEst2D, rExamples1D, rExamples2D, InvWavTransf1D, InvWavTransf2D, pdDist, pdMean, pdMedian, pdPgram, pdPgram2D, pdNeville, WavTransf1D, WavTransf2D, pdParTrans, Expm, Logm
  • Updated vignettes:
    • "Wavelet-based multivariate Fourier spectral estimation",
    • "Data depth and rank-based tests for HPD matrices"
  • Updated Shiny app (see README or DESCRIPTION for url)

pdSpecEst 1.2.1

  • Removed unnecessary package imports

pdSpecEst 1.2.0

  • New and updated features:
    • Updated 1D intrinsic wavelet regression and clustering with pdSpecEst1D and pdSpecClust1D based on various new metrics
    • 2D intrinsic wavelet regression and clustering with pdSpecEst2D and pdSpecClust2D
    • New tools for intrinsic 1D and 2D polynomial generation and interpolation
    • Time-varying periodograms with pdPgram2D
    • Tree-structured 1D and 2D wavelet thresholding with pdCART
    • Depth-based intrinsic confidence regions with pdConfInt1D
    • New example spectral matrices and benchmark procedures
  • New and updated functions: H.coeff, InvWavTransf1D, InvWavTransf2D, ParTrans, pdCART, pdConfInt1D, pdDepth, pdMean, pdNeville, pdPgram2D, pdPolynomial, pdRankTests, pdSpecClust1D, pdSpecClust2D, pdSpecEst1D, pdSpecEst2D, pdSplineReg, rExamples, rExamples2D, WavTransf1D, WavTransf2D
  • Updated vignettes: "Wavelet-based multivariate spectral analysis"
  • Updated Shiny app (see README or DESCRIPTION for url)

pdSpEcEst 1.1.1

  • New features: data depth and rank-based hypothesis tests for samples of Hermitian PD matrices
  • New functions: pdDist, pdDepth, pdRankTests
  • New vignette: "Data depth and rank-based tests for HPD matrices"
  • New demo Shiny app (see README or DESCRIPTION for url)

pdSpecEst 1.0.0

  • New release

Reference manual

It appears you don't have a PDF plugin for this browser. You can click here to download the reference manual.

install.packages("pdSpecEst")

1.2.3 by Joris Chau, 8 months ago


https://github.com/JorisChau/pdSpecEst, https://jchau.shinyapps.io/pdSpecEst/


Browse source code at https://github.com/cran/pdSpecEst


Authors: Joris Chau [aut, cre]


Documentation:   PDF Manual  


GPL-2 license


Imports multitaper, Rcpp, ddalpha, Rdpack

Suggests knitr, rmarkdown, testthat, grid, ggplot2, reshape2, viridis, ggthemes

Linking to Rcpp, RcppArmadillo

System requirements: GNU make, C++11


See at CRAN