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Diagonalizations.jl is a Julia signal processing package implementing several closed form and iterative diagonalization procedures for both real and complex data input:
| Acronym | Full Name | Datasets ( m ) | Observations ( k ) |
|---|---|---|---|
| PCA | Principal Component Analysis | 1 | 1 |
| Whitening | Whitening (Sphering) | 1 | 1 |
| MCA | Maximum Covariance Analysis | 2 | 1 |
| CCA | Canonical Correlation Analysis | 2 | 1 |
| gMCA | generalized MCA | >1 | 1 |
| gCCA | generalized CCA | >1 | 1 |
| CSP | Common Spatial Pattern | 1 | 2 |
| CSTP | Common Spatio-Temporal Pattern | 1 | >1 |
| AJD | Approximate Joint Diagonalization | 1 | >1 |
| mAJD | multiple AJD | >1 | >1 |
For example the MCA diagonalizes a cross-covariance matrix, like in this figure:
As compared to MultivariateStats.jl this package supports :
- the
dimskeyword like in the StatsBase.jl package - shrinkage covariance matrix estimations throught package CovarianceEstimation
- average covariance estimations using metrics for the manifold of positive definite matrices using the PosDefManifold package
- facilities to set the subspace dimension upon construction
- diagonalization procedures for the case m≥2 and k≥2.
This package implements state-of-the-art approximate joint diagonalization algorithms. For some benchmarking see here.
To install the package execute the following command in Julia's REPL:
]add CovarianceEstimation PosDefManifold Diagonalizations using Diagonalizations, PosDefManifold, Test n, t=10, 100 # generate an nxt data matrix X=genDataMatrix(n, t) # principal component analysis pX=pca(X) # the following is an equivalent constructor taking the covariance matrix as input pC=pca(Symmetric((X*X')/t)) @test pX==pC # the output of the two constructors above is equivalent @test C≈pC.F*pC.D*pC.F' # get only the first p eigenvectors, where p is the smallest integer # explaining at least 75% of the variance pX=pca(X; eVar=0.75) Y=genDataMatrix(n, t) # maximum covariance analysis mXY=mca(X, Y) # canonical correlation analysis cXY=cca(X, Y) # approximate joint diagonalization Xset=randP(5, 20) aXset=ajd(Xset; algorithm=:JADE) aXset=ajd(Xset; algorithm=:LogLike) # etc., etc. Marco Congedo, is a Research Director of CNRS (Centre National de la Recherche Scientifique), working at UGA (University of Grenoble Alpes). contact: marco dot congedo at gmail dot com
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