Dimension reduction

Wrapper function for dimension reduction on SPD matrices.

Usage

spd.dimred(X, method, ...)

Arguments

X

A list of SPD matrices.

method

Method of dimension reduction. See details

...

See details.

Value

• "congedo": A named list containing a list `Xred` of dimension reduced covariance matrices, and a `n x k` matrix `Z` of components.

• "pga": A named list containing the sample mean, the components (unit tangent vectors at the mean), the associated eigenvalues, variance explained, and the component scores of each observation.

Details

Allowable methods are:

• "congedo": Method proposed by Congedo et al. 2017. Maps a set of SPD matrices onto a set of lower dimensional SPD matrices. Useful as a preprocessing step for techniques which scale poorly with the dimension of the covariance matrix.

• "pga": Principal geodesic analysis (PGA) using the algorithm proposed by Fletcher and Joshi (2004). Projects data onto the tangent space around the sample mean, and estimates principal geodesics by applying PCA to tangent vectors.

Additional arguments may be passed to the functions which perform estimation. Specifically:

• "congedo": `k` gives the dimension of the output space. By default, `k=2`.

• "pga": `k` gives the dimension of the output space. By default, `k=2`.