subspaceDistance

0th

Percentile

Distance Between Linear Spaces

Evaluate the distance between two linear subspaces using the measure proposed by Li, Zha and Chiaromonte (2005).

Keywords
multivariate, algebra
Usage
subspaceDistance(B0, B1)
Arguments
B0

Matrix whose columns are a basis for the first subspace.

B1

Matrix whose columns are a basis for the second subspace.

Details

This algorithm calculates the maximum absolute value of the eigenvalues of \(P1-P0\) where \(P0,P1\) are the projection matrices onto the subspaces generated by B0,B1. This measure of distance was proposed by Li, Zha and Chiaromonte (2005). See also Xia (2007).

Value

A single numeric value.

References

Guan, Y. and Wang, H. (2010) Sufficient dimension reduction for spatial point processes directed by Gaussian random fields. Journal of the Royal Statistical Society, Series B, 72, 367--387.

Li, B., Zha, H. and Chiaromonte, F. (2005) Contour regression: a general approach to dimension reduction. Annals of Statistics 33, 1580--1616.

Xia, Y. (2007) A constructive approach to the estimation of dimension reduction directions. Annals of Statistics 35, 2654--2690.

Aliases
  • subspaceDistance
Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)

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