| dist {sdrt} | R Documentation |
Return the distance between two subspaces spanning by column space of matrices.
Description
The function calculates three metrics for measuring the distance between two subspaces spaning by the columns of two matrices.
Usage
dist(A, B)
Arguments
A |
Matrix 1 with dimension p-by-d. |
B |
Matrix 2 with dimension p-by-d. |
Value
The outputs include three scales and one d-dimensional vector.
r |
One minuse the summation of eiegenvalues of the matrix B^TAA^TB. |
q |
One minues the product of eiegenvalues of the matrix B^TAA^TB. |
rho |
rho=sqrt(A^TBB^TA) |
m^2 |
A d-variate vector giving the colum-wise distance between A and B. |
References
Samadi S. Y. and De Alwis T. P. (2023). Fourier Method of Estimating Time Series Central Mean Subspace. https://arxiv.org/pdf/2312.02110.
Ye Z. and Weiss R.E. (2003). Using the Bootstrap to Select One of a New Class of Dimension Reduction Methods, Journal of the American Statistical Association, 98,968-978.