The function calculates three metrics for measuring the distance between two subspaces spaning by the columns of two matrices.
dist(A, B)The outputs include three scales and one d-dimensional vector.
One minuse the summation of eiegenvalues of the matrix B^TAA^TB.
One minues the product of eiegenvalues of the matrix B^TAA^TB.
rho=sqrt(A^TBB^TA)
A d-variate vector giving the colum-wise distance between A and B.
Matrix 1 with dimension p-by-d.
Matrix 2 with dimension p-by-d.
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.