spd_learn.functional.upper

spd_learn.functional.upper(X)

Return the weighted upper triangular part of matrices.

This function computes the minimal representation of a matrix in tangent space [1]: it keeps the upper triangular part of the symmetric/Hermitian matrix and vectorizes it by applying unity weight for diagonal elements and \(\sqrt{2}\) weight for out-of-diagonal elements.

Parameters:

X (ndarray, shape (..., n, n)) – Symmetric/Hermitian matrices.

Returns:

T – Weighted upper triangular parts of symmetric/Hermitian matrices.

Return type:

ndarray, shape (…, n * (n + 1) / 2)

Notes

Added in version 0.4.

Changed in version 0.12: Add support for NumPy and PyTorch.

References

[1]

Pedestrian detection via classification on Riemannian manifolds O. Tuzel, F. Porikli, and P. Meer. IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 30, Issue 10, October 2008.