aspcol.distance

Calculates distance measures for some different types of quantities.

For all types of arrays, the mean square error can be computed. Vectors can be compared using angular distance or cosine similarity. For positive definite matrices, the correlation matrix distance, the affine invariant Riemannian metric, and the Kullback Leibler divergence between zero-mean Gaussian densities described by the compared matrices can be computed.

References

[herdinCorrelation2005] M. Herdin, N. Czink, H. Ozcelik, and E. Bonek, ‘Correlation matrix distance, a meaningful measure for evaluation of non-stationary MIMO channels,’ in 2005 IEEE 61st Vehicular Technology Conference, May 2005, pp. 136-140 Vol. 1. doi: 10.1109/VETECS.2005.1543265. [link]

[forstnermetric2003] W. Förstner and B. Moonen, ‘A metric for covariance matrices,’ in Geodesy-The Challenge of the 3rd Millennium, E. W. Grafarend, F. W. Krumm, and V. S. Schwarze, Eds., Berlin, Heidelberg: Springer Berlin Heidelberg, 2003, pp. 299–309. doi: 10.1007/978-3-662-05296-9_31. [link]

[duchiDerivations2016] J. Duchi, ‘Derivations for Linear Algebra and Optimization, 2016. [link]

[absilOptimization2008] P.-A. Absil, R. Mahony, and R. Sepulchre, Optimization algorithms on matrix manifolds. Princeton, N.J. ; Woodstock: Princeton University Press, 2008.

Functions

angular_distance(vec1, vec2[, sign_invariant])	A distance metric based on the cosine similary, that retains the
corr_matrix_distance(mat1, mat2)	Computes the correlation matrix distance
cos_similary(vec1, vec2)	Computes <vec1, vec2> / (||vec1|| ||vec2||) which is cosine of the angle between the two vectors.
covariance_distance_kl_divergence(mat1, mat2)	The Kullback Leibler divergence between two Gaussian distributions that has mat1 and mat2 as their covariance matrices.
covariance_distance_riemannian(mat1, mat2)	Computes the covariance matrix distance
mse(var1, var2)	The normalized mean square error
spatial_similarity(vec1, vec2)	Measures the spatial similarity between two vectors.