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Weighted Hellinger distance and in-betweenness property

Authors: 

Trung Hoa Dinh, Cong Trinh Le, Bich Khue Vo, Trung-Dung Vuong

Source title: 
Mathematical Inequalities and Applications, 24(1): 157-165, 2021 (ISI)
Academic year of acceptance: 
2020-2021
Abstract: 

In this paper we introduce the weighted Hellinger distance for matrices which is an interpolating between the Euclidean distance and the Hellinger distance. We show the equivalence of the weighted Hellinger distance and the Alpha Procrustes distance. As a consequence, we prove that the matrix power mean μp(t, A, B) = (tAp+(1-t)Bp)1/p satisfies in-betweenness property in the weighted Hellinger and Alpha Procrustes distances.