Independent Component Analysis (ICA) for the demixing of multiple source mixtures. We call it the Convex Cauchy-Schwarz Divergence (CCS-DIV), and it is formed by integrating convex functions into the Cauchy-Schwarz inequality. The new measure is symmetric and the degree of its curvature with respect to the joint-distribution can be tuned by a (convexity) parameter. The CCS-DIV is able to speed-...

—We present a new high-performance Convex Cauchy– Schwarz Divergence (CCS-DIV) measure for Independent Component Analysis (ICA) and Blind Source Separation (BSS). The CCS-DIV measure is developed by integrating convex functions into the Cauchy–Schwarz inequality. By including a convexity quality parameter, the measure has a broad control range of its convexity curvature. With this measure, a ne...

The symmetric shape of some inequalities between two sequences real numbers generates the same in operator theory. In this paper, we study a new refinement Cauchy–Bunyakovsky–Schwarz inequality for Euclidean spaces and several bounded linear operators on Hilbert space, where mention Bohr’s Bergström’s operators. We present an type operators, by technique monotony sequence. also prove Aczél spac...

in the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. in particular, it isshown that the cauchy-schwarz inequality holds. moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy hilbert space has a complementary subspace.finally, the notions of fuzzy bo...