Dark-Point Component Analysis: Nonnegative Blind Source Separation Based on Jaccard Index

A simplicial cone can be employed in nonnegative blind source separation (N-BSS). Nevertheless, the coordinate origin may not be a dark-point, and in this case, it is challenging to implement N-BSS with a simplicial cone. We propose an algorithm for finding dark-points based on the minimum Jaccard index (MJI) criterion-dark-point component analysis (DCA). This method only needs to assume source boundedness and nonnegativity instead of local dominance, full additivity, and sparsity. On the other hand, mixing data scatter plots are usually confined as tear-drop-shaped or deltoid. However, DCA does not need such restrictions. DCA can also be applied to blind source separation (BSS) in which the sources are strictly positive, and the result is the same as that of N-BSS.

Automated summary

This paper introduces an algorithm for nonnegative blind source separation (N-BSS) based on the minimum Jaccard index. The proposed method, called dark-point component analysis (DCA), aims to find dark-points without assuming local dominance, full additivity, and sparsity. DCA can also be applied to blind source separation (BSS) with strictly positive sources, yielding the same result as N-BSS.