Sparse non-negative multivariate curve resolution: L-0, L-1, or L-2 norms?

摘要

Several constraints are designed to further restrict bilinear decompositions to a unique solution. Constraints are physico-chemical restrictions on the curve resolution task. Sparsity, as a constraint, was introduced to create solutions with zero elements. As neither the number of zeros nor the places of zeros are not initially available, sparsity constraint should be implemented with caution. Regarding sparsity constraint, two important issues can be addressed. The first issue is the effect of sparsity constraint on the possible solutions of bilinear decompositions, i.e., set of sparse solutions. The second issue is the type of Lp( )norm, {p = 0, 1, 2}, for the sparsity implementation. Self-modeling curve resolution (SMCR) tools (say Borgen-Rajko plot) draw a clear picture of the data micro-structure. Focusing on the geometry of bilinear data sets, outer-polygon as the non-negativity boundary of possible solutions contains all the sparse solutions.