Sparse and nonnegative sparse D-MORPH regression

作者：Li Genyuan; Rey de Castro Roberto; Xing Xi; Rabitz Herschel^*

来源：Journal of Mathematical Chemistry, 2015, 53(8): 1885-1914.

DOI：10.1007/s10910-015-0527-1

• Underdetermined system
• D-MORPH regression
• Least-squares regression
• IRLS
• RRLS
• Quantum-control-mechanism identification
• Mass spectrum analysis

An underdetermined linear algebraic equation system , where is an rectangular constant matrix with rank and (range of , has an infinite number of solutions. Diffeomorphic modulation under observable response preserving homotopy (D-MORPH) regression seeks a solution satisfying the extra requirement of minimizing a chosen cost function, . A wide variety of choices of the cost function makes it possible to achieve diverse goals, and hence D-MORPH regression has been successfully applied to solve a range of problems. In this paper, D-MORPH regression is extended to determine a sparse or a nonnegative sparse solution of the vector . For this purpose, recursive reweighted least-squares (RRLS) minimization is adopted and modified to construct the cost function for D-MORPH regression. The advantage of sparse and nonnegative sparse D-MORPH regression is that the matrix does not need to have row-full rank, thereby enabling flexibility to search for sparse solutions with ancillary properties in practical applications. These tools are applied to (a) simulation data for quantum-control-mechanism identification utilizing high dimensional model representation (HDMR) modeling and (b) experimental mass spectral data for determining the composition of an unknown mixture of chemical species.

• 出版日期2015-9