Abstract

In this paper a least squares method is developed for estimating a matrix B that will minimize #Y - XB# subject to the constraint that the rows of B are unimodal, i.e., each has only one peak, and 2 2 #M# being the sum of squares of all elements of M. This method is directly applicable in many 2 2 curve resolution problems, but also for stabilizing other problems where unimodality is known to be a valid assumption. Typical problems arise in certain types of time series analysis like chromatography or flow injection analysis. A fundamental and surprising result of this work is that unimodal least squares regression (including optimization of mode location) is not anymore difficult than two simple Kruskal monotone regressions. The new method is useful in and exemplified with two- and multi-way methods based on alternating least squares regression solving problems from fluorescence spectroscopy and flow injection analysis. Keywords: Unimodal Least Squares Regression, alternating l...

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