Structure preserving feature selection in PARAFAC using a genetic algorithm and Procrustes analysis

In this paper, a method is proposed to select subsets of variables in parallel factor analysis (PARAFAC), such that information in the complete multi-way data set is preserved as much as possible. The information retained is measured by means of the percentage of consensus in Procrustes analysis. The best N-way subset is obtained by applying a genetic algorithm (GA) to optimize the consensus between the subset and the complete N-way data set in order to prevent exhaustive searching. The method was applied to two industrial data sets: a three-way sensory data set and a four-way gas chromatography (GC) data set. The results showed that the proposed method successfully identified structure-bearing variables in both data sets and that it led to better subsets of variables than feature selection based on loadings.