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Title: Identification of significant pairwise logratios in compositional data based on sparse PCA Authors:  Viktorie Nesrstova - Palacky University, Olomouc (Czech Republic) [presenting]
Karel Hron - Palacky University (Czech Republic)
Peter Filzmoser - Vienna University of Technology (Austria)
Ines Wilms - Maastricht University (Netherlands)
Abstract: Compositional data consist of observations that carry relative information in the ratios between the parts. They are commonly expressed as log-ratio coordinates with respect to an orthonormal basis of their sample space. However, for modern high-dimensional data, analyzing all pairwise logratios rapidly becomes infeasible due to their sheer size. The focus is on the high-dimensional analysis by identifying the most significant pairwise logratios. To this end, sparse PCA is leveraged when constructing backward pivot coordinates that highlight a pairwise logratio within a complete set of logratio coordinates. The significant pairwise logratios are identified while balancing sufficient sparsity of the resulting loadings and explained variance. The performance of the procedure is demonstrated both in simulation and applications on real-world data.