Dimensionality reduction of longitudinal 'omics data using modern tensor factorizations

Uria Mor, Yotam Cohen, Rafael Valdes-Mas, Denise Kviatcovsky, Eran Elinav, Haim Avron

Abstract: Author summary Tensor methods have proven useful for exploration of high-dimensional, multiway data that is produced in longitudinal ’omics studies. However, even the most recent applications of these methods to ’omics data are based on the canonical polyadic tensor-rank factorization whose results heavily depend on the choice of target rank, lack any guarantee for optimal approximation, and do not allow for out-of-sample extension in a straightforward manner. In this paper, we present a method for tensor component analysis for the analysis of longitudinal ’omics data, built on top of cutting-edge developments in the field of tensor-tensor algebra. We show that our method, in contrast to existing tensor-methods, enjoys provable optimal properties on the distortion and variance in the embedding space, enabling direct and meaningful interpretation, supporting traditional multivariate statistical analysis to be performed in the embedding space. Due to the method’s construction using tensor-tensor products, the procedure of mapping a point to the embedding space of a pre-trained factorization is simple and scalable, giving rise to the application of our method as a feature engineering step in standard machine learning workflows.