An ISA algorithm with unknown group sizes identifies meaningful clusters in metabolomics data

Independent Subspace Analysis (ISA) denotes the task of linearly separating multivariate observations into statistically independent multi-dimensional sources, where dependencies only exist within these subspaces but not between them. So far ISA algorithms have mostly been described in the context of known group sizes. Here, we extend a previously proposed ISA algorithm based on joint block diagonalization of 4-th order cumulant matrices to separate subspaces of unknown sizes. Further automated interpretation of the demixed sources then requires a means of recovering the subspace structure within them, and we propose two distinct methods for this. We then apply the method to a novel application field, namely clustering of metabolites, which seems to be well-fit to the ISA model. We are able to successfully identify dependencies between metabolites that could not be recovered using conventional methods.