Before revision: We introduce a tensor-based algebraic clustering method to extract sparse, low-dimensional structure from multidimensional arrays of experimental data. Our methodology is applicable to high dimensional data structures that arise across the sciences. Specifically we introduce a new way to cluster data subject to multi-indexed structural constraints via integer programming. The method can work as a stand-alone clustering tool or in combination with established methods. We implement this approach on a dataset consisting of genetically diverse breast cancer cell lines exposed to a range of signaling molecules, where each experiment is labelled by its combination of cell line and ligand.
After revision: We introduce a tensor-based algebraic clustering method to extract sparse, low-dimensional structure from high-dimensional, multi-indexed datasets. Specifically, this framework is designed to enable detection of clusters of data in the presence of structural requirements which we encode as algebraic constraints in a linear program. We illustrate our method on a collection of experiments measuring the response of genetically diverse breast cancer cell lines exposed to a range of signaling molecules, where each experiment is labelled by its combination of cell line and ligand.