Tensor clustering with algebraic constraints gives interpretable groups of crosstalk mechanisms in breast cancer

Muti-dimensional datasets are now prevalent across the sciences; their ubiquity and importance will only continue to grow [1-4]. The analysis of data demands methods that preserve multidimensional structures, and that exploit them. We introduce a versatile data clustering framework based on tensors (high dimensional arrays) and algebra to analyze multidimensional datasets. One key feature of this method is that it can incorporate general, application-specific constraints on the composition of a cluster, and is guaranteed to find optimal partitions. The flexibility of the method allows it to be used directly on a dataset (i.e., as a standalone clustering tool), or in combination with other clustering methods. We apply our method on an extensive set of timecourse measurements of the activation levels of the mitogen-activated protein kinase (MAPK) and phosphoinositide 3-kinase (PI3K) pathways that are involved in cellular decisions and fates [10-13], and are known to dysfunction in cancer [10-13, 16]. The key signaling proteins and subtype responses in breast cancer cells are known; however, among genetically diverse cell lines the dysfunction varies and is not well understood [1, 15, 16]. Our objective is to find groups of cell lines whose signal transduction networks have similar dynamics. A high similarity suggests that the cell lines share pathway features that can be relevant for the responses to the ligands.