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. The data consist of time-course measurements of the immediate-early signaling of mitogen activated protein kinase (MAPK ), and phosphoinositide 3-kinase (PI3K)/Protein kinase B (AKT ). By respecting the multi-indexed structure of the experimental data, the analysis can be optimized for biological interpretation and therapeutic understanding. We  quantify the heterogeneity of breast cancer cell subtypes and systematically explore mechanistic models of MAP Kinase and PI3K (phosphoinositide 3-kinase)/AKT crosstalk based on the results of our method .
We introduce a tensor-based 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 to an array of ligands. Each experiment consists of a cell line-ligand combination, and contains time-course measurements of the early-signalling kinases MAPK and AKT at two different ligand dose levels. By imposing appropriate structural constraints and respecting the multi-indexed structure of the data, our clustering analysis can be optimized for biological interpretation and therapeutic understanding. We then perform a systematic, large-scale exploration of mechanistic models of MAPK-AKT crosstalk for each cluster. This analysis allows us to quantify the heterogeneity of breast cancer cell subtypes , and leads to hypotheses about the mechanisms by which cell lines respond to ligands. Our clustering method is general and can be tailored to a variety of applications in science and industry .
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algebraic
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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
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
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exposed to a range of signaling molecules, where each experiment is labelled by its combination of cell line and ligand. The data consist of
to an array of ligands. Each experiment consists of a cell line-ligand combination, and contains
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immediate-early signaling of mitogen activated protein kinase (MAPK ), and phosphoinositide 3-kinase (PI3K)/Protein kinase B (AKT ). By
early-signalling kinases MAPK and AKT at two different ligand dose levels. By imposing appropriate structural constraints and
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experimental data, the
data, our clustering
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then perform a systematic, large-scale exploration of mechanistic models of MAPK-AKT crosstalk for each cluster. This analysis allows us to
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and systematically explore mechanistic models of MAP Kinase and PI3K (phosphoinositide 3-kinase)/AKT crosstalk based on the results of our method
, and leads to hypotheses about the mechanisms by which cell lines respond to ligands. Our clustering method is general and can be tailored to a variety of applications in science and industry