Paul Fogel, Consultant, Paul Fogel Consultant
Orson Jay, Intern, Sanofi
Galina Boldina, Principal Data Scientist, Sanofi
Franck Augé, Senior Director, Omics Data Sciences, Sanofi
Matrices are second-order tensors. In some applications, the input data are third- or higher-order tensors. For example, gene expression data from different cell types found in a single donor form a second-order tensor of the form {cell type × gene}, while the collection of similar cell types on different donors results in a third-order tensor of the form {cell type × gene × donor}. We present two JMP Add-ins, the first of which performs multi-way data analysis of a third-order tensor using non-negative tensor factorization. The second Add-in allows visualization of the major expression patterns found in the tensor in the form of parallel heatmaps. Using a public transcriptome dataset, we show how these tools enable the discovery and visualization of tri-clusters of cell types, genes, and donors that share similar transcriptomic patterns, resulting in cell type signatures that can be used to deconvolute bulk mixtures of different cell types. We also show that the Python package used to perform the core computations can be integrated seamlessly into JSL scripts.
