Before revision:  Single-cell RNA sequencing can measure the expression of thousands of genes in thousands of neurons. How to interpret the data in the context of neuronal phenotypes? We propose a supervised learning approach that factorizes the gene expression data into components corresponding to individual phenotypic characteristics and their interactions. This new method, which we call factorized linear discriminant analysis (FLDA), seeks a linear transformation of gene expressions that varies highly with only one phenotypic factor and minimally with the others.
After revision:  This representation is often sought from a linear transformation of the original data, for the reasons of model interpretability and computational simplicity. Here we propose a novel method of linear dimensionality reduction to address this problem. This method, which we call factorized linear discriminant analysis (FLDA), seeks a linear transformation of gene expressions that varies highly with only one phenotypic factor and minimally with the others.