Factorized linear discriminant analysis for phenotype-guided representation learning of neuronal gene expression data

A central goal in neurobiology is to relate the expression of genes to the structural and functional properties of neuronal types, collectively called their phenotypes. 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. We further leverage our approach with a sparsity-based regularization algorithm, which selects a few genes important to a specific phenotypic feature or feature combination. We applied this approach to a single-cell RNA-Seq dataset of Drosophila T4/T5 neurons, focusing on their dendritic and axonal phenotypes. The analysis confirms results obtained by conventional methods but also points to new genes related to the phenotypes and an intriguing hierarchy in the genetic organization of these cells.