  Navigating the complex landscape of single-cell transcriptomic data presents
significant challenges. Central to this challenge is the identification of a
meaningful representation of high-dimensional gene expression patterns that
sheds light on the structural and functional properties of cell types. Pursuing
model interpretability and computational simplicity, we often look for a linear
transformation of the original data that aligns with key phenotypic features of
cells. In response to this need, we introduce factorized linear discriminant
analysis (FLDA), a novel method for linear dimensionality reduction. The crux
of FLDA lies in identifying a linear function of gene expression levels that is
highly correlated with one phenotypic feature while minimizing the influence of
others. To augment this method, we integrate it with a sparsity-based
regularization algorithm. This integration is crucial as it selects a subset of
genes pivotal to a specific phenotypic feature or a combination thereof. To
illustrate the effectiveness of FLDA, we apply it to transcriptomic datasets
from neurons in the Drosophila optic lobe. We demonstrate that FLDA not only
captures the inherent structural patterns aligned with phenotypic features but
also uncovers key genes associated with each phenotype.
