The discovery of subtypes is pivotal for disease diagnosis and targeted therapy, considering the diverse responses of different cells or patients to specific treatments. Exploring the heterogeneity within disease or cell states provides insights into disease progression mechanisms and cell differentiation. The advent of high-throughput technologies has enabled the generation and analysis of various molecular data types, such as single-cell RNA-seq, proteomic, and imaging datasets, at large scales. While presenting opportunities for subtype discovery, these datasets pose challenges in finding relevant signatures due to their high dimensionality. Feature selection, a crucial step in the analysis pipeline, involves choosing signatures that reduce the feature size for more efficient downstream computational analysis. Numerous existing methods focus on selecting signatures that differentiate known diseases or cell states, yet they often fall short in identifying features that preserve heterogeneity and reveal subtypes. To identify features that can capture the diversity within each class while also maintaining the discrimination of known disease states, we employed deep metric learning-based feature embedding to conduct a detailed exploration of the statistical properties of features essential in preserving heterogeneity. Our analysis revealed that features with a significant difference in interquartile range (IQR) between classes possess crucial subtype information. Guided by this insight, we developed a robust statistical method, termed PHet (Preserving Heterogeneity) that performs iterative subsampling differential analysis of IQR and Fisher's method between classes, identifying a minimal set of heterogeneity-preserving discriminative features to optimize subtype clustering quality. Validation using public single-cell RNA-seq and microarray datasets showcased PHet's effectiveness in preserving sample heterogeneity while maintaining discrimination of known disease/cell states, surpassing the performance of previous outlier-based methods. Furthermore, analysis of a single-cell RNA-seq dataset from mouse tracheal epithelial cells revealed, through PHet-based features, the presence of two distinct basal cell subtypes undergoing differentiation toward a luminal secretory phenotype. Notably, one of these subtypes exhibited high expression of BPIFA1. Interestingly, previous studies have linked BPIFA1 secretion to the emergence of secretory cells during mucociliary differentiation of airway epithelial cells. PHet successfully pinpointed the basal cell subtype associated with this phenomenon, a distinction that pre-annotated markers and dispersion-based features failed to make due to their admixed feature expression profiles. These findings underscore the potential of our method to deepen our understanding of the mechanisms underlying diseases and cell differentiation and contribute significantly to personalized medicine.
