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.

中文翻译：

---

神经元表型遗传特征的因子判别分析

浏览复杂的单细胞转录组数据面临着巨大的挑战。这一挑战的核心是识别高维基因表达模式的有意义的表示，从而揭示细胞类型的结构和功能特性。为了追求模型的可解释性和计算的简单性，我们经常寻找与细胞关键表型特征相符的原始数据的线性变换。为了满足这一需求，我们引入了因式线性判别分析（FLDA），这是一种线性降维的新方法。 FLDA 的关键在于确定基因表达水平的线性函数，该函数与一种表型特征高度相关，同时最大限度地减少其他表型特征的影响。为了增强该方法，我们将其与基于稀疏性的正则化算法集成。这种整合至关重要，因为它选择了对特定表型特征或其组合至关重要的基因子集。为了说明 FLDA 的有效性，我们将其应用于果蝇视叶神经元的转录组数据集。我们证明 FLDA 不仅捕获与表型特征一致的固有结构模式，而且还揭示了与每个表型相关的关键基因。