Gene expression in a developing embryo occurs in particular cells (spatial patterns) in a time-specific manner (temporal patterns), which leads to the differentiation of cell fates. Images of aDrosophila melanogasterembryo at a given developmental stage, showing a particular gene expression pattern revealed by a gene-specific probe, can be compared for spatial overlaps. The comparison is fundamentally important to formulating and testing gene interaction hypotheses. Expression pattern comparison is most biologically meaningful when images from a similar time point (developmental stage) are compared. In this paper, we present LdaPath, a novel formulation of Linear Discriminant Analysis (LDA) for automatic developmental stage range classification. It employs multivariate linear regression with theL1-norm penalty controlled by a regularization parameter for feature extraction and visualization. LdaPath computes an entire solution path for all values of regularization parameter with essentially the same computational cost as fitting one LDA model. Thus, it facilitates efficient model selection. It is based on the equivalence relationship between LDA and the least squares method for multiclass classifications. This equivalence relationship is established under a mild condition, which we show empirically to hold for many high-dimensional datasets, such as expression pattern images. Our experiments on a collection of 2705 expression pattern images show the effectiveness of the proposed algorithm. Results also show that the LDA model resulting from LdaPath is sparse, and irrelevant features may be removed. Thus, LdaPath provides a general framework for simultaneous feature selection and feature extraction.

中文翻译：

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通过 LDA 的整个解决方案路径对果蝇基因表达模式图像的发育阶段进行注释

发育中胚胎中的基因表达以特定时间的方式（时间模式）发生在特定细胞（空间模式）中，这导致细胞命运的分化。一个图像黑腹果蝇特定发育阶段的胚胎，显示由基因特异性探针揭示的特定基因表达模式，可以比较空间重叠。这种比较对于制定和测试基因相互作用假设至关重要。当比较来自相似时间点（发育阶段）的图像时，表达模式比较最具生物学意义。在本文中，我们介绍了 LdaPath，这是一种用于自动发育阶段范围分类的线性判别分析 (LDA) 的新公式。它采用多元线性回归与大号1-norm 惩罚由用于特征提取和可视化的正则化参数控制。LdaPath 为正则化参数的所有值计算完整的解决方案路径，其计算成本与拟合一个 LDA 模型的计算成本基本相同。因此，它有助于有效的模型选择。它基于 LDA 与最小二乘法之间的等价关系进行多类分类。这种等价关系是在温和条件下建立的，我们凭经验证明它适用于许多高维数据集，例如表情模式图像。我们对 2705 个表情模式图像的集合的实验表明了所提出算法的有效性。结果还表明，由 LdaPath 生成的 LDA 模型是稀疏的，并且可能会删除不相关的特征。因此，