Linear discriminant analysis improves class separability but struggles with non-linearly separable data. To overcome this, we introduce Deep Discriminant Analysis (DDA), which directly optimizes the Fisher criterion utilizing deep networks. To ensure stable training and avoid computational instabilities, we incorporate signed between-class variance, bound outputs with a sigmoid function, and convert multiplicative relationships into additive ones. We present two stable DDA loss functions and augment them with a probability loss, resulting in Probabilistic DDA (PDDA). PDDA effectively minimizes class overlap in output distributions, producing highly confident predictions with reduced within-class variance. When applied to wind blade segmentation, PDDA showcases notable advances in performance and consistency, critical for wind energy maintenance. To our knowledge, this is the first application of DDA to image segmentation.

翻译：线性判别分析虽能提升类别可分性，但难以处理非线性可分数据。为克服此局限，本文提出深度判别分析（DDA），其通过深度网络直接优化Fisher准则。为确保训练稳定性并避免计算失稳，我们引入符号化类间方差、采用sigmoid函数约束输出，并将乘法关系转化为加法关系。本文提出两种稳定的DDA损失函数，并辅以概率损失进行增强，最终形成概率深度判别分析（PDDA）。PDDA能有效缩小输出分布中的类别重叠区域，通过降低类内方差产生高置信度预测。在风力叶片分割任务中，PDDA展现出显著的性能提升与结果一致性——这对风电运维至关重要。据我们所知，这是DDA在图像分割领域的首次应用。