Linear discriminant analysis (LDA) is a classical method for discriminative dimensionality reduction. The original LDA may degrade in its performance for non-Gaussian data, and may be unable to extract sufficient features to satisfactorily explain the data when the number of classes is small. Two prominent extensions to address these problems are subclass discriminant analysis (SDA) and mixture subclass discriminant analysis (MSDA). They divide every class into subclasses and re-define the within-class and between-class scatter matrices on the basis of subclass. In this paper we study the issue of how to obtain subclasses more effectively in order to achieve higher class separation. We observe that there is significant overlap between models of the subclasses, which we hypothesise is undesirable. In order to reduce their overlap we propose an extension of LDA, separability oriented subclass discriminant analysis (SSDA), which employs hierarchical clustering to divide a class into subclasses using a separability oriented criterion, before applying LDA optimisation using re-defined scatter matrices. Extensive experiments have shown that SSDA has better performance than LDA, SDA and MSDA in most cases. Additional experiments have further shown that SSDA can project data into LDA space that has higher class separation than LDA, SDA and MSDA in most cases.

中文翻译：

---

面向可分离性的子类判别分析


线性判别分析（LDA）是判别降维的经典方法。原始LDA对于非高斯数据的性能可能会下降，并且当类别数量较小时可能无法提取足够的特征来令人满意地解释数据。解决这些问题的两个突出扩展是子类判别分析（SDA）和混合子类判别分析（MSDA）。他们将每个类划分为子类，并在子类的基础上重新定义类内和类间的散布矩阵。本文研究如何更有效地获取子类以实现更高的类分离的问题。我们观察到子类模型之间存在显着重叠，我们假设这是不希望的。为了减少它们的重叠，我们提出了 LDA 的扩展，即面向可分离性的子类判别分析 (SSDA)，它在使用重新定义的散点矩阵应用 LDA 优化之前，采用层次聚类，使用面向可分离性的标准将类划分为子类。大量实验表明SSDA在大多数情况下比LDA、SDA和MSDA具有更好的性能。额外的实验进一步表明，在大多数情况下，SSDA 可以将数据投影到比 LDA、SDA 和 MSDA 具有更高类分离度的 LDA 空间中。