Abstract A novel dimensionality reduction method, similarity order preserving discriminant analysis, is proposed to process high-dimensional data in this communication. Different from the collaborative representation or sparse representation based dimensionality reduction method, we use the pairwise similarity and within-class similarity order to define the more robust global and local structure of the sample. Also, in order to improve the discrimination of the sample in the projection space, we use a parameter to scale the between-class similarity scatter and within-class similarity order scatter. Using the graph embedding framework and the idea of maximum margin criterion, the optimal subspace projection matrix is obtained by eigenvalue decomposition. Experimental results on four public datasets demonstrate that the proposed method has encouraging performance compared to some state-of-the-art dimensionality reduction methods.

中文翻译：

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一种新的降维方法：相似顺序保持判别分析

摘要 提出了一种新的降维方法，即相似顺序保持判别分析，用于处理这种通信中的高维数据。与基于协同表示或稀疏表示的降维方法不同，我们使用成对相似度和类内相似度顺序来定义样本的更稳健的全局和局部结构。此外，为了提高投影空间中样本的区分度，我们使用一个参数来缩放类间相似度散布和类内相似度顺序散布。利用图嵌入框架和最大边距准则的思想，通过特征值分解得到最优子空间投影矩阵。