High-dimensional non-Gaussian data are ubiquitous in many real applications. Face recognition is a typical example of such scenarios. The sampled face images of each person in the original data space are more closely located to each other than to those of the same individuals due to the changes of various conditions like illumination, pose variation, and facial expression. They are often non-Gaussian and differentiating the importance of each data point has been recognized as an effective approach to process the high-dimensional non-Gaussian data. In this paper, to embed non-Gaussian data well, we propose a novel unified framework named adaptive discriminative analysis (ADA), which combines the sample’s importance measurement and subspace learning in a unified framework. Therefore, our ADA can preserve the within-class local structure and learn the discriminative transformation functions simultaneously by minimizing the distances of the projected samples within the same classes while maximizing the between-class separability. Meanwhile, an efficient method is developed to solve our formulated problem. Comprehensive analyses, including convergence behavior and parameter determination, together with the relationship to other related approaches, are as well presented. Systematical experiments are conducted to understand the work of our proposed ADA. Promising experimental results on various types of real-world benchmark data sets are provided to examine the effectiveness of our algorithm. Furthermore, we have also evaluated our method in face recognition. They all validate the effectiveness of our method on processing the high-dimensional non-Gaussian data.

中文翻译：

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基于自适应判别分析的非高斯数据降维

高维非高斯数据在许多实际应用中无处不在。人脸识别是这种情况的典型示例。由于光照，姿势变化和面部表情等各种条件的变化，原始数据空间中每个人的采样脸部图像比同一个人的脸部图像更靠近彼此。它们通常是非高斯的，区分每个数据点的重要性已被认为是处理高维非高斯数据的有效方法。在本文中，为了很好地嵌入非高斯数据，我们提出了一个名为自适应判别分析（ADA）的新型统一框架，该框架将样本的重要性测量和子空间学习结合在一个统一框架中。所以，我们的ADA可以通过最小化同一类内的投影样本之间的距离，同时最大化类间的可分离性，来保留类内的局部结构并同时学习判别式转换函数。同时，开发了一种有效的方法来解决我们提出的问题。还介绍了综合分析，包括收敛行为和参数确定，以及与其他相关方法的关系。进行系统实验以了解我们提出的ADA的工作。提供了关于各种类型的实际基准数据集的有希望的实验结果，以检验我们算法的有效性。此外，我们还评估了我们在人脸识别中的方法。