Yang Le, Song Shiji, Li Shuang, Chen Yiming, Chen C L Philip
IEEE Trans Cybern. 2021 Aug;51(8):4100-4111. doi: 10.1109/TCYB.2019.2912806. Epub 2021 Aug 4.
In this paper, we propose a novel discriminative dimension reduction (DR) method, maximin separation probability analysis (MSPA), which maximizes the minimum separation probability of all classes in the reduced low-dimensional subspace. Separation probability is a novel class separability measure, which gives a lower bound of the generalization accuracy for a learned linear classifier in a binary classification problem. The proposed MSPA duly considers the separation of all class pairs in multiclass linear discriminant analysis (LDA) and thus improves the subsequent classification performance. DR via MSPA leads to a nonconvex optimization problem. We develop an algorithm to solve the problem and the global optimal solution can be found by converting the original problem into a series of second-order cone programming problems. A low-computational cost extension and a non-LDA with kernel mapping of MSPA are also provided in this paper. The experimental results on 14 real-world datasets show our methods are superior to other state-of-the-art algorithms in discriminative DR tasks.
在本文中，我们提出了一种新颖的判别式降维（DR）方法——最大最小分离概率分析（MSPA），该方法能在降维后的低维子空间中最大化所有类别的最小分离概率。分离概率是一种新颖的类可分离性度量，它给出了二分类问题中学习到的线性分类器泛化准确率的下限。所提出的MSPA在多类线性判别分析（LDA）中充分考虑了所有类对之间的分离，从而提高了后续的分类性能。通过MSPA进行降维会导致一个非凸优化问题。我们开发了一种算法来解决该问题，通过将原始问题转化为一系列二阶锥规划问题可以找到全局最优解。本文还提供了一种低计算成本的扩展方法以及一种具有核映射的非LDA形式的MSPA。在14个真实世界数据集上的实验结果表明，我们的方法在判别式降维任务中优于其他现有最先进算法。
