Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology, Sydney, Australia.
IEEE Trans Pattern Anal Mach Intell. 2011 May;33(5):1037-50. doi: 10.1109/TPAMI.2010.189.
We propose a new criterion for discriminative dimension reduction, max-min distance analysis (MMDA). Given a data set with C classes, represented by homoscedastic Gaussians, MMDA maximizes the minimum pairwise distance of these C classes in the selected low-dimensional subspace. Thus, unlike Fisher's linear discriminant analysis (FLDA) and other popular discriminative dimension reduction criteria, MMDA duly considers the separation of all class pairs. To deal with general case of data distribution, we also extend MMDA to kernel MMDA (KMMDA). Dimension reduction via MMDA/KMMDA leads to a nonsmooth max-min optimization problem with orthonormal constraints. We develop a sequential convex relaxation algorithm to solve it approximately. To evaluate the effectiveness of the proposed criterion and the corresponding algorithm, we conduct classification and data visualization experiments on both synthetic data and real data sets. Experimental results demonstrate the effectiveness of MMDA/KMMDA associated with the proposed optimization algorithm.
我们提出了一种新的判别降维准则，即极大极小距离分析（MMDA）。给定一个具有 C 个类别的数据集，由同方差高斯分布表示，MMDA 最大化所选低维子空间中这些 C 个类别的最小成对距离。因此，与 Fisher 的线性判别分析（FLDA）和其他流行的判别降维准则不同，MMDA 适当考虑了所有类对的分离。为了处理数据分布的一般情况，我们还将 MMDA 扩展到核 MMDA（KMMDA）。通过 MMDA/KMMDA 进行降维会导致具有正交约束的非平滑极大极小优化问题。我们开发了一种顺序凸松弛算法来近似求解它。为了评估所提出的准则和相应算法的有效性，我们在合成数据集和真实数据集上进行了分类和数据可视化实验。实验结果表明，所提出的优化算法与 MMDA/KMMDA 相关联具有有效性。
