关键词: 判别性特征学习, 多维标度法, 降维, 模糊聚类, 迭代优化算法

Abstract: Traditional multidimensional scaling method achieves low dimensional embedding, which maintains the topological structure of data points but ignores the discriminability of the low dimensional embedding itself. Based on this, a novel multidimensional scaling model referred to as Discriminative Multidimensional Scaling (DMDS) was proposed to discover the cluster structure while learning the low dimensional data representation. DMDS model can make the low dimensional embedding of the same cluster closer to make the learned data representation be more discriminative. Firstly, a novel objective function corresponding to DMDS model was designed, which maintains the topology and enhances discriminability simultaneously. Secondly, the objective function was reasoned and solved, and an iterative optimization algorithm was proposed according to the reasoning process. Finally, extensive experiments were carried out on twelve open data sets, and two evaluation indices were used to evaluate the experiment results. The experimental results show that the low dimensional embedding learned by DMDS model is more discriminative. On the twelve data sets, the average accuracy of clustering is improved by 5.28% and 6.21% respectively compared with the original data representation and the traditional multidimensional scaling, and the average purity is improved by 1.59% and 1.72% respectively.

Key words: discriminative feature learning, multidimensional scaling, dimensionality reduction, fuzzy clustering, iterative optimization algorithm