Similarity-based clustering methods separate data into clusters according to the pairwise similarity between the data, and the pairwise similarity is crucial for their performance. In this paper, we propose Clustering by Discriminative Similarity (CDS), a novel method which learns discriminative similarity for data clustering. CDS learns an unsupervised similarity-based classifier from each data partition, and searches for the optimal partition of the data by minimizing the generalization error of the learnt classifiers associated with the data partitions. By generalization analysis via Rademacher complexity, the generalization error bound for the unsupervised similarity-based classifier is expressed as the sum of discriminative similarity between the data from different classes. It is proved that the derived discriminative similarity can also be induced by the integrated squared error bound for kernel density classification. In order to evaluate the performance of the proposed discriminative similarity, we propose a new clustering method using a kernel as the similarity function, CDS via unsupervised kernel classification (CDSK), with its effectiveness demonstrated by experimental results.

本文提出了一种名称为 CDS 的新的聚类方法，其使用学习出的判别式相似度对数据集进行无监督聚类，并通过 Rademacher 复杂度对其进行了一般化分析。同时，使用核密度分类的积分平方误差界也可以导出所得到的判别相似度。在使用核函数作为相似度函数的情况下，使用 CDS 聚类方法的有效性已通过实验结果得到证明。

数据聚类的判别相似度