In this paper, a new unsupervised metric learning algorithm with real-world application in clustering is proposed. To have a desirable clustering, the separability among different classes of data needs to be improved. A common manner in accomplishing this objective is to utilize the advantages of metric learning in clustering and vice versa. Clustering provides an estimation of class labels and metric learning maximizes the separability among these different estimated classes of data. This procedure is performed in an iterative fashion, alternating between clustering and metric learning. Here, a new method is proposed, called discriminative fuzzy c-means (Dis-FCM), in which FCM and metric learning are integrated into one joint formulation. Unlike traditional approaches, which simply alternate between clustering and metric learning, Dis-FCM applies both simultaneously. Here, FCM provides an estimation of class labels. This can avoid the problem of fast convergence, which is common in previous algorithm. Moreover, Dis-FCM is able to handle not only numerical data, but also categorical data, which are not found in traditional methods. The experimental results indicate its superiority over other state-of-the-art algorithms in terms of extrinsic and intrinsic clustering measures.

中文翻译：

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判别式模糊 C 均值作为大边距无监督度量学习

在本文中，提出了一种在聚类中具有实际应用的新的无监督度量学习算法。为了获得理想的聚类，需要提高不同类别数据之间的可分离性。实现这一目标的一种常见方式是利用度量学习在聚类中的优势，反之亦然。聚类提供了类标签的估计，度量学习最大化了这些不同估计数据类之间的可分离性。该过程以迭代方式执行，在聚类和度量学习之间交替进行。在这里，提出了一种称为判别模糊 c 均值 (Dis-FCM) 的新方法，其中将 FCM 和度量学习集成到一个联合公式中。与简单地在聚类和度量学习之间交替的传统方法不同，Dis-FCM 同时适用。在这里，FCM 提供了类标签的估计。这样可以避免之前算法常见的收敛速度快的问题。此外，Dis-FCM 不仅能够处理数值数据，还能够处理传统方法中没有的分类数据。实验结果表明它在外在和内在聚类措施方面优于其他最先进的算法。