Discriminative Fuzzy C-Means as a Large Margin Unsupervised Metric Learning Algorithm

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.