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Feature selections techniques have been used extensively in supervised learning to choose a set of features for a data set that win facilitate and improve classification. In particular, a few techniques exist to select a different subset of feature for each known class, which we refer to as discriminative feature selection. The main objective guiding discriminative feature selection has been the ultimate performance of the classifier system. Unsupervised learning, however, is plagued by the problem of absence of the class labels. In this paper, we propose a fast algorithm for fuzzy unsupervised learning in Web mining, for the case when the attributes/features do not have the same relevance in all clusters. Being a relative of the fuzzy c-means and k-means clustering algorithms, our approach is computationally and implementationally simple, and if desired, can easily be implemented in a scalable mode in an identical manner to previous well known scalable implementations of the k-means. Most importantly, our approach learns a different set of attribute weights for each cluster. The performance of the proposed algorithm is illustrated on real collections of Web documents and Web sessions extracted from a Web server log file.