A Survey on Soft Subspace Clustering <s> Other Model based ISSC <s> [Read before The Royal Statistical Society at a meeting organized by the Research Section on Wednesday, May 5th, 2004, Professor J. T. Kent in the Chair ] Summary. A new procedure is proposed for clustering attribute value data. When used in conjunction with conventional distance-based clustering algorithms this procedure encourages those algorithms to detect automatically subgroups of objects that preferentially cluster on subsets of the attribute variables rather than on all of them simultaneously. The relevant attribute subsets for each individual cluster can be different and partially (or completely) overlap with those of other clusters. Enhancements for increasing sensitivity for detecting especially low cardinality groups clustering on a small subset of variables are discussed. Applications in different domains, including gene expression arrays, are presented. <s> BIB001 </s> A Survey on Soft Subspace Clustering <s> Other Model based ISSC <s> This paper presents a new k-means type algorithm for clustering high-dimensional objects in sub-spaces. In high-dimensional data, clusters of objects often exist in subspaces rather than in the entire space. For example, in text clustering, clusters of documents of different topics are categorized by different subsets of terms or keywords. The keywords for one cluster may not occur in the documents of other clusters. This is a data sparsity problem faced in clustering high-dimensional data. In the new algorithm, we extend the k-means clustering process to calculate a weight for each dimension in each cluster and use the weight values to identify the subsets of important dimensions that categorize different clusters. This is achieved by including the weight entropy in the objective function that is minimized in the k-means clustering process. An additional step is added to the k-means clustering process to automatically compute the weights of all dimensions in each cluster. The experiments on both synthetic and real data have shown that the new algorithm can generate better clustering results than other subspace clustering algorithms. The new algorithm is also scalable to large data sets. <s> BIB002
In addition to the FCM/K-Means and mixture model based ISSC algorithms, other ISSC algorithms have also been proposed. Among them, the Clustering Objects on Subsets of Attributes (COSA) is a representative algorithm which was proposed by Friedman and Meulman BIB001 with the following objective function. where i  are the cluster weights and i n is the number of objects assigned to the ith cluster. COSA is an entropy-based subspace clustering algorithm. As discussed in BIB002 , a shortcoming of COSA is that it may not be scalable to accommodate large data sets.