A Survey on Soft Subspace Clustering <s> (2) EFWSSC <s> In fuzzy clustering algorithms each object has a fuzzy membership associated with each cluster indicating the degree of association of the object to the cluster. Here we present a fuzzy subspace clustering algorithm, FSC, in which each dimension has a weight associated with each cluster indicating the degree of importance of the dimension to the cluster. Using fuzzy techniques for subspace clustering, our algorithm avoids the difficulty of choosing appropriate cluster dimensions for each cluster during the iterations. Our analysis and simulations strongly show that FSC is very efficient and the clustering results produced by FSC are very high in accuracy. <s> BIB001 </s> A Survey on Soft Subspace Clustering <s> (2) EFWSSC <s> We establish the convergence of the fuzzy subspace clustering (FSC) algorithm by applying Zangwill's convergence theorem. We show that the iteration sequence produced by the FSC algorithm terminates at a point in the solution set S or there is a subsequence converging to a point in S. In addition, we present experimental results that illustrate the convergence properties of the FSC algorithm in various scenarios. <s> BIB002 </s> A Survey on Soft Subspace Clustering <s> (2) EFWSSC <s> While within-cluster information is commonly utilized in most soft subspace clustering approaches in order to develop the algorithms, other important information such as between-cluster information is seldom considered for soft subspace clustering. In this study, a novel clustering technique called enhanced soft subspace clustering (ESSC) is proposed by employing both within-cluster and between-class information. First, a new optimization objective function is developed by integrating the within-class compactness and the between-cluster separation in the subspace. Based on this objective function, the corresponding update rules for clustering are then derived, followed by the development of the novel ESSC algorithm. The properties of this algorithm are investigated and the performance is evaluated experimentally using real and synthetic datasets, including synthetic high dimensional datasets, UCI benchmarking datasets, high dimensional cancer gene expression datasets and texture image datasets. The experimental studies demonstrate that the accuracy of the proposed ESSC algorithm outperforms most existing state-of-the-art soft subspace clustering algorithms. <s> BIB003
Using a similar strategy, Guan improved the FSC algorithm BIB001 BIB002 by making use of between-cluster separation and proposed the Enhanced Fuzzy Weighting Soft Subspace Clustering (EFWSSC) algorithm  . The objective function of the algorithm is Similarly, when 1 m  and 0   , the EFWSSC algorithm degenerates into the FSC algorithm, i.e., the FSC algorithm is as a special case of the EFWSSC algorithm.  Although the IEWKM algorithm here and the ESSC algorithm BIB003 are both based on EWKM and they both employ the between-cluster separation, the former is much more difficult to be optimized. Besides, from the viewpoint of optimization, the learning rules for the cluster centers in the IEWKM algorithm lack rigorous derivation  .