A survey on soft subspace clustering

Abstract

Subspace clustering (SC) is a promising technology involving clusters that are identified based on their association with subspaces in high-dimensional spaces. SC can be classified into hard subspace clustering (HSC) and soft subspace clustering (SSC). While HSC algorithms have been studied extensively and are well accepted by the scientific community, SSC algorithms are relatively new. However, as they are said to be more adaptable than their HSC counterparts, SSC algorithms have been attracting more attention in recent years. A comprehensive survey of existing SSC algorithms and recent developments in the field are presented in this paper. SSC algorithms have been systematically classified into three main categories: conventional SSC (CSSC), independent SSC (ISSC), and extended SSC (XSSC). The characteristics of these algorithms are highlighted and potential future developments in the area of SSC are discussed. Through a comprehensive review of SSC, this paper aims to provide readers with a clear profile of existing SSC methods and to foster the development of more effective clustering technologies and significant research in this area.As discussed previously, SSC algorithms can be broadly classified into three main categories: CSSC, ISSC, and XSSC. Each of these categories can be further divided into subcategories based on the clustering mechanisms that are adopted, as shown in Table 3. In CSSC, clustering is performed by first identifying the subspace using some strategies, and then carrying out clustering in the subspace that was obtained, in order to partition the data. This is referred to as separated feature weighting, where data partitioning involves two separate processessubspace identification and clustering in subspace. Clustering can also be conducted by performing the two processes simultaneously, an approach known as coupled feature weighting. In ISSC, algorithms are developed based on the K-means model, fuzzy C-means (FCM) model, and probability mixture model, in a process where fuzzy weighting, entropy weighting, or other weighting mechanisms are adopted to implement feature weighting. Finally, XSSC algorithms can be subdivided into eight subcategories, depending on the strategies used to enhance the CSSC and ISSC algorithms. These subcategories are between-class separation, evolutionary learning, the adoption of new metrics, ensemble learning, multi-view learning, imbalanced * Denotes the values achieved by each algorithm when the lowest value of the loss function is obtained within the 10 runs.

Concise Fuzzy System Modeling Integrating Soft Subspace Clustering and Sparse Learning

“…Many SSC algorithms have been proposed to cluster highdimensional data and to find the important subspace for each group [44][45][46]. Unlike most existing SSC algorithms that only 1063-6706 (c) 2018 IEEE.…”

An Entropy Regularization k-Means Algorithm with a New Measure of between-Cluster Distance in Subspace Clustering

“…The research on subspace clustering [24] has always been an important direction in clustering algorithms. In order to achieve high performance, many methods, such as sparse clustering-based methods [25][26][27], weight entropy-based methods [16,28], between-cluster information-based methods [29][30][31], and so on, have been proposed.…”

“…Similar to [16], assume that we have U t 1 = U t 2 , where t 1 = t 2 and t i represents the number of iterations. Then, based on U t i , we can obtain Z t i by minimizing Q(W, U t i , Z) according to (24). Subsequently, Z t 1 and Z t 2 are obtained respectively, and furthermore, Z t 1 = Z t 2 because U t 1 = U t 2 .…”

A Review of Feature Selection Techniques for Clustering High Dimensional Structured Data

“…Several new subspace clustering methods were developed after CLIQUE. In clustering, many clusters may exist in different subspaces for small dimensionality with overlapped or non-overlapped dimensions [2]. Subspace searching is not only the feature selection problem.…”