A Survey on Soft Subspace Clustering <s> Introduction <s> Subspace clustering is an extension of traditional clustering that seeks to find clusters in different subspaces within a dataset. Often in high dimensional data, many dimensions are irrelevant and can mask existing clusters in noisy data. Feature selection removes irrelevant and redundant dimensions by analyzing the entire dataset. Subspace clustering algorithms localize the search for relevant dimensions allowing them to find clusters that exist in multiple, possibly overlapping subspaces. There are two major branches of subspace clustering based on their search strategy. Top-down algorithms find an initial clustering in the full set of dimensions and evaluate the subspaces of each cluster, iteratively improving the results. Bottom-up approaches find dense regions in low dimensional spaces and combine them to form clusters. This paper presents a survey of the various subspace clustering algorithms along with a hierarchy organizing the algorithms by their defining characteristics. We then compare the two main approaches to subspace clustering using empirical scalability and accuracy tests and discuss some potential applications where subspace clustering could be particularly useful. <s> BIB001 </s> A Survey on Soft Subspace Clustering <s> Introduction <s> Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the profusion of options causes confusion. We survey clustering algorithms for data sets appearing in statistics, computer science, and machine learning, and illustrate their applications in some benchmark data sets, the traveling salesman problem, and bioinformatics, a new field attracting intensive efforts. Several tightly related topics, proximity measure, and cluster validation, are also discussed. <s> BIB002 </s> A Survey on Soft Subspace Clustering <s> Introduction <s> As a prolific research area in data mining, subspace clustering and related problems induced a vast quantity of proposed solutions. However, many publications compare a new proposition—if at all—with one or two competitors, or even with a so-called “naive” ad hoc solution, but fail to clarify the exact problem definition. As a consequence, even if two solutions are thoroughly compared experimentally, it will often remain unclear whether both solutions tackle the same problem or, if they do, whether they agree in certain tacit assumptions and how such assumptions may influence the outcome of an algorithm. In this survey, we try to clarify: (i) the different problem definitions related to subspace clustering in general; (ii) the specific difficulties encountered in this field of research; (iii) the varying assumptions, heuristics, and intuitions forming the basis of different approaches; and (iv) how several prominent solutions tackle different problems. <s> BIB003 </s> A Survey on Soft Subspace Clustering <s> Introduction <s> Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms into a system of ranked taxa: domain, kingdom, phylum, class, etc. Cluster analysis is the formal study of methods and algorithms for grouping, or clustering, objects according to measured or perceived intrinsic characteristics or similarity. Cluster analysis does not use category labels that tag objects with prior identifiers, i.e., class labels. The absence of category information distinguishes data clustering (unsupervised learning) from classification or discriminant analysis (supervised learning). The aim of clustering is to find structure in data and is therefore exploratory in nature. Clustering has a long and rich history in a variety of scientific fields. One of the most popular and simple clustering algorithms, K-means, was first published in 1955. In spite of the fact that K-means was proposed over 50 years ago and thousands of clustering algorithms have been published since then, K-means is still widely used. This speaks to the difficulty in designing a general purpose clustering algorithm and the ill-posed problem of clustering. We provide a brief overview of clustering, summarize well known clustering methods, discuss the major challenges and key issues in designing clustering algorithms, and point out some of the emerging and useful research directions, including semi-supervised clustering, ensemble clustering, simultaneous feature selection during data clustering, and large scale data clustering. <s> BIB004 </s> A Survey on Soft Subspace Clustering <s> Introduction <s> Subspace clustering finds sets of objects that are homogeneous in subspaces of high-dimensional datasets, and has been successfully applied in many domains. In recent years, a new breed of subspace clustering algorithms, which we denote as enhanced subspace clustering algorithms, have been proposed to (1) handle the increasing abundance and complexity of data and to (2) improve the clustering results. In this survey, we present these enhanced approaches to subspace clustering by discussing the problems they are solving, their cluster definitions and algorithms. Besides enhanced subspace clustering, we also present the basic subspace clustering and the related works in high-dimensional clustering. <s> BIB005
Despite extensive studies of clustering techniques over the past decades in various application areas like statistics, machine learning and database BIB002 BIB004 , the conventional clustering techniques fall short when clustering is performed in high dimensional spaces BIB001 BIB005 BIB003 . A key challenge to most clustering algorithms is that, in many real world problems, data points in different clusters are often correlated with some subsets of features, i.e., clusters may exist in different subspaces or a certain subspace of all features. Therefore, for any given pair of data points within the same cluster, it is possible that the points are indeed far apart from each other in a few dimensions of high dimensional space.