Clustering algorithms with new automatic variables weighting

Abstract

Every day a large amount of information is stored or represented as data for further analysis and management. Data analysis plays an indispensable role in understanding different phenomena. One of the vital means of handling these data is to classify or group them into a set of categories or clusters. Clustering or cluster analysis aims to divide a collection of data items into clusters given a measure of similarity. Clustering has been used in various fields, such as image processing, data mining, pattern recognition, and statistical analysis. Usually, clustering methods deal with objects described by real-valued variables. Nevertheless, this representation is too restrictive for representing complex data, such as lists, histograms, or even intervals. Furthermore, in some problems, many dimensions are irrelevant and can mask existing clusters, e.g., groups may exist in different subsets of features. This work focuses on the clustering analysis of data points described by both real-valued and interval-valued variables. In this regard, new clustering algorithms have been proposed, in which the correlation and relevance of variables are considered to improve their performance. In the case of interval- valued data, we assume that the boundaries of the interval-valued variables have the same and different importance for the clustering process. Since regularization-based methods are robust for initializations, the proposed approaches introduce a regularization term for controlling the membership degree of the objects. Such regularizations are popular due to high performance in large-scale data clustering and low computational complexity. These three-step iterative algorithms provide a fuzzy partition, a representative for each cluster, and the relevance weight of the variables or their correlation by minimizing a suitable objective function. Experiments on synthetic and real datasets corroborate the robustness and usefulness of the proposed clustering methods.