Robust and Efficient Fuzzy C-Means Clustering Constrained on Flexible Sparsity

Abstract

Clustering is an effective technique in data mining to group a set of objects in terms of some attributes. Among various clustering approaches, the family of K-Means algorithms gains popularity due to simplicity and efficiency. However, most of existing K-Means based clustering algorithms cannot deal with outliers well and are difficult to efficiently solve the problem embedded the L0-norm constraint. To address the above issues and improve the performance of clustering significantly, we propose a novel clustering algorithm, named REFCMFS, which develops a L2,1-norm robust loss as the data-driven item and imposes a L0-norm constraint on the membership matrix to make the model more robust and sparse flexibly. In particular, REFCMFS designs a new way to simplify and solve the L0-norm constraint without any approximate transformation by absorbing• 0 into the objective function through a ranking function. These improvements not only make REFCMFS efficiently obtain more promising performance but also provide a new tractable and skillful optimization method to solve the problem embedded the L0-norm constraint. Theoretical analyses and extensive experiments on several public datasets demonstrate the effectiveness and rationality of our proposed REFCMFS method.

Accelerated Fuzzy C-Means Clustering Based on New Affinity Filtering and Membership Scaling

“…However, all samples-centers distance computations also leads to high computing cost. Meanwhile, all samples are involved in the update of all centers by the memberships, which leads to low efficiency of FCM in the clustering process (see [18], [19])…”

“…Although the above-mentioned FCM variants usually improve the efficiency and effectiveness of the algorithms, they ignore the low efficiency in the mid-to-late stage of the clustering process. There are three reasons: 1) the convergence rate of the alternating optimization algorithm (AO) drops, when the algorithms are in the mid-to-late stage [22]; 2) the FCM variants still need to do a full inverse-distance weighting [18]; 3) all samples are still involved in the update of all centers [19]. (see detail analysis in Subsection 3.2).…”