Search

Fuzzy C-Means is a clustering algorithm widely used in many applications. However, its computational complexity is very large, which prevents its use for large problem instances. Therefore, a hybrid improvement is proposed for the algorithm, which considerably reduces the number of iterations and, in many cases, improves the solution quality, expressed as the value of the objective function. This improvement integrates two heuristics, one in the initialization phase and the other in the convergence phase or the convergence criterion. This improvement was called HPFCM. A set of experiments was designed to validate this proposal; to this end, four sets of real data were solved from a prestigious repository. The solutions obtained by HPFCM were compared against those of the Fuzzy C-Means algorithm. In the best case, reductions of an average of 97.65% in the number of required iterations and an improvement in quality solution of 82.42% were observed when solving the SPAM dataset. Finally, we consider that the proposed heuristics may inspire improvements in other specific purpose variants of Fuzzy C-Means.

One of the most used algorithms to solve the fuzzy clustering problem is Fuzzy C-Means; however, one of its main limitations is its high computational complexity. It is known that the efficiency of an algorithm depends, among other factors, on the strategies for its initialization and convergence. In this research, a new convergence strategy is proposed, which is based on the difference of the objective function values, in two consecutive iterations, expressed as a percentage of its value in the next to the last one. Additionally, a new method is proposed to optimize the selection of values of the convergence or stop threshold of the algorithm, which is based on the Pareto principle. To validate our approach, a collection of real datasets was solved, and a significant reduction in the number of iterations was observed, without affecting significantly the solution quality. Based on the proposed method and the experiments carried out, we found it is convenient to use threshold values equal to 0.73 and 0.35 if a decrease in the number of iterations of approximately 75.2% and 64.56%, respectively, is wanted, at the expense of a reduction in solution quality of 2% and 1%, respectively. It is worth mentioning that, as the size of the datasets is increased, the proposed approach tends to obtain better results, and therefore, its use is suggested for datasets found in Big Data and Data Science.

Clustering algorithms have proven to be a useful tool to extract knowledge and support decision making by processing large volumes of data. Hard and fuzzy clustering algorithms have been used successfully to identify patterns and trends in many areas, such as finance, healthcare, and marketing. However, these algorithms significantly increase their solution time as the size of the datasets to be solved increase, making their use unfeasible. In this sense, the parallel processing of algorithms has proven to be an efficient alternative to reduce their solution time. It has been established that the parallel implementation of algorithms requires its redesign to optimise the hardware resources of the platform that will be used. In this article, we propose a new parallel implementation of the Hybrid OK-Means Fuzzy C-Means (HOFCM) algorithm, which is an efficient variant of Fuzzy C-Means, in OpenMP. An advantage of using OpenMP is its scalability. The efficiency of the implementation is compared against the HOFCM algorithm. The experimental results of processing large real and synthetic datasets show that our implementation tends to more efficiently solve instances with a large number of clusters and dimensions. Additionally, the implementation shows excellent results concerning speedup and parallel efficiency metrics. Our main contribution is a Fuzzy clustering algorithm for large datasets that is scalable and not limited to a specific domain.

A hybrid variant of the Fuzzy C-Means and K-Means algorithms is proposed to solve large datasets such as those presented in Big Data. The Fuzzy C-Means algorithm is sensitive to the initial values of the membership matrix. Therefore, a special configuration of the matrix can accelerate the convergence of the algorithm. In this sense, a new approach is proposed, which we call Hybrid OK-Means Fuzzy C-Means (HOFCM), and it optimizes the values of the membership matrix parameter. This approach consists of three steps: (a) generate a set of n solutions of an x dataset, applying a variant of the K-Means algorithm; (b) select the best solution as the basis for generating the optimized membership matrix; (c) resolve the x dataset with Fuzzy C-Means. The experimental results with four real datasets and one synthetic dataset show that HOFCM reduces the time by up to 93.94% compared to the average time of the standard Fuzzy C-Means. It is highlighted that the quality of the solution was reduced by 2.51% in the worst case.