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Big data with a large number of observations (samples) have posed genuine challenges for fuzzy clustering algorithms and fuzzy C-means (FCM), in particular. In this article, we propose an original algorithm referred to as a hyperplane division method to split the entire data set into disjoint subsets. By disjoint subsets, we mean that the data subspaces (parts of the entire data space), each of which is supported or spanned by the data points in the corresponding subset, do not overlap each other. The disjoint subsets turned out to be beneficial to the improvement of the quality of the clusters formed by the clustering algorithms. Moreover, considering that either a large number (say, thousands) or a small number (say, a few) of clusters may be pursued in the clustering task, we propose corresponding strategies (based on the hyperplane division method) to make clustering processes feasible, efficient, and effective. By validating the proposed strategies on both synthetic and publicly available data, we show their superiority (in terms of both efficiency and effectiveness) manifested in a visible way over the method of clustering the entire data and over some representative big data clustering methods. [ABSTRACT FROM AUTHOR]

In this study, we discuss a design of fuzzy associative structures (memories) realized within the framework of fuzzy clustering. Associative memories are inherently direction-free structures (and the recall of objects can be realized for any variable or a subset of variables). Fuzzy clustering being direction-free comes here as a sound design alternative. Two recall proposals are studied: one involves prototypes (being the key descriptors of the structure of the data) and their activation in the presence of partially available data to be recalled whereas the second proposal involves fuzzy correlation matrices and in principle exhibits some resemblance with a standard correlation associative memories. In the setting of associative memories, Fuzzy C-Means (FCM) is studied. The recall error is discussed with regard to the essential parameters of the FCM (the number of clusters and the fuzzification coefficient). Furthermore we discuss an optimization of the distance function used in the clustering algorithm realized with regard to the recall error. Experimental results are provided along with a comparative study involving correlation-based associative memories. [ABSTRACT FROM AUTHOR]

In this study, we introduce a concept of hierarchical granular clustering and establish its algorithmic framework. We show that the proposed model naturally gives rise to information granules that are both of higher order and higher type, offering a compelling justification behind their emergence. In a concise way, we can capture the overall architecture of information granules as a hierarchy exhibiting conceptual layers of increasing abstraction: numeric data → information granules → information granules of type-2, order-2 → … information granules of higher type/order. The elevated type of information granules is reflective of the visible hierarchical facet of processing and the inherent diversity of the individual locally revealed structures in data. While the concept and the methodology deliver some general settings, the detailed algorithmic aspects are discussed in detail when using fuzzy clustering realized by means of fuzzy c-means. Furthermore, for illustrative purposes, we mainly focus on interval-valued fuzzy sets and granular interval fuzzy sets arising at the higher level of the hierarchy. Higher type fuzzy sets are formed with the help of the principle of justifiable granularity. The conceptually sound hierarchy is established in a general way, which makes it equally applicable to various formalisms of representation of information granules. Experiments are reported for synthetic and publicly available datasets. [ABSTRACT FROM AUTHOR]

Clustering is a powerful vehicle to reveal and visualize structure of data. When dealing with time series, selecting a suitable measure to evaluate the similarities/dissimilarities within the data becomes necessary and subsequently it exhibits a significant impact on the results of clustering. This selection should be based upon the nature of time series and the application itself. When grouping time series based on their shape information is of interest (shape-based clustering), using a Dynamic Time Warping (DTW) distance is a desirable choice. Using stretching or compressing segments of temporal data, DTW determines an optimal match between any two time series. In this way, time series exhibiting similar patterns occurring at different time periods, are considered as being similar. Although DTW is a suitable choice for comparing data with respect to their shape information, calculating the average of a collection of time series (which is required in clustering methods) based on this distance becomes a challenging problem. As the result, employing clustering techniques like K-Means and Fuzzy C-Means (where the cluster centers – prototypes are calculated through averaging the data) along with the DTW distance is a challenging task and may produce unsatisfactory results. In this study, three alternatives for fuzzy clustering of time series using DTW distance are proposed. In the first method, a DTW-based averaging technique proposed in the literature, has been applied to the Fuzzy C-Means clustering. The second method considers a Fuzzy C-Medoids clustering, while the third alternative comes as a hybrid technique, which exploits the advantages of both the Fuzzy C-Means and Fuzzy C-Medoids when clustering time series. Experimental studies are reported over a set of time series coming from the UCR time series database. [ABSTRACT FROM AUTHOR]

In the framework of Axiomatic Fuzzy Set (AFS) theory, we propose a new approach to data clustering. The objective of this clustering is to adhere to some principles of grouping exercised by humans when determining a structure in data. Compared with other clustering approaches, the proposed approach offers more detailed insight into the cluster's structure and the underlying decision making process. This contributes to the enhanced interpretability of the results via the representation capabilities of AFS theory. The effectiveness of the proposed approach is demonstrated by using real-world data, and the obtained results show that the performance of the clustering is comparable with other fuzzy rule-based clustering methods, and benchmark fuzzy clustering methods FCM and K -means. Experimental studies have shown that the proposed fuzzy clustering method can discover the clusters in the data and help specify them in terms of some comprehensive fuzzy rules. [ABSTRACT FROM AUTHOR]