Fuzzy Data Clustering Research Articles

Some new fuzzy query processing methods based on similarity measurement and fuzzy data clustering

In relational and object-oriented database systems there is always data that is naturally fuzzy or uncertain. However, to deal with complex data types with fuzzy nature, these systems have many limitations. Therefore, in order to represent and manage fuzzy data, it is necessary to have a fuzzy interrogation system to facilitate non-expert users. To solve this challenge, the paper proposes two different approaches to increase the flexibility of the fuzzy interrogation system. Firstly, based on similarity measures and fuzzy logic, we develop three fuzzy query processing algorithms for single-condition and multi-condition cases such as FQSIMSC (Fuzzy Query Sim Single Condition), FQSIMMC (Fuzzy Query Sim Multi-Condition) and FQSEM (Fuzzy Query SEM). Secondly, we combine the fuzzy clustering algorithm EMC (Expectation maximization Coefficient) and the query processing algorithm that is based on fuzzy partitions FQINTERVAL (Fuzzy Query Interval). With this approach, we not only improve query processing cost but also support applications and devices equipped with intelligent interactive function that easily interacts with the fuzzy query system. The results of our theoretical and experimental analysis, it can be seen that both the proposed methods significantly reduce the processing time and memory space for a data set (extracted from UCI) that has a fuzzy and incomplete natural element with the resulting data size being optimal

CREDIBILISTIC ROBUST ONLINE FUZZY CLUSTERING IN DATA STREAM MINING TASKS

Context. The task of clustering-classification without a teacher of data arrays occupies an important place in the general problem of Data Mining, and for its solution there exists currently many approaches, methods and algorithms. There are quite a lot of situations where the real data to be clustered are corrupted with anomalous outliers or disturbances with non-Gaussian distributions. It is clear that “classical” methods of artificial intelligence (both batch and online) are ineffective in this situation. The goal of the paper is to develop a credibilistic robust online fuzzy clustering method that combines the advantages of credibilistic and robust approaches in fuzzy clustering tasks.
 Objective. The goal of the work is online credibilistic fuzzy clustering of distorted data, using of credibility theory in data stream mining.
 Method. The procedure of fuzzy clustering of data using credibilistic approach based on the use of both robust goal functions of a special type, insensitive to outliers and designed to work both in batch and its recurrent online version designed to solve Data Stream Mining problems when data are fed to processing sequentially in real time.
 Results. Analyzing the obtained results overall accuracy of clustering methods and algorithm, proposed method similar with result of credibilistic fuzzy clustering method, but has time superiority regardless of the number observations that fed on clustering process.
 Conclusions. The problem of fuzzy clustering of data streams contaminated by anomalous non-Gaussian distributions is considered. A recurrent credibilistic online algorithm based on the objective function of a special form is introduced, which suppresses these outliers by using the hyperbolic tangent function, which, in addition to neural networks, is used in robust estimation tasks. The proposed algorithm is quite simple in numerical implementation and is a generalization of some well-known online fuzzy clustering procedures intended for solving Data Stream Mining problems.

Two-Dimensional Embedded Fuzzy Data Clustering

Fuzzy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -means (FKM) is a popular clustering method by assigning data points into respective clusters with uncertainty measured by the membership degree. Usually, FKM performs clustering according to the distance between data points in the original space, which might contain undesirable noises and redundant features; therefore, the underlying data semantic connections cannot be accurately captured. Moreover, the vectorized representation of the two-dimensional data such as image inevitably leads to the loss of structural information. In this paper, we propose a novel FKM method termed two-dimensional embedded fuzzy data clustering (2DEFC) which has two merits. First, 2DEFC directly takes 2D data as input without vectorizing them in order to retain more structural information of data. Second, the two subspace projection matrices are jointly optimized with the data membership degree for better collaborating with each other, which effectively avoids the sub-optimality limitation caused by the conventional mode of sequentially performing dimensionality reduction and clustering. An efficient algorithm is proposed to optimize the 2DEFC objective function. Besides, we provide comprehensive analysis on 2DEFC including its convergence behavior, computational complexity, and the fuzzy weighting exponent. Extensive comparative studies on benchmark 2D data sets demonstrate that the competitive performance of 2DEFC in 2D data clustering.

FAST FUZZY CREDIBILISTIC CLUSTERING BASED ON DENSITY PEAKS DISTRIBUTION OF DATA BROAKYSIS

Context. The problem of clustering (classification without a teacher) is often occures when processing data arrays of various natures, which is quite an interesting and integral part of artificial intelligence. To solve this problem, there are many known methods and algorithms based on the principles of the distribution density of observations in the analyzed data. However, these methods are rather complicated in software implementation and are not without drawbacks, namely: the problem of determining significant clusters in datasets of different densities, multiepoch self-learning, getting stuck in local extrema of goal functions, etc. It should be noted that the methods based on the analysis of the peaks of the data distribution density are clear in nature, therefore, to expand the capabilities of these methods, it is advisable to introduce their fuzzy modification. Objective. The aim of the work is to introduce fast fuzzy data clustering using density peaks distribution of the datasets, that can find the prototypes (centroids) of clusters that overlapping regardless of the amount of incoming data. Method. The problem of fuzzy clustering data arrays based on a hybrid method that based on the simultaneous use of a credibilistic approach to fuzzy clustering and an algorithm for finding the types of distribution density of the initial data is proposed. A feature of the proposed method is computational simplicity and high speed, due to the fact that the entire array is processed only once, that is, eliminates the need for multi-era self-learning, implemented in traditional fuzzy clustering algorithms. Results. A feature of the proposed method of fast fuzzy credibilistic clustering using of density peaks distribution is characterized by computational simplicity and high speed due to the fact that the entire array is processed only once, that is, the need for multiepoch self-learning is eliminated, which is implemented in traditional fuzzy clustering algorithms. The results of the computational experiment confirm the effectiveness of the proposed approach in clustering problems under conditions in the case when the clusters are ovelap. Conclusions. The experimental results allow us to recommend the developed method for solving the problems of automatic clustering and data classification, as quickly as possible to find the centroids of clusters. The proposed method of fast fuzzy credibilistic clustering using of density peaks distribution of dataset is intended for use in computational intelligence systems, neuro-fuzzy systems, in training artificial neural networks and in clustering problems.

Fuzzy Clustering Analysis of Power Incomplete Data based on Improved IVAEGAN Model

The scale of data generated by the complex and huge power system during operation is also very large. With the data acquisition of various information systems, it is easy to form the situation of incomplete power data information, which cannot guarantee the efficiency and quality of work, and reduce the security and reliability of the entire power grid. When incomplete data and incomplete data sets are caused by data storage failure or data acquisition errors, fuzzy clustering of data will face great difficulties. The fuzzy clustering of incomplete data of the power equipment is divided into the processing of incomplete data and the clustering analysis of "recovered" complete data. This paper proposes an IVAEGAN-IFCM interval fuzzy clustering algorithm, which uses interval data sets to fill in the incomplete data, and then completes the clustering of interval data. At the same time, the whole numerical data set is transformed into a complete interval data set. The final clustering result is obtained by interval fuzzy mean clustering analysis of the whole interval data set. Finally, the algorithm proposed in this paper and other machine learning training data sets is made for experimental analysis. The experimental results show that the algorithm proposed in this paper can complete incomplete data sets with high precision clustering. Compared with other contrast methods, it shows higher clustering accuracy. Compared with the numerical clustering algorithm, the clustering accuracy is improved by more than 4.3%, and it has better robustness. It also shows better generalization on the artificial data sets and other complex data sets. It is helpful to improve the technical level of the existing power grid and has important theoretical research value and engineering practice significance.

Cluster Data Analysis with a Fuzzy Equivalence Relation to Substantiate a Medical Diagnosis

This study aims to develop a methodology for the justification of medical diagnostic decisions based on the clustering of large volumes of statistical information stored in decision support systems. This aim is relevant since the analyzed medical data are often incomplete and inaccurate, negatively affecting the correctness of medical diagnosis and the subsequent choice of the most effective treatment actions. Clustering is an effective mathematical tool for selecting useful information under conditions of initial data uncertainty. The analysis showed that the most appropriate algorithm to solve the problem is based on fuzzy clustering and fuzzy equivalence relation. The methods of the present study are based on the use of this algorithm forming the technique of analyzing large volumes of medical data due to prepare a rationale for making medical diagnostic decisions. The proposed methodology involves the sequential implementation of the following procedures: preliminary data preparation, selecting the purpose of cluster data analysis, determining the form of results presentation, data normalization, selection of criteria for assessing the quality of the solution, application of fuzzy data clustering, evaluation of the sample, results and their use in further work. Fuzzy clustering quality evaluation criteria include partition coefficient, entropy separation criterion, separation efficiency ratio, and cluster power criterion. The novelty of the results of this article is related to the fact that the proposed methodology makes it possible to work with clusters of arbitrary shape and missing centers, which is impossible when using universal algorithms. Doi: 10.28991/esj-2021-01305 Full Text: PDF

ONLINE PROBABILISTIC FUZZY CLUSTERING METHOD BASED ON EVOLUTIONARY OPTIMIZATION OF CAT SWARM

Context. The problems of big data clustering today is a very relevant area of artificial intelligence. This task is often found in many applications related to data mining, deep learning, etc. To solve these problems, traditional approaches and methods require that the entire data sample be submitted in batch form.&#x0D; Objective. The aim of the work is to propose a method of fuzzy probabilistic data clustering using evolutionary optimization of cat swarm, that would be devoid of the drawbacks of traditional data clustering approaches.&#x0D; Method. The procedure of fuzzy probabilistic data clustering using evolutionary algorithms, for faster determination of sample extrema, cluster centroids and adaptive functions, allowing not to spend machine resources for storing intermediate calculations and do not require additional time to solve the problem of data clustering, regardless of the dimension and the method of presentation for processing.&#x0D; Results. The proposed data clustering algorithm based on evolutionary optimization is simple in numerical implementation, is devoid of the drawbacks inherent in traditional fuzzy clustering methods and can work with a large size of input information processed online in real time.&#x0D; Conclusions. The results of the experiment allow to recommend the developed method for solving the problems of automatic clustering and classification of big data, as quickly as possible to find the extrema of the sample, regardless of the method of submitting the data for processing. The proposed method of online probabilistic fuzzy data clustering based on evolutionary optimization of cat swarm is intended for use in hybrid computational intelligence systems, neuro-fuzzy systems, in training artificial neural networks, in clustering and classification problems.

Parallel FCM clustering algorithm of fuzzy number based on cut set

Aiming at the problem of complex method and low efficiency of fuzzy numbers in classification processing, a parallel Fuzzy CMeans (FCM) clustering method based on cut set is proposed. Firstly, according to the decomposition theorem, the fuzzy numbers are divided horizontally into the form of the union of interval numbers, and then the interval numbers are transformed into the determined “real” data, and the parallel FCM clustering algorithm is used to classify the fuzzy numbers. The theoretical analysis and application show that the method has good classification accuracy and efficiency for fuzzy data clustering.

Fuzzy clustering of fuzzy data based on robust loss functions and ordered weighted averaging

In many real cases the data are not expressed in term of single values but are imprecise. In all these cases, standard clustering methods for single-valued data are unable to properly take into account the imprecise nature of the data. In this paper, by considering the Partitioning Around Medoids (PAM) approach in a fuzzy framework, we propose a fuzzy clustering method for imprecise data formalized in a fuzzy manner. In particular, in order to neutralize the negative effects of possible outlier fuzzy data in the clustering process, we proposed a robust fuzzy c-medoids clustering method for fuzzy data based on the combination of Huber's M-estimators and Yager's OWA (Ordered Weighted Averaging) operators. The proposed method is able to smooth the influence of anomalous data by means of a suitable parameter, the so-called typicality parameter, capable to tune the influence of the outliers. The performance of the proposed method has been shown by means of a simulation study, composed of experiments on: (i) simple two-dimensional dataset, (ii) benchmark datasets and (iii) the fuzzy-art-outliers dataset. The comparison made with the robust clustering methods known from the literature indicates the competitiveness of the introduced method to others. An application of the suggested method to a real dataset is also provided and the results of the method has been compared with other clustering methods suggested in the literature. In the application, the comparative assessment has shown the informational gain (in term of additional information) of the proposed method vs the other robust methods.

A fuzzy clustering method for periodic data, applied for processing turbomachinery beamforming maps

In the present paper, the fuzzy c-means method is extended, and an algorithm is proposed for fuzzy clustering of data lying in a feature space of arbitrary dimensions, with one of them being periodic. To aid in determining the optimal number of clusters, the Xie-Beni validity index is extended, to account for the periodicity. Furthermore, the relative weights of the dimensions in the calculation of distances are investigated. The method is incorporated into a procedure for processing turbomachinery beamforming maps. Thus, an objective, robust way of identifying the sound sources being present in such machines is obtained. These properties are ensured by selecting the required parameters through parameter studies. Presented through a case study, the method is used to determine the most significant sound source mechanisms in an axial fan.

An interval type 2 hesitant fuzzy MCDM approach and a fuzzy c means clustering for retailer clustering

Owing to the advancements in information and telecommunication technologies, mobile location-based services are able to use previously collected mobile check-in data. This multi-dimensional data can provide new opportunities for research problems such as establishing new platforms for location-based advertising and location-based personalized recommendations. In other words, location data of potential customers indicate personal interests and visiting preferences. In some cases, customers’ preferences could not be easily determined or predicted while considering visiting patterns of mobile users. In this respect, this study provides a novel retailer segmentation approach based on multi-criteria decision-making (MCDM) combined fuzzy data clustering. The proposed model consists of two phases: (1) an interval type 2 hesitant MCDM approach for the determination of location perceived value and (2) retailer (store) clustering via different product sale prices with fuzzy data-based fuzzy c means (FcM) clustering. Proposed approach enables the simplification of FcM clustering adaptation to non-symmetric fuzzy data using dissimilarity measure. Using this integrated approach, advertisers and recommender system suppliers will be able to manage their product-special offerings to customers considering retailer segments and shopping mall characteristics. Additionally, the proposed approach constitutes the infrastructure of location-based recommender systems under imprecise environment.

Underdetermined blind separation of three-way fluorescence spectra of PAHs in water

In this work, underdetermined blind decomposition method is developed to recognize individual components from the three-way fluorescent spectra of their mixtures by using sparse component analysis (SCA). The mixing matrix is estimated from the mixtures using fuzzy data clustering algorithm together with the scatters corresponding to local energy maximum value in the time-frequency domain, and the spectra of object components are recovered by pseudo inverse technique. As an example, using this method three and four pure components spectra can be blindly extracted from two samples of their mixture, with similarities between resolved and reference spectra all above 0.80. This work opens a new and effective path to realize monitoring PAHs in water by three-way fluorescence spectroscopy technique.

Clustering of fuzzy data and simultaneous feature selection: A model selection approach

Fuzzy data occurs frequently in the fields of decision making, social sciences, and control theory. We consider the problem of clustering fuzzy data along with automatic component number detection and feature selection. A model selection criterion called minimum message length is used to address the problem of component number selection. The Bayesian framework can be adopted here, by applying an explicit prior distribution over the parameter values. We discuss both uninformative and informative priors. For the latter, a gradient descent algorithm for automatic optimization of the prior hyper-parameters is presented. The problem of simultaneous feature selection involves ordering the discriminative features according to their relative importance, and at the same time eliminating non-discriminative features. The feature selection problem is also formulated as a parameter estimation problem by extending the concept of feature saliency. Then the estimation can be computed simultaneously with the clustering steps. By combining the clustering, the cluster number detection and the feature selection into one estimation problem, we modified the fuzzy Expectation–Maximization (EM) algorithm to perform all of the estimation. Evaluation criteria are proposed and empirical study results are reported to showcase the efficacy of our proposals.

A Fuzzy Mean-Shift Approach to Lidar Waveform Decomposition

Waveform decomposition is a common step for exploitation of full-waveform lidar data. Much effort has been focused on designing algorithms based on the assumption that the returned waveforms follow a Gaussian mixture model where each component is a Gaussian. However, many real examples show that the waveform components can be neither Gaussian nor symmetric even when the emitted signal is Gaussian or symmetric. This paper proposes a nonparametric mixture model to represent lidar waveforms without any constraints on the shape of the waveform components. A fuzzy mean-shift algorithm is then developed to decompose the waveforms. This approach has the following properties: 1) It does not assume that the waveforms follow any parametric or functional distributions; 2) the waveform decomposition is treated as a fuzzy data clustering problem and the number of components is determined during the time of decomposition; and 3) neither peak selection nor noise floor filtering prior to the decomposition is needed. Experiments are conducted on a dataset collected over a dense forest area where significant skewed waveforms are demonstrated. As the result of the waveform decomposition, a highly dense point cloud is generated, followed by a subsequent filtering step to create a fine digital elevation model. Compared with the conventional expectation–maximization method, the fuzzy mean-shift approach yielded practically comparable and similar results. However, it is about three times faster and tends to lead to slightly fewer artifacts in the resultant digital elevation model.

Support of decision-making in the conditions of uncertainty of different types

At the present stage the solution to the problem of decision-making support in the conditions of uncertainty is seen in the application of decision-making support systems (DMSS), which are based on the theory of fuzzy sets and fuzzy logic. One of the most important stages of decision-making support in the conditions of uncertainty is the analysis of the accumulated statistical data. At present, the fuzzy algorithms, including the algorithms of fuzzy clustering of data, are successfully applied to effective research of such data. In recent years, for the effective solution to problems of fuzzy clustering, the device of fuzzy relations that is based on building fuzzy relations of data objects and their properties is widely and successfully used.

Application of global optimization in data clustering analisys

On the basis of global optimization methods in the system of computer mathematics «Matlab» algorithms of clear and fuzzy data clustering had developed to determine the parameters of prototypes of clusters. A method of finding the clusters boundaries was proposed. On simulated data it had been show that the cluster centers derived by algorithms based on «patternsearch» and «K-means» are the same. Applied to the processing of geological data, the developed algorithms simplify the analysis of rocks, for example, allow on the image of the rocks assess their mineral composition.

A Dolphin Herding Inspired Fuzzy Data Clustering Model and Its Applications

In this world of overwhelming data, efficient techniques are required to maintain this gigantic bulk of data. One of the renowned methods to serve this purpose is data clustering and hence is the objective of this paper. An algorithm is proposed which imitates the concept of herding, i.e., how dolphins catch their prey. It is an intelligent technique as all the data points are considered for every possible solution, providing clustering and ideal centroids in a short time. This paper presents the working of the algorithm on real datasets and extracts the results. The results of the proposed algorithm are then compared with well-known fuzzy c-means in terms of clusters formed presenting number of data items in each cluster, simplicity and coverage. The later part of the paper presents the association analysis technique on the clusters formed by the proposed approach with final section showing the cross comparisons made with respect to before and after clustering of data and for inter- and intra-clusters.

A fast and efficient fuzzy approximation-based indexing for CBIR

Crisp index structures introduce the problem of having sharp decision boundaries which may not be found in the real life clustering problems. In real world, specifically in the CBIR context, each data may not be fully assigned to one cluster and it may partially belong to other clusters, as opposed to the crisp index structures which fully affect data to clusters according to their proximity in terms of distance in the high-dimensional vector space. Based on kernel-fuzzy C-means clustering (KFCM) mechanism, this paper presents a fast and efficient index structure to support high-dimensional indexing for both crisp and fuzzy data. The proposed index structure offers a number of advantages such as a compact and efficient fuzzy data clustering. The experimental study demonstrates the efficiency and effectiveness of our method.

By-Passing Infected Areas in Wireless Sensor Networks using BPR

Abnormalities in sensed data streams indicate the spread of malicious attacks, hardware failure and software corruption among the different nodes in a wireless sensor network. These factors of node infection can affect generated and incoming data streams resulting in high chances of inaccurate data, misleading packet translation, wrong decision making and severe communication disruption. This problem is detrimental to real-time applications having stringent quality-of-service (QoS) requirements. The sensed data from other uninfected regions might also get stuck in an infected region should no prior alternative arrangements are made. Although several existing methods (BOUNDHOLE and GAR) can be used to mitigate these issues, their performance is bounded by some limitations, mainly the high risk of falling into routing loops and involvement in unnecessary transmissions. This paper provides a solution to by-pass the infected nodes dynamically using a twin rolling balls technique and also divert the packets that are trapped inside the identified area. The identification of infected nodes is done by adapting a Fuzzy data clustering approach which classifies the nodes based on the fraction of anomalous data that is detected in individual data streams. This information is then used in the proposed by-passed routing (BPR) which rotates two balls in two directions simultaneously: clockwise and counter-clockwise. The first node that hits any ball in any direction and is uninfected, is selected as the next hop. We are also concerned with the incoming packets or the packets-on-the-fly that may be affected when this problem occurs. Besides solving both of the problems in the existing methods, the proposed BPR technique has greatly improved the studied QoS parameters as shown by almost 40 percent increase in the overall performance.

An efficient approach for unsupervised fuzzy clustering based on grouping evolution strategies

Fuzzy data clustering plays an important role in practical use and has become a prerequisite step for decision-making in fuzzy environment. In this paper we propose a new algorithm, called FuzzyGES for unsupervised fuzzy clustering based on adaptation of the recently proposed Grouping Evolution Strategy (GES). To adapt GES for fuzzy clustering we devise a fuzzy counterpart of the grouping mutation operator typically used in GES, and employ it in a two phase procedure to generate a new clustering solution. Unlike conventional clustering algorithms which should get the number of clusters as an input, FuzzyGES tries to determine the true number of clusters as well as providing the optimal cluster centroids after several iterations. The proposed approach is validated through using several data sets and results are compared with those of fuzzy c-means algorithm, particle swarm optimization algorithm (PSO), differential evolution (DE) and league championship algorithm (LCA). We also investigate the performance of FuzzyGES through using different cluster validity indices. Our results indicate that FuzzyGES is fast and provides acceptable results in terms of both determining the correct number of clusters and the accurate cluster centroids.