Optimal Set of Overlapping Clusters Using Multi-objective Genetic Algorithm

An approach to construct interpretable and precise fuzzy models from data is proposed. Interpretability, which is one of the most important features of fuzzy models, is analyzed first. Then a modified fuzzy clustering algorithm, combined with the least square method, is used to identify the initial fuzzy model. Third, the multi-objective genetic algorithm and interpretability-driven simplification techniques are proposed to evolve the initial fuzzy model to optimize its structure and parameters iteratively, thus interpretability and precision of the fuzzy model are improved. Finally, the proposed approach is applied to the Mackey-Glass tine series, and the results show its validity

The development of various applications of wireless sensor networks has aroused great interest in using these types of networks in various fields. These networks, without infrastructure and self‐organization, are easily deployed in most environments and collect information about environmental phenomena for analysis and proper response to accidents and send them to the basic centers. They do. Wireless sensor networks are made up of some sensor nodes that both act as sensors and act as relay nodes concerning to each other. On the other hand, the lack of infrastructure in these networks has limited resources so that the nodes of the battery are fed with limited energy. Due to the location of networks in difficult and impassable areas, it is not possible to recharge or replace the node battery. Therefore, saving energy consumption in this type of network is one of the most important challenges. Since the rate of energy consumption when sensing information and receiving data packets from another node is a fixed value, so sensor nodes have the highest energy consumption when sending data. Therefore, routing methods try to reduce energy consumption based on systematic approaches. One of the most promising solutions to reduce energy consumption in wireless sensor networks is to cluster the nodes and select the threaded node based on the data transfer parameters so that the average energy consumption in the nodes is reduced and the network lifetime is increased. Therefore, in this research, a new optimization approach using multiobjective genetic algorithm and cuckoo algorithm for clustering wireless sensor networks is presented. In this study, in order to select clustered nodes from a multiobjective genetic algorithms based on reducing intracluster distances and reducing energy consumption in cluster member nodes and near‐optimal routing based on cuckoo optimization algorithm to transfer information between nodes have been used in the direction of the cavity. The implementation results show that considering the evolutionary capabilities of the multiobjective genetic algorithm and the cuckoo optimization algorithm, the proposed method in terms of energy consumption, efficiency, delivery rate, and packet transmission latency, compared to previous methods, has improved.

Several criminal profiling systems have been developed to assist the Law Enforcement Agencies in solving crimes but the techniques employed in most of the systems lack the ability to cluster criminal based on their behavioral characteristics. This paper reviewed different clustering techniques used in criminal profiling and then selects one fuzzy clustering algorithm (Expectation Maximization) and two hard clustering algorithm (K-means and Hierarchical). The selected algorithms were then developed and tested on real life data to produce "profiles" of criminal activity and behavior of criminals. The algorithms were implemented using WEKA software package. The performance of the algorithms was evaluated using cluster accuracy and time complexity. The results show that Expectation Maximization algorithm gave a 90.5% clusters accuracy in 8.5s, while K-Means had 62.6% in 0.09s and Hierarchical with 51.9% in 0.11s. In conclusion, soft clustering algorithm performs better than hard clustering algorithm in analyzing criminal data.
 Keywords: Clustering Algorithm, Profiling, Crime, Membership value

Gene selection from microarray gene expression datasets and clustering of samples into different groups are important data mining tasks for disease identification. Selection of more interpretable genes from the gene expression dataset is an essential data-preprocessing task, which helps to study on cancer diseases. Gene selection during sample clustering is inherently a difficult task as there is no obvious criterion to guide the search. Simultaneous gene selection and sample clustering is a two-way data analysis technique which has recently gained attention in research area. The traditional clustering techniques are unable to handle noisy data properly. So, effective clustering algorithms are more desirable which can deal with the relevant and noise free data. Therefore, target genes selection before sample clustering is essential and of course effective if both the tasks are done simultaneously. In this chapter, optimal gene subset is selected and sample clustering is performed simultaneously using Multi-Objective Genetic Algorithm (MOGA). Different versions of MOGA are employed to choose the optimal gene subset, where natural number of optimal clusters of samples is automatically obtained at the end of the process. Non-dominated sorting genetic algorithm (NSGA), Strength pareto evolutionary algorithm (SPEA) and its modified version SPEA2 are applied for the purpose. The methods use nonlinear hybrid uniform cellular automata for generating initial population, tournament selection strategy, two-point crossover operation, and a suitable jumping gene mutation mechanism to maintain diversity in the population. It uses mutual correlation coefficient; internal and external cluster validation indices as objective functions to find out the non-dominated solutions. To measure the cluster validation indices, clustering algorithm is applied on data subset associated to chromosomes in the population to find out different clusters. After the convergence of genetic algorithm, the best solution from the non-dominated solutions is identified that provides the important genes and categorizes the samples into clusters. The experimental results express the correctness of the proposed simultaneous gene selection and sample categorization method. The goodness of optimality of the clusters obtained using different genetic algorithms is expressed by comparing various cluster validation indices.

Many components of intelligent transportation systems require different levels of the traffic flow forecasting. This paper presents a novel short-term traffic flow forecasting model using a distributed radial basis function neural network (RBFNN) based on adaptive fuzzy c-means (FCM) clustering algorithm. FCM clustering algorithm is used to classify training objects into a couple of clusters, each cluster is trained by a sub RBFNN, and membership values are used for combining several RBFNN outputs to obtain the final result. In the online stage, the membership values are computed using an adaptive fuzzy clustering algorithm for the new object. The real traffic data are used to demonstrate the effectiveness of the method.

Forecasting activities play an important role in our daily life. In recent years, fuzzy time series (FTS) methods were developed to deal with forecasting problems. FTS attracted researchers because of its ability to predict the future values in some critical situations where most standard forecasting models are doubtfully applicable or produce bad fittings. However, some critical issues in FTS are still open; these issues are often subjective and affect the accuracy of forecasting. In this paper, we focus on improving the accuracy of FTS forecasting methods. The new method integrates the fuzzy clustering and genetic algorithm with FTS to reduce subjectivity and improve its accuracy. In the new method, the genetic algorithm is responsible for selecting the proper model. Also, the fuzzy clustering algorithm is responsible for fuzzifying the historical data, based on its membership degrees to each cluster, and using these memberships to defuzzify the results. This method provides better forecasting accuracy when compared with other extant researches.

To solve the problem of fuzzy identification of nonlinear systems, a novel fuzzy identification method based on fuzzy c-means clustering (FCM) algorithm and Gaussian function is proposed. Firstly, fuzzy clustering algorithm is used to divide the input space to obtain the clustering center, then the clustering center is used as the gaussian function center to determine the membership function to obtain the premise parameters of the fuzzy model, and the conclusion parameters of the fuzzy model are identified by recursive least squares (RLS). Finally, three simulation examples are given to verify the effectiveness of the proposed method in identifying T-S fuzzy model.

The storage and calculation of the larger amount of data in the cloud data center brings more abnormal data. In order to accurately and efficiently find anomalies in the data in the cloud data center, this paper proposes an anomaly detection parameter optimization algorithm for data center data. Methods Fuzzy C-means clustering (FCM) algorithm is used for anomaly detection. At the same time, in order to overcome the problem that the fuzzy clustering algorithm is sensitive to the initial value and easy to fall into the local optimum, the adaptive bat algorithm is used to optimize the FCM algorithm. And add distributed entropy and average distance to the algorithm, adaptively adjust the optimization ability of traditional bat algorithm. Finally, experiments prove the detection accuracy of the algorithm.

Image segmentation plays an important role in machine vision, image recognition, and imaging applications. Based on the fuzzy c-means clustering algorithm, a kernel-distance-based intuitionistic fuzzy c-means clustering (KIFCM) algorithm is proposed. First, a fuzzy complement operator is used to generate the membership degree whereby the hesitation degree of intuitionistic fuzzy set is generated; second, a kernel-induced function is used to calculate the distance from each point to the cluster center instead of the Euclidean distance; third, a new objective function that includes the hesitation degree is established, and the optimization of the objective function results in new iterative expressions for the membership degree and the cluster center. The proposed KIFCM algorithm is compared with the fuzzy c-means clustering (FCM) algorithm, the kernel fuzzy c-means clustering (KFCM) algorithm, and the intuitionistic fuzzy c-means clustering (IFCM) algorithm in segmenting five images. The experimental results verify the effectiveness and superiority of our proposed KIFCM algorithm.

There is a trend in recent machine learning community to construct a nonlinear version of a linear algorithm using the 'kernel method', e.g. Support Vector Machines (SVMs), kernel principal component analysis, kernel fisher discriminant analysis and the recent kernel clustering algorithms. In unsupervised clustering algorithms using kernel method, typically, a nonlinear mapping is used first to map the data into a potentially much higher feature space, where clustering is then performed. A drawback of these kernel clustering algorithms is thatthe clustering prototypes lie in high dimensional feature space and hence lack clear and intuitive descriptions unless using additional projection approximation from the feature to the data space as done in the existing literatures. In this paper, a novel clustering algorithm using the 'kernel method' based on the classical fuzzy clustering algorithm (FCM) is proposed and called as kernel fuzzy c-means algorithm (KFCM). KFCM adopts a new kernel-induced metric in the data space to replace the original Euclidean norm metric in FCM and the clustered prototypes still lie in the data space so that the clustering results can be reformulated and interpreted in the original space. Our analysis shows that KFCM is robust to noise and outliers and also tolerates unequal sized clusters. And finally this property is utilized to cluster incomplete data. Experiments on two artificial and one real datasets show that KFCM hasbetter clustering performance and more robust than several modifications of FCM for incomplete data clustering.

Over the years, research on fuzzy clustering algorithms has attracted the attention of many researchers, and they have been applied to various areas, such as image segmentation and data clustering. Various fuzzy clustering algorithms have been put forward based on the initial Fuzzy C-Means clustering (FCM) with Euclidean distance. However, the existing fuzzy clustering approaches ignore two problems. Firstly, clustering algorithms based on Euclidean distance have a high error rate, and are more sensitive to noise and outliers. Secondly, the parameters of the fuzzy clustering algorithms are hard to determine. In practice, they are often determined by the user’s experience, which results in poor performance of the clustering algorithm. Therefore, considering the above deficiencies, this paper proposes a novel fuzzy clustering algorithm by combining the Gaussian kernel function and Grey Wolf Optimizer (GWO), called Kernel-based Picture Fuzzy C-Means clustering with Grey Wolf Optimizer (KPFCM-GWO). In KPFCM-GWO, the Gaussian kernel function is used as a symmetrical measure of distance between data points and cluster centers, and the GWO is utilized to determine the parameter values of PFCM. To verify the validity of KPFCM-GWO, a comparative study was conducted. The experimental results indicate that KPFCM-GWO outperforms other clustering methods, and the improvement of KPFCM-GWO is mainly attributed to the combination of the Gaussian kernel function and the parameter optimization capability of the GWO. What is more, the paper applies KPFCM-GWO to analyzes the value of an airline’s customers, and five levels of customer categories are defined.

This paper proposes a new robust approach to nonlinear clustering based on the Principal Component Analysis (PCA) approach. A robust c‐means partition is derived by using the natural PCA noise‐rejection mechanism and the nonlinearity captured by a sliding process of the clusters prototype. A non‐linear extension of PCA has been developed for detecting the lower‐dimensional representation of real world data sets. For these cases local linear approaches are used widely because of their computational simplicity and understandability. We will present a new method that joins (merges) the fuzzy clustering algorithm with a local sliding PCA analysis. With this strategy it is possible to identify the non‐linear relations and obtain morphological information of the data. The Sliding PCA‐Fuzzy cluster algorithm (SPCA‐FCA) is a fuzzy clustering algorithm that estimates local principal component vectors as the vectors spanning prototypes of clusters, performed on the neighborhood of the center of cluster and normal approximations in order to estimate a tangent surface that characterizes the trend and curvature of the data points or contours region. Numerical experiments demonstrate that the proposed method is useful for capturing cluster cores by rejecting noise samples, and we can easily assess cluster validity by using cluster‐crossing curves.

The main moan that can addressed to the pioneering approaches of fuzzy clustering stand in their approximate management of a noisy surroundings as well as their snugness dependency of an apriori determination of the number of clusters. The aim of this paper is twofold: First, we introduce a new algorithm, called PFKCN, based on neural network. This algorithm introduces both membership and typicality values, simultaneously, into the Kohonen Network clustering. Then, we tackle the problem of estimating the number of clusters, by using a multi level PFKCN based clustering algorithm, called Multi-PFKCN. The latter is able to find the optimal number of clusters by using a statistical criterion, that aims at measuring the quality of obtained partitions. Carried out experiments on real-life data sets highlights a very encouraging results in terms of exact determination of optimal number of clusters.

In this paper, a learning method is proposed to improve the retrieval process in image databases. This method uses the search transaction logs in the system and user relevance feedback scores to create a semantic space of the image database. The semantic space includes many semantic classes and all the images in the database are clustered to these classes with different membership values. The sparsity problem in the transaction logs data is solved by filling the missing values by an estimation based on the image contents and image similarities. A Fuzzy clustering algorithm is developed to create the semantic classes and find image memberships in the classes.

Intuitionistic time series fuzzy inference system