Search results for: Clustering efficiency

Authors: S. Sutor, R. Röhr, G. Pujolle, R. Reda

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This paper presents a highly efficient algorithm for detecting and tracking humans and objects in video surveillance sequences. Mean shift clustering is applied on backgrounddifferenced image sequences. For efficiency, all calculations are performed on integral images. Novel corresponding exponential integral kernels are introduced to allow the application of nonuniform kernels for clustering, which dramatically increases robustness without giving up the efficiency of the integral data structures. Experimental results demonstrating the power of this approach are presented.

Keywords: Clustering, Integral Images, Kernels, Person Detection, Person Tracking, Intelligent Video Surveillance.

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Authors: Moslem Afrashteh Mehr

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Wireless Sensor Networks consist of small battery powered devices with limited energy resources. once deployed, the small sensor nodes are usually inaccessible to the user, and thus replacement of the energy source is not feasible. Hence, One of the most important issues that needs to be enhanced in order to improve the life span of the network is energy efficiency. to overcome this demerit many research have been done. The clustering is the one of the representative approaches. in the clustering, the cluster heads gather data from nodes and sending them to the base station. In this paper, we introduce a dynamic clustering algorithm using genetic algorithm. This algorithm takes different parameters into consideration to increase the network lifetime. To prove efficiency of proposed algorithm, we simulated the proposed algorithm compared with LEACH algorithm using the matlab

Keywords: Wireless Sensor Networks, Clustering, Geneticalgorithm, Energy Consumption

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Authors: Seo Young Kim, Tai Myong Choi

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The main goal of microarray experiments is to quantify the expression of every object on a slide as precisely as possible, with a further goal of clustering the objects. Recently, many studies have discussed clustering issues involving similar patterns of gene expression. This paper presents an application of fuzzy-type methods for clustering DNA microarray data that can be applied to typical comparisons. Clustering and analyses were performed on microarray and simulated data. The results show that fuzzy-possibility c-means clustering substantially improves the findings obtained by others.

Keywords: Clustering, microarray data, Fuzzy-type clustering, Validation

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Authors: Binu Thomas, Raju G., Sonam Wangmo

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In Data mining, Fuzzy clustering algorithms have demonstrated advantage over crisp clustering algorithms in dealing with the challenges posed by large collections of vague and uncertain natural data. This paper reviews concept of fuzzy logic and fuzzy clustering. The classical fuzzy c-means algorithm is presented and its limitations are highlighted. Based on the study of the fuzzy c-means algorithm and its extensions, we propose a modification to the cmeans algorithm to overcome the limitations of it in calculating the new cluster centers and in finding the membership values with natural data. The efficiency of the new modified method is demonstrated on real data collected for Bhutan-s Gross National Happiness (GNH) program.

Keywords: Adaptive fuzzy clustering, clustering, fuzzy logic, fuzzy clustering, c-means.

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Authors: A.M. Fahim, A. M. Salem, F. A. Torkey, M. A. Ramadan

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Clustering algorithms are attractive for the task of class identification in spatial databases. However, the application to large spatial databases rises the following requirements for clustering algorithms: minimal requirements of domain knowledge to determine the input parameters, discovery of clusters with arbitrary shape and good efficiency on large databases. The well-known clustering algorithms offer no solution to the combination of these requirements. In this paper, a density based clustering algorithm (DCBRD) is presented, relying on a knowledge acquired from the data by dividing the data space into overlapped regions. The proposed algorithm discovers arbitrary shaped clusters, requires no input parameters and uses the same definitions of DBSCAN algorithm. We performed an experimental evaluation of the effectiveness and efficiency of it, and compared this results with that of DBSCAN. The results of our experiments demonstrate that the proposed algorithm is significantly efficient in discovering clusters of arbitrary shape and size.

Keywords: Clustering Algorithms, Arbitrary Shape of clusters, cluster Analysis.

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Authors: Vipin Pal, Girdhari Singh, R P Yadav

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As wireless sensor networks are energy constraint networks so energy efficiency of sensor nodes is the main design issue. Clustering of nodes is an energy efficient approach. It prolongs the lifetime of wireless sensor networks by avoiding long distance communication. Clustering algorithms operate in rounds. Performance of clustering algorithm depends upon the round time. A large round time consumes more energy of cluster heads while a small round time causes frequent re-clustering. So existing clustering algorithms apply a trade off to round time and calculate it from the initial parameters of networks. But it is not appropriate to use initial parameters based round time value throughout the network lifetime because wireless sensor networks are dynamic in nature (nodes can be added to the network or some nodes go out of energy). In this paper a variable round time approach is proposed that calculates round time depending upon the number of active nodes remaining in the field. The proposed approach makes the clustering algorithm adaptive to network dynamics. For simulation the approach is implemented with LEACH in NS-2 and the results show that there is 6% increase in network lifetime, 7% increase in 50% node death time and 5% improvement over the data units gathered at the base station.

Keywords: Wireless Sensor Network, Clustering, Energy Efficiency, Round Time.

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Authors: Dharmveer Singh Rajput , P. K. Singh, Mahua Bhattacharya

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Clustering in high dimensional space is a difficult problem which is recurrent in many fields of science and engineering, e.g., bioinformatics, image processing, pattern reorganization and data mining. In high dimensional space some of the dimensions are likely to be irrelevant, thus hiding the possible clustering. In very high dimensions it is common for all the objects in a dataset to be nearly equidistant from each other, completely masking the clusters. Hence, performance of the clustering algorithm decreases. In this paper, we propose an algorithmic framework which combines the (reduct) concept of rough set theory with the k-means algorithm to remove the irrelevant dimensions in a high dimensional space and obtain appropriate clusters. Our experiment on test data shows that this framework increases efficiency of the clustering process and accuracy of the results.

Keywords: High dimensional clustering, sub-space, k-means, rough set, discernibility matrix.

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Authors: Bashar Al-Shboul, Sung-Hyon Myaeng

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K-Means (KM) is considered one of the major algorithms widely used in clustering. However, it still has some problems, and one of them is in its initialization step where it is normally done randomly. Another problem for KM is that it converges to local minima. Genetic algorithms are one of the evolutionary algorithms inspired from nature and utilized in the field of clustering. In this paper, we propose two algorithms to solve the initialization problem, Genetic Algorithm Initializes KM (GAIK) and KM Initializes Genetic Algorithm (KIGA). To show the effectiveness and efficiency of our algorithms, a comparative study was done among GAIK, KIGA, Genetic-based Clustering Algorithm (GCA), and FCM [19].

Keywords: Clustering, Genetic Algorithms, K-means.

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Authors: Bainian Li, Kongsheng Zhang, Jian Xu

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In this paper we study the fuzzy c-mean clustering algorithm combined with principal components method. Demonstratively analysis indicate that the new clustering method is well rather than some clustering algorithms. We also consider the validity of clustering method.

Keywords: FCM algorithm, Principal Components Analysis, Clustervalidity

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Authors: Pornpimol Bungkomkhun, Surapong Auwatanamongkol

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This paper presents a supervised clustering algorithm, namely Grid-Based Supervised Clustering (GBSC), which is able to identify clusters of any shapes and sizes without presuming any canonical form for data distribution. The GBSC needs no prespecified number of clusters, is insensitive to the order of the input data objects, and is capable of handling outliers. Built on the combination of grid-based clustering and density-based clustering, under the assistance of the downward closure property of density used in bottom-up subspace clustering, the GBSC can notably reduce its search space to avoid the memory confinement situation during its execution. On two-dimension synthetic datasets, the GBSC can identify clusters with different shapes and sizes correctly. The GBSC also outperforms other five supervised clustering algorithms when the experiments are performed on some UCI datasets.

Keywords: supervised clustering, grid-based clustering, subspace clustering

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Authors: Neveen I. Ghali, Nahed El-Dessouki, Mervat A. N., Lamiaa Bakrawi

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In this paper we use exponential particle swarm optimization (EPSO) to cluster data. Then we compare between (EPSO) clustering algorithm which depends on exponential variation for the inertia weight and particle swarm optimization (PSO) clustering algorithm which depends on linear inertia weight. This comparison is evaluated on five data sets. The experimental results show that EPSO clustering algorithm increases the possibility to find the optimal positions as it decrease the number of failure. Also show that (EPSO) clustering algorithm has a smaller quantization error than (PSO) clustering algorithm, i.e. (EPSO) clustering algorithm more accurate than (PSO) clustering algorithm.

Keywords: Particle swarm optimization, data clustering, exponential PSO.

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Authors: Sara El Manar El Bouanani, Ismail Kassou

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Our objective in this paper is to propose an approach capable of clustering web messages. The clustering is carried out by assigning, with a certain probability, texts written by the same web user to the same cluster based on Stylometric features and using fuzzy clustering algorithms. Focus in the present work is on comparing the most popular algorithms in fuzzy clustering theory namely, Fuzzy C-means, Possibilistic C-means and Fuzzy Possibilistic C-Means.

Keywords: Authorship detection, fuzzy clustering, profiling, stylometric features.

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Authors: S. Sarumathi, N. Shanthi, M. Sharmila

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Clustering in data mining is an unsupervised learning technique of aggregating the data objects into meaningful groups such that the intra cluster similarity of objects are maximized and inter cluster similarity of objects are minimized. Over the past decades several clustering tools were emerged in which clustering algorithms are inbuilt and are easier to use and extract the expected results. Data mining mainly deals with the huge databases that inflicts on cluster analysis and additional rigorous computational constraints. These challenges pave the way for the emergence of powerful expansive data mining clustering softwares. In this survey, a variety of clustering tools used in data mining are elucidated along with the pros and cons of each software.

Keywords: Cluster Analysis, Clustering Algorithms, Clustering Techniques, Association, Visualization.

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Authors: Z. Abdullah, A. R. Hamdan

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Clustering is a process of grouping objects and data into groups of clusters to ensure that data objects from the same cluster are identical to each other. Clustering algorithms in one of the area in data mining and it can be classified into partition, hierarchical, density based and grid based. Therefore, in this paper we do survey and review four major hierarchical clustering algorithms called CURE, ROCK, CHAMELEON and BIRCH. The obtained state of the art of these algorithms will help in eliminating the current problems as well as deriving more robust and scalable algorithms for clustering.

Keywords: Clustering, method, algorithm, hierarchical, survey.

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Authors: Reza Ghaemi , Md. Nasir Sulaiman , Hamidah Ibrahim , Norwati Mustapha

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The clustering ensembles combine multiple partitions generated by different clustering algorithms into a single clustering solution. Clustering ensembles have emerged as a prominent method for improving robustness, stability and accuracy of unsupervised classification solutions. So far, many contributions have been done to find consensus clustering. One of the major problems in clustering ensembles is the consensus function. In this paper, firstly, we introduce clustering ensembles, representation of multiple partitions, its challenges and present taxonomy of combination algorithms. Secondly, we describe consensus functions in clustering ensembles including Hypergraph partitioning, Voting approach, Mutual information, Co-association based functions and Finite mixture model, and next explain their advantages, disadvantages and computational complexity. Finally, we compare the characteristics of clustering ensembles algorithms such as computational complexity, robustness, simplicity and accuracy on different datasets in previous techniques.

Keywords: Clustering Ensembles, Combinational Algorithm, Consensus Function, Unsupervised Classification.

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Authors: O. Siriporn, S. Benjawan

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This paper represents four unsupervised clustering algorithms namely sIB, RandomFlatClustering, FarthestFirst, and FilteredClusterer that previously works have not been used for network traffic classification. The methodology, the result, the products of the cluster and evaluation of these algorithms with efficiency of each algorithm from accuracy are shown. Otherwise, the efficiency of these algorithms considering form the time that it use to generate the cluster quickly and correctly. Our work study and test the best algorithm by using classify traffic anomaly in network traffic with different attribute that have not been used before. We analyses the algorithm that have the best efficiency or the best learning and compare it to the previously used (K-Means). Our research will be use to develop anomaly detection system to more efficiency and more require in the future.

Keywords: Unsupervised, clustering, anomaly, machine learning.

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Authors: Hmway Hmway Tar, Thi Thi Soe Nyaunt

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Documents clustering become an essential technology with the popularity of the Internet. That also means that fast and high-quality document clustering technique play core topics. Text clustering or shortly clustering is about discovering semantically related groups in an unstructured collection of documents. Clustering has been very popular for a long time because it provides unique ways of digesting and generalizing large amounts of information. One of the issues of clustering is to extract proper feature (concept) of a problem domain. The existing clustering technology mainly focuses on term weight calculation. To achieve more accurate document clustering, more informative features including concept weight are important. Feature Selection is important for clustering process because some of the irrelevant or redundant feature may misguide the clustering results. To counteract this issue, the proposed system presents the concept weight for text clustering system developed based on a k-means algorithm in accordance with the principles of ontology so that the important of words of a cluster can be identified by the weight values. To a certain extent, it has resolved the semantic problem in specific areas.

Keywords: Clustering, Concept Weight, Document clustering, Feature Selection, Ontology

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Authors: A. M. Fahim, G. Saake, A. M. Salem, F. A. Torkey, M. A. Ramadan

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Data clustering is an important data exploration technique with many applications in data mining. We present an enhanced version of the well known single link clustering algorithm. We will refer to this algorithm as DCBOR. The proposed algorithm alleviates the chain effect by removing the outliers from the given dataset. So this algorithm provides outlier detection and data clustering simultaneously. This algorithm does not need to update the distance matrix, since the algorithm depends on merging the most k-nearest objects in one step and the cluster continues grow as long as possible under specified condition. So the algorithm consists of two phases; at the first phase, it removes the outliers from the input dataset. At the second phase, it performs the clustering process. This algorithm discovers clusters of different shapes, sizes, densities and requires only one input parameter; this parameter represents a threshold for outlier points. The value of the input parameter is ranging from 0 to 1. The algorithm supports the user in determining an appropriate value for it. We have tested this algorithm on different datasets contain outlier and connecting clusters by chain of density points, and the algorithm discovers the correct clusters. The results of our experiments demonstrate the effectiveness and the efficiency of DCBOR.

Keywords: Data Clustering, Clustering Algorithms, Handling Noise, Arbitrary Shape of Clusters.

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Authors: Achmad Nizar Hidayanto, Elisabeth Martha Koeanan

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Image clustering is a process of grouping images based on their similarity. The image clustering usually uses the color component, texture, edge, shape, or mixture of two components, etc. This research aims to explore image clustering using color composition. In order to complete this image clustering, three main components should be considered, which are color space, image representation (feature extraction), and clustering method itself. We aim to explore which composition of these factors will produce the best clustering results by combining various techniques from the three components. The color spaces use RGB, HSV, and L*a*b* method. The image representations use Histogram and Gaussian Mixture Model (GMM), whereas the clustering methods use KMeans and Agglomerative Hierarchical Clustering algorithm. The results of the experiment show that GMM representation is better combined with RGB and L*a*b* color space, whereas Histogram is better combined with HSV. The experiments also show that K-Means is better than Agglomerative Hierarchical for images clustering.

Keywords: Image clustering, feature extraction, RGB, HSV, L*a*b*, Gaussian Mixture Model (GMM), histogram, Agglomerative Hierarchical Clustering (AHC), K-Means, Expectation-Maximization (EM).

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Authors: Li Ni, Pen ManMan, Li KenLi

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Clustering is an intensive research for some years because of its multifaceted applications, such as biology, information retrieval, medicine, business and so on. The expectation maximization (EM) is a kind of algorithm framework in clustering methods, one of the ten algorithms of machine learning. Traditionally, optimization of objective function has been the standard approach in EM. Hence, research has investigated the utility of evolutionary computing and related techniques in the regard. Chemical Reaction Optimization (CRO) is a recently established method. So the property embedded in CRO is used to solve optimization problems. This paper presents an algorithm framework (EM-CRO) with modified CRO operators based on EM cluster problems. The hybrid algorithm is mainly to solve the problem of initial value sensitivity of the objective function optimization clustering algorithm. Our experiments mainly take the EM classic algorithm:k-means and fuzzy k-means as an example, through the CRO algorithm to optimize its initial value, get K-means-CRO and FKM-CRO algorithm. The experimental results of them show that there is improved efficiency for solving objective function optimization clustering problems.

Keywords: Chemical reaction optimization, expectation maximization, initial, objective function clustering.

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Authors: U. Idachaba, F. Z. Wang, A. Qi, N. Helian

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Artificial Bee Colony (ABC) algorithm is a relatively new swarm intelligence technique for clustering. It produces higher quality clusters compared to other population-based algorithms but with poor energy efficiency, cluster quality consistency and typically slower in convergence speed. Inspired by energy saving foraging behavior of natural honey bees this paper presents a Quality and Quantity Aware Artificial Bee Colony (Q2ABC) algorithm to improve quality of cluster identification, energy efficiency and convergence speed of the original ABC. To evaluate the performance of Q2ABC algorithm, experiments were conducted on a suite of ten benchmark UCI datasets. The results demonstrate Q2ABC outperformed ABC and K-means algorithm in the quality of clusters delivered.

Keywords: Artificial bee colony algorithm, clustering.

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Authors: M. Sangeetha, A. Sabari, K. Elakkiya

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Recent advancement in wireless internetworking has presented a number of dynamic routing protocols based on sensor networks. At present, a number of revisions are made based on their energy efficiency, lifetime and mobility. However, to the best of our knowledge no extensive survey of this special type has been prepared. At present, review is needed in this area where cluster-based structures for dynamic wireless networks are to be discussed. In this paper, we examine and compare several aspects and characteristics of some extensively explored hierarchical dynamic clustering protocols in wireless sensor networks. This document also presents a discussion on the future research topics and the challenges of dynamic hierarchical clustering in wireless sensor networks.

Keywords: Dynamic cluster, Hierarchical clustering, Wireless sensor networks.

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Authors: Jung-Eun Park, Kyung-Whan Oh

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Intelligent systems are required in order to quickly and accurately analyze enormous quantities of data in the Internet environment. In intelligent systems, information extracting processes can be divided into supervised learning and unsupervised learning. This paper investigates intelligent clustering by unsupervised learning. Intelligent clustering is the clustering system which determines the clustering model for data analysis and evaluates results by itself. This system can make a clustering model more rapidly, objectively and accurately than an analyzer. The methodology for the automatic clustering intelligent system is a multi-agent system that comprises a clustering agent and a cluster performance evaluation agent. An agent exchanges information about clusters with another agent and the system determines the optimal cluster number through this information. Experiments using data sets in the UCI Machine Repository are performed in order to prove the validity of the system.

Keywords: Intelligent Clustering, Multi-Agent System, PCA, SOM, VC(Variance Criterion)

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Authors: Miin-Shen Yang, Yee-Shan Pan

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Although there have been many researches in cluster analysis to consider on feature weights, little effort is made on sample weights. Recently, Yu et al. (2011) considered a probability distribution over a data set to represent its sample weights and then proposed sample-weighted clustering algorithms. In this paper, we give a sample-weighted version of generalized fuzzy clustering regularization (GFCR), called the sample-weighted GFCR (SW-GFCR). Some experiments are considered. These experimental results and comparisons demonstrate that the proposed SW-GFCR is more effective than the most clustering algorithms.

Keywords: Clustering; fuzzy c-means, fuzzy clustering, sample weights, regularization.

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Authors: Amir Sepasi Zahmati, Bahman Abolhassani, Ali Asghar Beheshti Shirazi, Ali Shojaee Bakhtiari

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A wireless sensor network with a large number of tiny sensor nodes can be used as an effective tool for gathering data in various situations. One of the major issues in wireless sensor networks is developing an energy-efficient routing protocol which has a significant impact on the overall lifetime of the sensor network. In this paper, we propose a novel hierarchical with static clustering routing protocol called Energy-Efficient Protocol with Static Clustering (EEPSC). EEPSC, partitions the network into static clusters, eliminates the overhead of dynamic clustering and utilizes temporary-cluster-heads to distribute the energy load among high-power sensor nodes; thus extends network lifetime. We have conducted simulation-based evaluations to compare the performance of EEPSC against Low-Energy Adaptive Clustering Hierarchy (LEACH). Our experiment results show that EEPSC outperforms LEACH in terms of network lifetime and power consumption minimization.

Keywords: Clustering methods, energy efficiency, routingprotocol, wireless sensor networks.

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Authors: Billel Kenidra, Mohamed Benmohammed

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Data mining technique used in the field of clustering is a subject of active research and assists in biological pattern recognition and extraction of new knowledge from raw data. Clustering means the act of partitioning an unlabeled dataset into groups of similar objects. Each group, called a cluster, consists of objects that are similar between themselves and dissimilar to objects of other groups. Several clustering methods are based on partitional clustering. This category attempts to directly decompose the dataset into a set of disjoint clusters leading to an integer number of clusters that optimizes a given criterion function. The criterion function may emphasize a local or a global structure of the data, and its optimization is an iterative relocation procedure. The K-Means algorithm is one of the most widely used partitional clustering techniques. Since K-Means is extremely sensitive to the initial choice of centers and a poor choice of centers may lead to a local optimum that is quite inferior to the global optimum, we propose a strategy to initiate K-Means centers. The improved K-Means algorithm is compared with the original K-Means, and the results prove how the efficiency has been significantly improved.

Keywords: Microarray data mining, biological pattern recognition, partitional clustering, k-means algorithm, centroid initialization.

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Authors: T. Niknam, M. Nayeripour, B.Bahmani Firouzi

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Clustering techniques have received attention in many areas including engineering, medicine, biology and data mining. The purpose of clustering is to group together data points, which are close to one another. The K-means algorithm is one of the most widely used techniques for clustering. However, K-means has two shortcomings: dependency on the initial state and convergence to local optima and global solutions of large problems cannot found with reasonable amount of computation effort. In order to overcome local optima problem lots of studies done in clustering. This paper is presented an efficient hybrid evolutionary optimization algorithm based on combining Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO), called PSO-ACO, for optimally clustering N object into K clusters. The new PSO-ACO algorithm is tested on several data sets, and its performance is compared with those of ACO, PSO and K-means clustering. The simulation results show that the proposed evolutionary optimization algorithm is robust and suitable for handing data clustering.

Keywords: Ant Colony Optimization (ACO), Data clustering, Hybrid evolutionary optimization algorithm, K-means clustering, Particle Swarm Optimization (PSO).

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Authors: Guadalupe J. Torres, Ram B. Basnet, Andrew H. Sung, Srinivas Mukkamala, Bernardete M. Ribeiro

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This paper introduces a measure of similarity between two clusterings of the same dataset produced by two different algorithms, or even the same algorithm (K-means, for instance, with different initializations usually produce different results in clustering the same dataset). We then apply the measure to calculate the similarity between pairs of clusterings, with special interest directed at comparing the similarity between various machine clusterings and human clustering of datasets. The similarity measure thus can be used to identify the best (in terms of most similar to human) clustering algorithm for a specific problem at hand. Experimental results pertaining to the text categorization problem of a Portuguese corpus (wherein a translation-into-English approach is used) are presented, as well as results on the well-known benchmark IRIS dataset. The significance and other potential applications of the proposed measure are discussed.

Keywords: Clustering Algorithms, Clustering Applications, Similarity Measures, Text Clustering

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Authors: Uttam Vijay, Nitin Gupta

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Due to heavy energy constraints in WSNs clustering is an efficient way to manage the energy in sensors. There are many methods already proposed in the area of clustering and research is still going on to make clustering more energy efficient. In our paper we are proposing a minimum spanning tree based clustering using divide and conquer approach. The MST based clustering was first proposed in 1970’s for large databases. Here we are taking divide and conquer approach and implementing it for wireless sensor networks with the constraints attached to the sensor networks. This Divide and conquer approach is implemented in a way that we don’t have to construct the whole MST before clustering but we just find the edge which will be the part of the MST to a corresponding graph and divide the graph in clusters there itself if that edge from the graph can be removed judging on certain constraints and hence saving lot of computation.

Keywords: Algorithm, Clustering, Edge-Weighted Graph, Weighted-LEACH.

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Authors: Ágnes Vathy-Fogarassy, Balázs Feil, János Abonyi

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Most of fuzzy clustering algorithms have some discrepancies, e.g. they are not able to detect clusters with convex shapes, the number of the clusters should be a priori known, they suffer from numerical problems, like sensitiveness to the initialization, etc. This paper studies the synergistic combination of the hierarchical and graph theoretic minimal spanning tree based clustering algorithm with the partitional Gath-Geva fuzzy clustering algorithm. The aim of this hybridization is to increase the robustness and consistency of the clustering results and to decrease the number of the heuristically defined parameters of these algorithms to decrease the influence of the user on the clustering results. For the analysis of the resulted fuzzy clusters a new fuzzy similarity measure based tool has been presented. The calculated similarities of the clusters can be used for the hierarchical clustering of the resulted fuzzy clusters, which information is useful for cluster merging and for the visualization of the clustering results. As the examples used for the illustration of the operation of the new algorithm will show, the proposed algorithm can detect clusters from data with arbitrary shape and does not suffer from the numerical problems of the classical Gath-Geva fuzzy clustering algorithm.

Keywords: Clustering, fuzzy clustering, minimal spanning tree, cluster validity, fuzzy similarity.

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