Search results for: Modified Pole Clustering

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

Abstract:

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

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Over the past epoch a rampant amount of work has been done in the data clustering research under the unsupervised learning technique in Data mining. Furthermore several algorithms and methods have been proposed focusing on clustering different data types, representation of cluster models, and accuracy rates of the clusters. However no single clustering algorithm proves to be the most efficient in providing best results. Accordingly in order to find the solution to this issue a new technique, called Cluster ensemble method was bloomed. This cluster ensemble is a good alternative approach for facing the cluster analysis problem. The main hope of the cluster ensemble is to merge different clustering solutions in such a way to achieve accuracy and to improve the quality of individual data clustering. Due to the substantial and unremitting development of new methods in the sphere of data mining and also the incessant interest in inventing new algorithms, makes obligatory to scrutinize a critical analysis of the existing techniques and the future novelty. This paper exposes the comparative study of different cluster ensemble methods along with their features, systematic working process and the average accuracy and error rates of each ensemble methods. Consequently this speculative and comprehensive analysis will be very useful for the community of clustering practitioners and also helps in deciding the most suitable one to rectify the problem in hand.

Keywords: Clustering, Cluster Ensemble methods, Co-association matrix, Consensus function, Median partition.

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Authors: R. Matousek, S. Lang, P. Minar, P. Pivonka

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In the control theory one attempts to find a controller that provides the best possible performance with respect to some given measures of performance. There are many sorts of controllers e.g. a typical PID controller, LQR controller, Fuzzy controller etc. In the paper will be introduced polynomial controller with novel tuning method which is based on the special pole placement encoding scheme and optimization by Genetic Algorithms (GA). The examples will show the performance of the novel designed polynomial controller with comparison to common PID controller.

Keywords: Evolutionary design, Genetic algorithms, PID controller, Pole placement, Polynomial controller

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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: Mohamed Essahafi, Mustapha Ait Lafkih

Abstract:

In industrial environments, the heat exchanger is a necessary component to any strategy of energy conversion. Much of thermal energy used in industrial processes passes at least one times by a heat exchanger, and methods systems recovering thermal energy. This survey paper tries to presents in a systemic way an sample control of a heat exchanger by comparison between three controllers LQR (linear quadratic regulator), PID (proportional, integrator and derivate) and Pole Placement. All of these controllers are used mainly in industrial sectors (chemicals, petrochemicals, steel, food processing, energy production, etc…) of transportation (automotive, aeronautics), but also in the residential sector and tertiary (heating, air conditioning, etc...) The choice of a heat exchanger, for a given application depends on many parameters: field temperature and pressure of fluids, and physical properties of aggressive fluids, maintenance and space. It is clear that the fact of having an exchanger appropriate, well-sized, well made and well used allows gain efficiency and energy processes.

Keywords: LQR linear-quadratic regulator, PID control, Pole Placement, Heat exchanger.

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Authors: S.Aranganayagi, K.Thangavel

Abstract:

K-Modes is an extension of K-Means clustering algorithm, developed to cluster the categorical data, where the mean is replaced by the mode. The similarity measure proposed by Huang is the simple matching or mismatching measure. Weight of attribute values contribute much in clustering; thus in this paper we propose a new weighted dissimilarity measure for K-Modes, based on the ratio of frequency of attribute values in the cluster and in the data set. The new weighted measure is experimented with the data sets obtained from the UCI data repository. The results are compared with K-Modes and K-representative, which show that the new measure generates clusters with high purity.

Keywords: Clustering, categorical data, K-Modes, weighted dissimilarity measure

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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: Sumith Matharage, Damminda Alahakoon

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Textual data plays an important role in the modern world. The possibilities of applying data mining techniques to uncover hidden information present in large volumes of text collections is immense. The Growing Self Organizing Map (GSOM) is a highly successful member of the Self Organising Map family and has been used as a clustering and visualisation tool across wide range of disciplines to discover hidden patterns present in the data. A comprehensive analysis of the GSOM’s capabilities as a text clustering and visualisation tool has so far not been published. These functionalities, namely map visualisation capabilities, automatic cluster identification and hierarchical clustering capabilities are presented in this paper and are further demonstrated with experiments on a benchmark text corpus.

Keywords: Text Clustering, Growing Self Organizing Map, Automatic Cluster Identification, Hierarchical Clustering.

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Authors: Salima Kouici, Abdelkader Khelladi

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In this work, we begin with the presentation of the Tθ family of usual similarity measures concerning multidimensional binary data. Subsequently, some properties of these measures are proposed. Finally the impact of the use of different inter-elements measures on the results of the Agglomerative Hierarchical Clustering Methods is studied.

Keywords: Binary data, similarity measure, Tθ measures, Agglomerative Hierarchical Clustering.

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

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Clustering is a very well known technique in data mining. One of the most widely used clustering techniques is the kmeans algorithm. Solutions obtained from this technique depend on the initialization of cluster centers and the final solution converges to local minima. In order to overcome K-means algorithm shortcomings, this paper proposes a hybrid evolutionary algorithm based on the combination of PSO, SA and K-means algorithms, called PSO-SA-K, which can find better cluster partition. The performance is evaluated through several benchmark data sets. The simulation results show that the proposed algorithm outperforms previous approaches, such as PSO, SA and K-means for partitional clustering problem.

Keywords: Data clustering, Hybrid evolutionary optimization algorithm, K-means algorithm, Simulated Annealing (SA), Particle Swarm Optimization (PSO).

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Authors: Moth'd Belal. Al-Daoud

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Clustering is a very well known technique in data mining. One of the most widely used clustering techniques is the k-means algorithm. Solutions obtained from this technique are dependent on the initialization of cluster centers. In this article we propose a new algorithm to initialize the clusters. The proposed algorithm is based on finding a set of medians extracted from a dimension with maximum variance. The algorithm has been applied to different data sets and good results are obtained.

Keywords: clustering, k-means, data mining.

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Authors: A. Hellany, M. Nassereddine, M. Nagrial, J. Rizk

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The demand on High voltage (HV) infrastructures is growing due to the corresponding growth in industries and population. New or upgraded HV infrastructure has safety implications since Transmission mains usually occupy the same easement in the vicinity of neighbouring residents. Transmission mains consist of underground (UG) and overhead (OH) sections and the transition between the UG and OH section is known as the UGOH pole. The existence of two transmission mains in the same easement can dictate to resort to more complicated earthing design in order to mitigate the effect of AC interference, and in some cases it can also necessitates completing a Split Study of the system. This paper provides an overview of the AC interference, Split Study and the earthing of an underground feeder including the UGOH pole .In addition, this paper discusses the use of different link boxes on the UG feeder and presents a case study that represent a clear example of the Ac interference and Split factor. Finally, a few recommendations are provided to achieve a safety zone in the area beyond the boundary of the HV system.

Keywords: UGOH, High Voltage, AC interference, Earthing Design.

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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: Dongmin Cai, Stephen S-T Yau

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Lacking an inherent “natural" dissimilarity measure between objects in categorical dataset presents special difficulties in clustering analysis. However, each categorical attributes from a given dataset provides natural probability and information in the sense of Shannon. In this paper, we proposed a novel method which heuristically converts categorical attributes to numerical values by exploiting such associated information. We conduct an experimental study with real-life categorical dataset. The experiment demonstrates the effectiveness of our approach.

Keywords: Categorical, Clustering, Converting, Information

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Authors: Mahamed G.H. Omran, Andries P Engelbrecht, Ayed Salman

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A new dynamic clustering approach (DCPSO), based on Particle Swarm Optimization, is proposed. This approach is applied to unsupervised image classification. The proposed approach automatically determines the "optimum" number of clusters and simultaneously clusters the data set with minimal user interference. The algorithm starts by partitioning the data set into a relatively large number of clusters to reduce the effects of initial conditions. Using binary particle swarm optimization the "best" number of clusters is selected. The centers of the chosen clusters is then refined via the Kmeans clustering algorithm. The experiments conducted show that the proposed approach generally found the "optimum" number of clusters on the tested images.

Keywords: Clustering Validation, Particle Swarm Optimization, Unsupervised Clustering, Unsupervised Image Classification.

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Authors: Parvinder S. Sandhu, Jagdeep Singh, Vikas Gupta, Mandeep Kaur, Sonia Manhas, Ramandeep Sidhu

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Prediction of fault-prone modules provides one way to support software quality engineering. Clustering is used to determine the intrinsic grouping in a set of unlabeled data. Among various clustering techniques available in literature K-Means clustering approach is most widely being used. This paper introduces K-Means based Clustering approach for software finding the fault proneness of the Object-Oriented systems. The contribution of this paper is that it has used Metric values of JEdit open source software for generation of the rules for the categorization of software modules in the categories of Faulty and non faulty modules and thereafter empirically validation is performed. The results are measured in terms of accuracy of prediction, probability of Detection and Probability of False Alarms.

Keywords: K-Means, Software Fault, Classification, ObjectOriented Metrics.

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Authors: Surender Kumar Soni

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Wireless Sensor Networks (WSNs) are wireless networks consisting of number of tiny, low cost and low power sensor nodes to monitor various physical phenomena like temperature, pressure, vibration, landslide detection, presence of any object, etc. The major limitation in these networks is the use of nonrechargeable battery having limited power supply. The main cause of energy consumption WSN is communication subsystem. This paper presents an efficient grid formation/clustering strategy known as Grid based level Clustering and Aggregation of Data (GCAD). The proposed clustering strategy is simple and scalable that uses low duty cycle approach to keep non-CH nodes into sleep mode thus reducing energy consumption. Simulation results demonstrate that our proposed GCAD protocol performs better in various performance metrics.

Keywords: Ad hoc network, Cluster, Grid base clustering, Wireless sensor network.

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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: Semeh Ben Salem, Sami Naouali, Moetez Sallami

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Clustering is a well known data mining technique used in pattern recognition and information retrieval. The initial dataset to be clustered can either contain categorical or numeric data. Each type of data has its own specific clustering algorithm. In this context, two algorithms are proposed: the k-means for clustering numeric datasets and the k-modes for categorical datasets. The main encountered problem in data mining applications is clustering categorical dataset so relevant in the datasets. One main issue to achieve the clustering process on categorical values is to transform the categorical attributes into numeric measures and directly apply the k-means algorithm instead the k-modes. In this paper, it is proposed to experiment an approach based on the previous issue by transforming the categorical values into numeric ones using the relative frequency of each modality in the attributes. The proposed approach is compared with a previously method based on transforming the categorical datasets into binary values. The scalability and accuracy of the two methods are experimented. The obtained results show that our proposed method outperforms the binary method in all cases.

Keywords: Clustering, k-means, categorical datasets, pattern recognition, unsupervised learning, knowledge discovery.

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Authors: Christian H. Sanabria-Montaña, Rodrigo Huerta-Quintanilla

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A lattice network is a special type of network in which all nodes have the same number of links, and its boundary conditions are periodic. The most basic lattice network is the ring, a one-dimensional network with periodic border conditions. In contrast, the Cartesian product of d rings forms a d-dimensional lattice network. An analytical expression currently exists for the clustering coefficient in this type of network, but the theoretical value is valid only up to certain connectivity value; in other words, the analytical expression is incomplete. Here we obtain analytically the clustering coefficient expression in d-dimensional lattice networks for any link density. Our analytical results show that the clustering coefficient for a lattice network with density of links that tend to 1, leads to the value of the clustering coefficient of a fully connected network. We developed a model on criminology in which the generalized clustering coefficient expression is applied. The model states that delinquents learn the know-how of crime business by sharing knowledge, directly or indirectly, with their friends of the gang. This generalization shed light on the network properties, which is important to develop new models in different fields where network structure plays an important role in the system dynamic, such as criminology, evolutionary game theory, econophysics, among others.

Keywords: Clustering coefficient, criminology, generalized, regular network d-dimensional.

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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: Saran Satsangi, Ashish Saini, Amit Saraswat

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In this paper, a new K-means clustering based approach for identification of voltage control areas is developed. Voltage control areas are important for efficient reactive power management in power systems operating under deregulated environment. Although, voltage control areas are formed using conventional hierarchical clustering based method, but the present paper investigate the capability of K-means clustering for the purpose of forming voltage control areas. The proposed method is tested and compared for IEEE 14 bus and IEEE 30 bus systems. The results show that this K-means based method is competing with conventional hierarchical approach

Keywords: Voltage control areas, reactive power management, K-means clustering algorithm

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Authors: Y. Q. Lv, C.K.M. Lee

Abstract:

This paper develops a quality estimation method with the application of fuzzy hierarchical clustering. Quality estimation is essential to quality control and quality improvement as a precise estimation can promote a right decision-making in order to help better quality control. Normally the quality of finished products in manufacturing system can be differentiated by quality standards. In the real life situation, the collected data may be vague which is not easy to be classified and they are usually represented in term of fuzzy number. To estimate the quality of product presented by fuzzy number is not easy. In this research, the trapezoidal fuzzy numbers are collected in manufacturing process and classify the collected data into different clusters so as to get the estimation. Since normal hierarchical clustering methods can only be applied for real numbers, fuzzy hierarchical clustering is selected to handle this problem based on quality standards.

Keywords: Quality Estimation, Fuzzy Quality Mean, Fuzzy Hierarchical Clustering, Fuzzy Number, Manufacturing system

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Authors: Ashok Kumar, Narottam Chand, Vinod Kumar

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Due to the limited energy resources, energy efficient operation of sensor node is a key issue in wireless sensor networks. Clustering is an effective method to prolong the lifetime of energy constrained wireless sensor network. However, clustering in wireless sensor network faces several challenges such as selection of an optimal group of sensor nodes as cluster, optimum selection of cluster head, energy balanced optimal strategy for rotating the role of cluster head in a cluster, maintaining intra and inter cluster connectivity and optimal data routing in the network. In this paper, we propose a protocol supporting an energy efficient clustering, cluster head selection/rotation and data routing method to prolong the lifetime of sensor network. Simulation results demonstrate that the proposed protocol prolongs network lifetime due to the use of efficient clustering, cluster head selection/rotation and data routing.

Keywords: Wireless sensor networks, clustering, energy efficient, localization.

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Authors: Faruq A. Al-Omari, Nabeel I. Al-Fayoumi

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In this paper, we present a new algorithm for clustering data in large datasets using image processing approaches. First the dataset is mapped into a binary image plane. The synthesized image is then processed utilizing efficient image processing techniques to cluster the data in the dataset. Henceforth, the algorithm avoids exhaustive search to identify clusters. The algorithm considers only a small set of the data that contains critical boundary information sufficient to identify contained clusters. Compared to available data clustering techniques, the proposed algorithm produces similar quality results and outperforms them in execution time and storage requirements.

Keywords: Data clustering, Data mining, Image-mapping, Pattern discovery, Predictive analysis.

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Authors: Sungju Lee, Jangsoo Lee , Hongjoong Sin, Seunghwan Yoo, Sanghyuck Lee, Jaesik Lee, Yongjun Lee, Sungchun Kim

Abstract:

The wireless sensor networks have been extensively deployed and researched. One of the major issues in wireless sensor networks is a developing energy-efficient clustering protocol. Clustering algorithm provides an effective way to prolong the lifetime of a wireless sensor networks. In the paper, we compare several clustering protocols which significantly affect a balancing of energy consumption. And we propose an Energy-Efficient Distributed Unequal Clustering (EEDUC) algorithm which provides a new way of creating distributed clusters. In EEDUC, each sensor node sets the waiting time. This waiting time is considered as a function of residual energy, number of neighborhood nodes. EEDUC uses waiting time to distribute cluster heads. We also propose an unequal clustering mechanism to solve the hot-spot problem. Simulation results show that EEDUC distributes the cluster heads, balances the energy consumption well among the cluster heads and increases the network lifetime.

Keywords: Wireless Sensor Network, Distributed UnequalClustering, Multi-hop, Lifetime.

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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: P. Ashok, G. M. Kadhar Nawaz

Abstract:

Rough set theory is used to handle uncertainty and incomplete information by applying two accurate sets, Lower approximation and Upper approximation. In this paper, the rough clustering algorithms are improved by adopting the Similarity, Dissimilarity–Similarity and Entropy based initial centroids selection method on three different clustering algorithms namely Entropy based Rough K-Means (ERKM), Similarity based Rough K-Means (SRKM) and Dissimilarity-Similarity based Rough K-Means (DSRKM) were developed and executed by yeast dataset. The rough clustering algorithms are validated by cluster validity indexes namely Rand and Adjusted Rand indexes. An experimental result shows that the ERKM clustering algorithm perform effectively and delivers better results than other clustering methods. Outlier detection is an important task in data mining and very much different from the rest of the objects in the clusters. Entropy based Rough Outlier Factor (EROF) method is seemly to detect outlier effectively for yeast dataset. In rough K-Means method, by tuning the epsilon (ᶓ) value from 0.8 to 1.08 can detect outliers on boundary region and the RKM algorithm delivers better results, when choosing the value of epsilon (ᶓ) in the specified range. An experimental result shows that the EROF method on clustering algorithm performed very well and suitable for detecting outlier effectively for all datasets. Further, experimental readings show that the ERKM clustering method outperformed the other methods.

Keywords: Clustering, Entropy, Outlier, Rough K-Means, validity index.

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Authors: G. Lavanya Devi, Allam Appa Rao, A. Damodaram, GR Sridhar, G. Jaya Suma

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Cluster analysis divides data into groups that are meaningful, useful, or both. Analysis of biological data is creating a new generation of epidemiologic, prognostic, diagnostic and treatment modalities. Clustering of protein sequences is one of the current research topics in the field of computer science. Linear relation is valuable in rule discovery for a given data, such as if value X goes up 1, value Y will go down 3", etc. The classical linear regression models the linear relation of two sequences perfectly. However, if we need to cluster a large repository of protein sequences into groups where sequences have strong linear relationship with each other, it is prohibitively expensive to compare sequences one by one. In this paper, we propose a new technique named General Regression Model Technique Clustering Algorithm (GRMTCA) to benignly handle the problem of linear sequences clustering. GRMT gives a measure, GR*, to tell the degree of linearity of multiple sequences without having to compare each pair of them.

Keywords: Clustering, General Regression Model, Protein Sequences, Similarity Measure.

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Authors: George E. Tsekouras, Dimitris Papageorgiou, Sotiris Kotsiantis, Christos Kalloniatis, Panagiotis Pintelas

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We develop a three-step fuzzy logic-based algorithm for clustering categorical attributes, and we apply it to analyze cultural data. In the first step the algorithm employs an entropy-based clustering scheme, which initializes the cluster centers. In the second step we apply the fuzzy c-modes algorithm to obtain a fuzzy partition of the data set, and the third step introduces a novel cluster validity index, which decides the final number of clusters.

Keywords: Categorical data, cultural data, fuzzy logic clustering, fuzzy c-modes, cluster validity index.

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