Similarity-Driven Cluster Merging Method for Unsupervised Fuzzy Clustering

In this paper, a similarity-driven cluster merging method is proposed for unsupervised fuzzy clustering. The cluster merging method is used to resolve the problem of cluster validation. Starting with an overspecified number of clusters in the data, pairs of similar clusters are merged based on the proposed similarity-driven cluster merging criterion. The similarity between clusters is calculated by a fuzzy cluster similarity matrix, while an adaptive threshold is used for merging. In addition, a modified generalized objective function is used for prototype-based fuzzy clustering. The function includes the p-norm distance measure as well as principal components of the clusters. The number of the principal components is determined automatically from the data being clustered. The performance of this unsupervised fuzzy clustering algorithm is evaluated by several experiments of an artificial data set and a gene expression data set.Singapore-MIT Alliance (SMA

Fuzzy clustering with volume prototypes and adaptive cluster merging

Two extensions to the objective function-based fuzzy clustering are proposed. First, the (point) prototypes are extended to hypervolumes, whose size can be fixed or can be determined automatically from the data being clustered. It is shown that clustering with hypervolume prototypes can be formulated as the minimization of an objective function. Second, a heuristic cluster merging step is introduced where the similarity among the clusters is assessed during optimization. Starting with an overestimation of the number of clusters in the data, similar clusters are merged in order to obtain a suitable partitioning. An adaptive threshold for merging is proposed. The extensions proposed are applied to Gustafson–Kessel and fuzzy c-means algorithms, and the resulting extended algorithm is given. The properties of the new algorithm are illustrated by various examples

An Intelligent System A Comparative Study Of Fuzzy C-Means And K-Means Clustering Techniques

Clustering analysis has been considered as useful means for identifying patterns of dataset. The aim for this analysis is to decide what is the most suitable algorithm to be used when dealings with new scatter data. In this analysis, two important clustering algorithms namely fuzzy c-means and k-means clustering algorithms are compared. These algorithms are applied to synthetic data 2-dimensional dataset. The numbers of data points as well as the number of clusters are determined, with that the behavior patterns of both the algorithm are analyzed. Quality of clustering is based on lowest distance and highest membership similarity between the points and the centre cluster in one cluster, known as inter-class cluster similarity. Fuzzy c-means and k-means clustering are compared based on the inter-class cluster similarity by obtaining the minimum value of summation of distance. Additionally, in fuzzy c-means algorithm, most researchers fix weighting exponent (m) to a conventional value of 2 which might not be the appropriate for all applications. In order to find m, also called as fuzziness coefficient, optimal in fuzzy c-means on particular dataset is based on minimal reconstruction error

Noise-robust method for image segmentation

Segmentation of noisy images is one of the most challenging problems in image analysis and any improvement of segmentation methods can highly influence the performance of many image processing applications. In automated image segmentation, the fuzzy c-means (FCM) clustering has been widely used because of its ability to model uncertainty within the data, applicability to multi-modal data and fairly robust behaviour. However, the standard FCM algorithm does not consider any information about the spatial linage context and is highly sensitive to noise and other imaging artefacts. Considering above mentioned problems, we developed a new FCM-based approach for the noise-robust fuzzy clustering and we present it in this paper. In this new iterative algorithm we incorporated both spatial and feature space information into the similarity measure and the membership function. We considered that spatial information depends on the relative location and features of the neighbouring pixels. The performance of the proposed algorithm is tested on synthetic image with different noise levels and real images. Experimental quantitative and qualitative segmentation results show that our method efficiently preserves the homogeneity of the regions and is more robust to noise than other FCM-based methods

A robust clustering procedure for fuzzy data

AbstractIn this paper we propose a robust clustering method for handling LR-type fuzzy numbers. The proposed method based on similarity measures is not necessary to specify the cluster number and initials. Several numerical examples demonstrate the effectiveness of the proposed robust clustering method, especially robust to outliers, different cluster shapes and initial guess. We then apply this algorithm to three real data sets. These are Taiwanese tea, student data and patient blood pressure data sets. Because tea evaluation comes under an expert subjective judgment for Taiwanese tea, the quality levels are ambiguity and imprecision inherent to human perception. Thus, LR-type fuzzy numbers are used to describe these quality levels. The proposed robust clustering method successfully establishes a performance evaluation system to help consumers better understand and choose Taiwanese tea. Similarly, LR-type fuzzy numbers are also used to describe data types for student and patient blood pressure data. The proposed method actually presents good clustering results for these real data sets

A Comparative Study of Fuzzy C-Means Algorithm and Entropy-Based Fuzzy Clustering Algorithms

Fuzzy clustering is useful to mine complex and multi-dimensional data sets, where the members have partial or fuzzy relations. Among the various developed techniques, fuzzy-C-means (FCM) algorithm is the most popular one, where a piece of data has partial membership with each of the pre-defined cluster centers. Moreover, in FCM, the cluster centers are virtual, that is, they are chosen at random and thus might be out of the data set. The cluster centers and membership values of the data points with them are updated through some iterations. On the other hand, entropy-based fuzzy clustering (EFC) algorithm works based on a similarity-threshold value. Contrary to FCM, in EFC, the cluster centers are real, that is, they are chosen from the data points. In the present paper, the performances of these algorithms have been compared on four data sets, such as IRIS, WINES, OLITOS and psychosis (collected with the help of forty doctors), in terms of the quality of the clusters (that is, discrepancy factor, compactness, distinctness) obtained and their computational time. Moreover, the best set of clusters has been mapped into 2-D for visualization using a self-organizing map (SOM)

Fuzzy Distance Measure Based Affinity Propagation Clustering

Affinity Propagation (AP) is an effective algorithm that find exemplars repeatedly exchange real valued messages between pairs of data points. AP uses the similarity between data points to calculate the messages. Hence, the construction of similarity is essential in the AP algorithm. A common choice for similarity is the negative Euclidean distance. However, due to the simplicity of Euclidean distance, it cannot capture the real structure of data. Furthermore, Euclidean distance is sensitive to noise and outliers such that the performance of the AP might be degraded. Therefore, researchers have intended to utilize different similarity measures to analyse the performance of AP. nonetheless, there is still a room to enhance the performance of AP clustering. A clustering method called fuzzy based Affinity propagation (F-AP) is proposed, which is based on a fuzzy similarity measure. Experiments shows the efficiency of the proposed F-AP, experiments is performed on UCI dataset. Results shows a promising improvement on AP

Pemodelan Sistem Tangki-terhubung Dengan Menggunakan Model Fuzzy Takagi-sugeno

Modeling of Coupled-Tank System Using Fuzzy Takagi-Sugeno Model. This paper describes modeling of coupledtanksystem based on data measurement using fuzzy Takagi-Sugeno model. The fuzzy clustering method of Gustafson-Kessel algorithm is used to classify input-output data into several clusters based on distance similarity of a member ofinput-output data from center of cluster. The formed clusters are projected orthonormally into each linguistic variablesof premise part to determine membership function of fuzzy Takagi-Sugeno model. By estimating data in each cluster,the consequent parameters of fuzzy Takagi-Sugeno model are calculated using weighted least-squares method. Theresulted fuzzy Takagi-Sugeno model is validated by using model performance parameters variance-accounted-for (VAF)and root mean square (RMS) as performance indicators. The simulation results show that the fuzzy Takagi-Sugenomodel is able to mimic nonlinear characteristic of coupled-tank system with good value of model performanceindicators

Development of novel fuzzy clustering techniques in the context of e-learning

This thesis investigates the performance of fuzzy clustering for dynamically discovering content relationships in e-Learning material based on document metadata descriptions. This form of knowledge representation is exploited to enable flexible content navigation in eLearning environments. However, the methods and tools developed in this thesis have wider applicability. The purpose of clustering techniques is to determine underlying structures and relations in data sets usually based on distance or proximity measures. A number of clustering methods to suit particular applications have been developed throughout the years. This thesis specifically considers the well-known Fuzzy c-Means (FCM) clustering technique as the basis for document clustering. Initially, novel expressions are developed to extend the FCM algorithm, which is based on the Euclidean metric, to an algorithm based on other proximity measures more appropriate for quantifying document relationships. These include the cosine, Jaccard and overlap similarity coefficients. This novel algorithm works with normalised k-dimensional data vectors that lie in hyper-sphere of unit radius and hence has been named Hyper-Spherical Fuzzy c-Means (H-FCN). Subsequently, the performance of the H-FCM algorithm is compared to that of the FCM as well as conventional hard (ie non-fuzzy) clustering algorithms with respect to four test document collections. Both the impact of different proximity measures as well as the impact of pre-processing the document vector representations for dimensionality reduction are thoroughly investigated. Results demonstrate that the H-FCM clustering method outperforms both the conventional FCM method as well as hard clustering techniques. This thesis also considers the integration of fuzzy clustering techniques in an end-to- end e-Leaming system. In particular, a tool to convert the H-FCM document clustering outcome into a knowledge representation, based on the Topic Maps standard, suitable for Web-based environments is developed. Moreover, a tool to enable flexible navigation of e-Learning material based on the fuzzy knowledge space is also developed. This tool is deployed in a real e-Learning environment where user trials are carried out. Finally, this thesis considers the important problem of defining a suitable number of clusters for appropriately capturing the concepts of the knowledge space. In particular, an hierarchical H-FCM algorithm is developed where the sought granularity level defines the number of clusters. In this algorithm, a novel heuristic based on asymmetric similarity measures is exploited to link document clusters hierarchically and to form a topic hierarchy