Meena Tushir

A new Kernelized hybrid c-mean clustering model with optimized parameters

A possibilistic approach was initially proposed for c-means clustering. Although the possibilistic approach is sound, this algorithm tends to find identical clusters. To overcome this shortcoming, a possibilistic Fuzzy c-means algorithm (PFCM) was proposed which produced memberships and possibilities simultaneously, along with the cluster centers. PFCM addresses the noise sensitivity defect of Fuzzy c-means (FCM) and overcomes the coincident cluster problem of possibilistic c-means (PCM). Here we propose a new model called Kernel-based hybrid c-means clustering (KPFCM) where PFCM is extended by adopting a Kernel induced metric in the data space to replace the original Euclidean norm metric. Use of Kernel function makes it possible to cluster data that is linearly non-separable in the original space into homogeneous groups in the transformed high dimensional space. From our experiments, we found that different Kernels with different Kernel widths lead to different clustering results. Thus a key point is to choose an appropriate Kernel width. We have also proposed a simple approach to determine the appropriate values for the Kernel width. The performance of the proposed method has been extensively compared with a few state of the art clustering techniques over a test suit of several artificial and real life data sets. Based on computer simulations, we have shown that our model gives better results than the previous models.

A New Kernel based Hybrid c-Means Clustering Model

A possibilistic approach was initially proposed for c-means clustering. Although the possibilistic approach is sound, this algorithm tends to find identical clusters. To overcome this shortcoming, a possibilistic fuzzy c-means algorithm (PFCM) was proposed which produced memberships and possibilities simultaneously, along with the cluster centers. PFCM addresses the noise sensitivity defect of fuzzy c-means (FCM) and overcomes the coincident cluster problem of possibilistic c means (PCM). Here we propose a new model called Kernel based hybrid c means clustering (KPFCM) where PFCM is extended by adopting a Kernel induced metric in the data space to replace the original Euclidean norm metric. Numerical examples show that our model gives better results than the previous models.

Application of hybrid fuzzy PID controller for three-area power system with generation rate constraint

This paper presents a new approach for load frequency control of three-area interconnected reheat thermal power system with the consideration of generation rate constraint (GRC). The PID-type fuzzy controller is combined with a conventional PID controller to enhance the performance and robustness of the controller. The proposed controller called hybrid fuzzy PID (HFLPID) controller has been designed for a three-area connected power system. Two performance criteria were utilised for the comparison. First, settling times and overshoots of the frequency deviation were compared. Later, integral of time multiplied absolute error (ITAE) analysis was carried out to compare all the controllers. All the models were simulated by MATLAB 7.0/Simulink software. The simulation results show that the proposed controller developed in this study performs better than the other controllers. Robustness of proposed controller is checked by analysing the system response with varying system parameters.

A novel clustering method for fuzzy model identification

Takagi-Sugeno models are an important class of fuzzy rule based oriented models, generally used for prediction and control. Fuzzy clustering is one of effective methods for identification. In this method, we propose to use a fuzzy clustering method (Kernel based fuzzy c-means method) for automatically constructing a multi-input fuzzy model to identify the structure of a fuzzy model. To clarify the advantages of the proposed method, it also shows some examples of modeling, among them a model of a human operators control action and a qualitative model to explain the trends in the time series data of the price of a stock.

Fuzzy c-Means Clustering Strategies: A Review of Distance Measures

In the process of clustering, our attention is to find out basic procedures that measures the degree of association between the variables. Many clustering methods use distance measures to find similarity or dissimilarity between any pair of objects. The fuzzy c-means clustering algorithm is one of the most widely used clustering techniques which uses Euclidean distance metrics as a similarity measurement. The choice of distance metrics should differ with the data and how the measure of their comparison is done. The main objective of this paper is to present mathematical description of different distance metrics which can be acquired with different clustering algorithm and comparing their performance using the number of iterations used in computing the objective function, the misclassification of the datum in the cluster, and error between ideal cluster center location and observed center location.

A New Log Kernel-Based Possibilistic Clustering

An unsupervised possibilistic (UPC) algorithm with the use of validity indexes has already been proposed. Although UPC works well, it does not show a good accuracy for non-convex cluster structure. To overcome this limitation, we have proposed a kernel version of UPC with a conditionally positive-definite kernel function. It has the ability to detect clusters with different shapes and convex structures because it transforms data into high-dimensional space. Our proposed algorithm, the kernelized UPC-Log(UKPC-L), is an extension of UPC, by introducing log kernel function, which is only conditionally positive-definite function. This makes the performance of our proposed algorithm better than UPC in case of non-convex cluster structures. This has been demonstrated by the results obtained on several real and synthetic datasets. We have compared the performance of UPC and our proposed algorithm using the concept of misclassification, accuracy and error rate to show its efficiency and accuracy.

Performance Assessment for Clustering Techniques for Image Segmentation

The analysis and processing of large datasets is a challenge for researchers. Several approaches have been developed to model these complex data, based on some mathematical theories. In this paper, we are comparing image segmentation techniques based on unsupervised clustering approaches such as probability approach, possibilistic approach, credibilistic, and intuitionistic approach. This paper presents comparison of these approaches. The four approaches are studied and analyzed both quantitatively and qualitatively. These approaches are implemented on synthetic images, and performance is analyzed.

A conditionally positive definite kernel function for possibilistic clustering

In the past few years, the kernel-based clustering methods have overpowered the conventional clustering techniques in the field of unsupervised learning due to its strength and effectiveness to deal with nonlinearly separable data and mapping it into higher dimensional feature space by preserving the inner structure of the data. Many kernel functions exist in the literature which works effectively depending on the type of dataset to be used. In this paper, we have proposed a new log kernel function which is embedded in the unsupervised possibilistic clustering and this kernel function is not explored much in research. We have done extensive comparison of the proposed algorithm with few clustering techniques over a test suite of several synthetic and real life datasets. Based on the experimental results, we have proved that our algorithm gives better performance than the previous methods on various comparative parameters like ideal centroids, error rate, misclassification, accuracy and elapsed time.

Exploring different kernel functions for kernel-based clustering

Kernel methods are ones that, by replacing the inner product with positive definite function, implicitly perform a non-linear mapping of input data into a high dimensional feature space. Kernel functions are used to make this mapping in higher dimension redundant. These kernel functions play an important role in classification. The kernel-based clustering methods are found to be superior in accuracy to the conventional ones. The choice of kernel function is neither easy nor trivial. Various types of kernel based clustering methods have been studied so far by many researchers, where Gaussian kernel, in particular, has been found to be useful. In this study, we present a comprehensive comparative analysis of kernel based hybrid c-means clustering using different kernel functions. We have incorporated Mercer kernel functions positive definite kernels as well as conditionally positive definite kernel functions. Various synthetic datasets and real-life datasets are used for analysis. Experiments results show that there exist other robust kernel functions which hold like Gaussian kernel.

Performance Assessment of Kernel-Based Clustering

Kernel methods are ones that, by replacing the inner product with positive definite function, implicitly perform a nonlinear mapping of input data into a high-dimensional feature space. Various types of kernel-based clustering methods have been studied so far by many researchers, where Gaussian kernel, in particular, has been found to be useful. In this paper, we have investigated the role of kernel function in clustering and incorporated different kernel functions. We discussed numerical results in which different kernel functions are applied to kernel-based hybrid c-means clustering. Various synthetic data sets and real-life data set are used for analysis. Experiments results show that there exist other robust kernel functions which hold like Gaussian kernel.