Performance and Convergence Analysis of Modified C-Means Using Jeffreys-Divergence for Clustering

The size of data that we generate every day across the globe is undoubtedly astonishing due to the growth of the Internet of Things. So, it is a common practice to unravel important hidden facts and understand the massive data using clustering techniques. However, non- linear relations, which are essentially unexplored when compared to linear correlations, are more widespread within data that is high throughput. Often, nonlinear links can model a large amount of data in a more precise fashion and highlight critical trends and patterns. Moreover, selecting an appropriate measure of similarity is a well-known issue since many years when it comes to data clustering. In this work, a non-Euclidean similarity measure is proposed, which relies on non-linear Jeffreys-divergence (JS). We subsequently develop c- means using the proposed JS (J-c-means). The various properties of the JS and J-c-means are discussed. All the analyses were carried out on a few real-life and synthetic databases. The obtained outcomes show that J-c-means outperforms some cutting-edge c-means algorithms empirically

Relational visual cluster validity

The assessment of cluster validity plays a very important role in cluster analysis. Most commonly used cluster validity methods are based on statistical hypothesis testing or finding the best clustering scheme by computing a number of different cluster validity indices. A number of visual methods of cluster validity have been produced to display directly the validity of clusters by mapping data into two- or three-dimensional space. However, these methods may lose too much information to correctly estimate the results of clustering algorithms. Although the visual cluster validity (VCV) method of Hathaway and Bezdek can successfully solve this problem, it can only be applied for object data, i.e. feature measurements. There are very few validity methods that can be used to analyze the validity of data where only a similarity or dissimilarity relation exists – relational data. To tackle this problem, this paper presents a relational visual cluster validity (RVCV) method to assess the validity of clustering relational data. This is done by combining the results of the non-Euclidean relational fuzzy c-means (NERFCM) algorithm with a modification of the VCV method to produce a visual representation of cluster validity. RVCV can cluster complete and incomplete relational data and adds to the visual cluster validity theory. Numeric examples using synthetic and real data are presente

Generalized fuzzy clustering for segmentation of multi-spectral magnetic resonance images.

An integrated approach for multi-spectral segmentation of MR images is presented. This method is based on the fuzzy c-means (FCM) and includes bias field correction and contextual constraints over spatial intensity distribution and accounts for the non-spherical cluster\u27s shape in the feature space. The bias field is modeled as a linear combination of smooth polynomial basis functions for fast computation in the clustering iterations. Regularization terms for the neighborhood continuity of intensity are added into the FCM cost functions. To reduce the computational complexity, the contextual regularizations are separated from the clustering iterations. Since the feature space is not isotropic, distance measure adopted in Gustafson-Kessel (G-K) algorithm is used instead of the Euclidean distance, to account for the non-spherical shape of the clusters in the feature space. These algorithms are quantitatively evaluated on MR brain images using the similarity measures

Fuzzy C-Means Algorithm Based on Common Mahalanobis Distances

[[abstract]]Some of the well-known fuzzy clustering algorithms are based on Euclidean distance function, which can only be used to detect spherical structural clusters. Gustafson-Kessel (GK) clustering algorithm and Gath-Geva (GG) clustering algorithm were developed to detect non-spherical structural clusters. However, GK algorithm needs added constraint of fuzzy covariance matrix, GK algorithm can only be used for the data with multivariate Gaussian distribution. A Fuzzy C-Means algorithm based on Mahalanobis distance (FCM-M) was proposed by our previous work to improve those limitations of GG and GK algorithms, but it is not stable enough when some of its covariance matrices are not equal. In this paper, A improved Fuzzy C-Means algorithm based on a Common Mahalanobis distance (FCM-CM) is proposed The experimental results of three real data sets show that the performance of our proposed FCM-CM algorithm is better than those of the FCM, GG, GK and FCM-M algorithms

Dynamic calibration and occlusion handling algorithms for lane tracking

[[abstract]]Some of the well-known fuzzy clustering algorithms are based on Euclidean distance function, which can only be used to detect spherical structural clusters. Gustafson-Kessel (GK) clustering algorithm and Gath- Geva (GG) clustering algorithm were developed to detect non-spherical structural clusters. However, GK algorithm needs added constraint of fuzzy covariance matrix, GK algorithm can only be used for the data with multivariate Gaussian distribution. A Fuzzy C-Means algorithm based on Mahalanobis distance (FCM-M) was proposed by our previous work to improve those limitations of GG and GK algorithms, but it is not stable enough when some of its covariance matrices are not equal. In this paper, A improved Fuzzy C-Means algorithm based on a Common Mahalanobis distance (FCM-CM) is proposed The experimental results of three real data sets show that the performance of our proposed FCM-CM algorithm is better than those of the FCM, GG, GK and FCM-M algorithms. © 2009 Old City Publishing, Inc

Performance and Convergence Analysis of Modified C-Means Using Jeffreys-Divergence for Clustering

This work is partially supported by the project "Prediction of diseases through computer assisted diagnosis system using images captured by minimally-invasive and non-invasive modalities", Computer Science and Engineering, PDPM Indian Institute of Information Technology, Design and Manufacturing, Jabalpur India (under ID: SPARC-MHRD-231). This work is also partially supported by the project Grant Agency of Excellence, Univer-sity of Hradec Kralove, Faculty of Informatics and Management, Czech Republic (under ID: UHK-FIM-GE-2204-2021).The size of data that we generate every day across the globe is undoubtedly astonishing due to the growth of the Internet of Things. So, it is a common practice to unravel important hidden facts and understand the massive data using clustering techniques. However, non- linear relations, which are essentially unexplored when compared to linear correlations, are more widespread within data that is high throughput. Often, nonlinear links can model a large amount of data in a more precise fashion and highlight critical trends and patterns. Moreover, selecting an appropriate measure of similarity is a well-known issue since many years when it comes to data clustering. In this work, a non-Euclidean similarity measure is proposed, which relies on non-linear Jeffreys-divergence (JS). We subsequently develop c- means using the proposed JS (J-c-means). The various properties of the JS and J-c-means are discussed. All the analyses were carried out on a few real-life and synthetic databases. The obtained outcomes show that J-c-means outperforms some cutting-edge c-means algorithms empirically.project "Prediction of diseases through computer assisted diagnosis system using images captured by minimally-invasive and non-invasive modalities", Computer Science and Engineering, PDPM Indian Institute of Information Technology, Design and Manufacturing SPARC-MHRD-231project Grant Agency of Excellence, University of Hradec Kralove, Faculty of Informatics and Management, Czech Republic UHK-FIM-GE-2204-202

Dealing with non-metric dissimilarities in fuzzy central clustering algorithms

Clustering is the problem of grouping objects on the basis of a similarity measure among them. Relational clustering methods can be employed when a feature-based representation of the objects is not available, and their description is given in terms of pairwise (dis)similarities. This paper focuses on the relational duals of fuzzy central clustering algorithms, and their application in situations when patterns are represented by means of non-metric pairwise dissimilarities. Symmetrization and shift operations have been proposed to transform the dissimilarities among patterns from non-metric to metric. In this paper, we analyze how four popular fuzzy central clustering algorithms are affected by such transformations. The main contributions include the lack of invariance to shift operations, as well as the invariance to symmetrization. Moreover, we highlight the connections between relational duals of central clustering algorithms and central clustering algorithms in kernel-induced spaces. One among the presented algorithms has never been proposed for non-metric relational clustering, and turns out to be very robust to shift operations. (C) 2008 Elsevier Inc. All rights reserved

Approximation Algorithms for Bregman Co-clustering and Tensor Clustering

In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor clustering [8,34]. Like k-means, these more general problems also suffer from the NP-hardness of the associated optimization. Researchers have developed approximation algorithms of varying degrees of sophistication for k-means, k-medians, and more recently also for Bregman clustering [2]. However, there seem to be no approximation algorithms for Bregman co- and tensor clustering. In this paper we derive the first (to our knowledge) guaranteed methods for these increasingly important clustering settings. Going beyond Bregman divergences, we also prove an approximation factor for tensor clustering with arbitrary separable metrics. Through extensive experiments we evaluate the characteristics of our method, and show that it also has practical impact.Comment: 18 pages; improved metric cas