There are several algorithms used for data clustering and as imprecision has become an inherent part of datasets now days, many such algorithms have been developed so far using fuzzy sets, rough sets, intuitionistic fuzzy sets, and their hybrid models. In order to increase the flexibility of conventional rough approximations, a probability based rough sets concept was introduced in the 90s namely decision theoretic rough sets (DTRS). Using this model Li et al. extended the conventional rough c-means. Euclidean distance has been used to measure the similarity among data. As has been observed the Euclidean distance has the property of separability. So, as a solution to that several Kernel distances are used in literature. In fact, we have selected three of the most popular kernels and developed an improved Kernelized rough c-means algorithm. We compare the results with the basic decision theoretic rough c-means. For the comparison we have used three datasets namely Iris, Wine and Glass. The three Kernel functions used are the Radial Basis, the Gaussian, and the hyperbolic tangent. The experimental analysis by using the measuring indices DB and D show improved results for the Kernelized means. We also present various graphs to showcase the clustered data. © Springer Nature Singapore Pte Ltd. 2017.

Balakrushna Tripathy

Department of Analytics

School of Computer Science and Engineering

Vellore Campus

Jayaram Reddy A

Department of Software and Systems Engineering

School of Information Technology and Engineering

Ryan Serrao

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

An Analysis of Decision Theoretic Kernalized Rough C -Means

Advances in Intelligent Systems and Computing Artificial Intelligence and Evolutionary Computations in Engineering Systems

Over the years data clustering algorithms have been used for image segmentation. Due to the presence of uncertainty in real life datasets, several uncertainty based data clustering algorithms have been developed. The c-means clustering algorithms form one such family of algorithms. Starting with the fuzzy c-means (FCM) a subfamily of this family comprises of rough c-means (RCM), intuitionistic fuzzy c-means (IFCM) and their hybrids like rough fuzzy c-means (RFCM) and rough intuitionistic fuzzy c-means (RIFCM). In the basic subfamily of this family of algorithms, the Euclidean distance was being used to measure the similarity of data. However, the sub family of algorithms obtained replacing the Euclidean distance by kernel based similarities produced better results. Especially, these algorithms were useful in handling viably cluster data points which are linearly inseparable in original input space. During this period it was inferred by Krishnapuram and Keller that the membership constraints in some rudimentary uncertainty based clustering techniques like fuzzy c-means imparts them a probabilistic nature, hence they suggested its possibilistic version. In fact all the other member algorithms from basic subfamily have been extended to incorporate this new notion. Currently, the use of image data is growing vigorously and constantly, accounting to huge figures leading to big data. Moreover, since image segmentation happens to be one of the most time consuming processes, industries are in the need of algorithms which can solve this problem at a rapid pace and with high accuracy. In this paper, we propose to combine the notions of kernel and possibilistic approach together in a distributed environment provided by Apache™ Hadoop. We integrate this combined notion with map-reduce paradigm of Hadoop and put forth three novel algorithms; Hadoop based possibilistic kernelized rough c-means (HPKRCM), Hadoop based possibilistic kernelized rough fuzzy c-means (HPKRFCM) and Hadoop based possibilistic kernelized rough intuitionistic fuzzy c-means (HPKRIFCM) and study their efficiency in image segmentation. We compare their running times and analyze their efficiencies with the corresponding algorithms from the other three sub families on four different types of images, three different kernels and six different efficiency measures; the Davis Bouldin index (DB), Dunn index (D), alpha index (α), rho index (ρ), alpha star index (α*) and gamma index (γ). Our analysis shows that the hyper-tangent kernel with Hadoop based possibilistic kernelized rough intuitionistic fuzzy c-means is the best one for image segmentation among all these clustering algorithms. Also, the times taken to render segmented images by the proposed algorithms are drastically low in comparison to the other algorithms. The implementations of the algorithms have been carried out in Java and for the proposed algorithms we have used Hadoop framework installed on CentOS. For statistical plotting we have used matplotlib (python library). © 2016 Elsevier B.V.

Applied Soft Computing

Hadoop based uncertain possibilistic kernelized c-means algorithms for image segmentation and a comparative analysis

The RCM algorithm may lead to undesirable solutions in practice because the points close to data points being assigned are neglected which led to the development of the decision theoretic rough set (DTRS) model and the decision theoretic rough C-means algorithm (DTRCM). It was recently improved further with the introduction of decision theoretic rough fuzzy C-means (DTRFCM). Here, we present a further improved algorithm called the decision theoretic intuitionistic fuzzy rough C-means (DTRIFCM) and provide a comparative performance analysis of DTRCM, DTRFCM and DTRIFCM through experiments and efficiency measuring indices DB, D and Acc. According to DB and D indexes DTRIFCM is better than the other two, where as far as the accuracy is concerned DTRFCM is better. We have chosen the data sets Iris, Wine, WDBC and Glass from UCI repository as input for the experimental purpose. © Springer International Publishing Switzerland 2016.

Proceedings of First International Conference on Information and Communication Technology for Intelligent Systems: Volume 1 Smart Innovation, Systems and Technologies

Decision Theoretic Rough Intuitionistic Fuzzy C-Means Algorithm

Imprecision based data clustering algorithms have gained a lot of importance these days because of the imprecise character of modern day databases. Some such algorithms are the rough c-means (RCM), fuzzy c-means (FCM) and their hybrid versions. Li et al used the decision theoretic rough set (DTRS) model by the way improving the RCM. In their approach they have used a notion called loss function to limit the information lost due to neighbours. The method of allocation using decision-theoretic rough sets model deals with potentially high computational cost. It has been observed that hybrid models are better than individual models. Keeping this in view, here we develop a clustering algorithm using DTRS and fuzzy sets in view called the decision-theoretic rough fuzzy c-means (DTRFCM). Experiments carried out show that our approach is more efficient than the DTRS algorithm. For this purpose we used several well-known data sets and parameters like the DB-index, D-index and Accuracy measure. © 2015 IEEE.

2015 IEEE International Conference on Research in Computational Intelligence and Communication Networks (ICRCICN)

A decision theoretic rough fuzzy c-means algorithm

Clustering of real life data for analysis has gained popularity and imprecise methods or their hybrid approaches has attracted many researchers of late. Recently, rough intuitionistic fuzzy c-means algorithm was introduced and studied by Tripathy et al [3] and it was found to be superior to all other algorithms in this family. Kernel based counter part of these algorithms have been found to behave better than their corresponding Euclidean distance based algorithms. Very recently kernel based rough fuzzy algorithm was put forth by Bhargav et al [4]. A comparative analysis over standard datasets and images has established the superiority of this algorithm over its corresponding standard algorithm. In this paper we introduce the kernel based rough intuitionistic fuzzy c-means algorithm and show that it is superior to all the algorithms in the sequel; i.e. both normal and the kernel based algorithms. We establish it through experimental analysis by taking different type of inputs and using standard accuracy measures. © Springer International Publishing Switzerland 2014.

Smart Innovation, Systems and Technologies Advanced Computing, Networking and Informatics- Volume 1

On Kernel Based Rough Intuitionistic Fuzzy C-means Algorithm and a Comparative Analysis

From the beginning of the data analysis system cluster computing plays an important role on it. The very early developed clustering algorithms which can handle only numerical data and K-means clustering is one of them and was proposed by Macqueen [1] in 1967. This algorithm helps us to find the homogeneity of the data set. This K-means algorithm has been modified in many ways to get the modified K-means and kernel based K-means is one of them. It is a nonlinear transformation which transforms the sample data into high dimensional feature space. Though this kernel based K-means performs good almost on every data set but it is unable to handle uncertainty. After rough set theory has been proposed by Pawlak [2], we have many clustering algorithms based on it which can handle uncertainty and heterogeneous data and Rough based K-means is one of them. So in this paper we are proposing the combination of these two methods and known as kernel based K-Means using rough set. © 2012 IEEE.

Journal	Data powered by TypesetAdvances in Intelligent Systems and Computing Artificial Intelligence and Evolutionary Computations in Engineering Systems
Publisher	Data powered by TypesetSpringer Singapore
ISSN	2194-5357
Open Access	0