Data clustering has been playing important roles in many areas like pattern recognition, image segmentation, social networks and database anonymisation. Since most of the data available in real life situation are imprecise by nature, many imprecision based data clustering algorithms are found in literature using individual imprecise models as well as their hybrids. It was observed by Krishnapuram and Keller that the possibilistic approach to the basic clustering algorithms is more efficient as the drawbacks of the basic algorithms are removed. This approach was used to develop the possibilistic versions of fuzzy, rough and rough fuzzy C-Means algorithms to develop their corresponding possibilistic versions. In this paper, we extend these algorithms further by proposing a possibilistic rough intuitionistic fuzzy C-Means algorithm (PRIFCM) and compare its efficiency with other possibilistic algorithms and the RIFCM. Experimental analysis is carried out by taking both numeric as well as the image data. Also, DB and the D indices are used for the comparison which establishes the superiority of PRIFCM. © 2015 IEEE.

Balakrushna Tripathy

Department of Analytics

School of Computer Science and Engineering

Vellore Campus

Tripathy A

Govindarajulu K.

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

On PRIFCM algorithm for data clustering, image segmentation and comparative analysis

2015 IEEE International Advance Computing Conference (IACC)

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

Soft set theory is a new mathematical approach to vagueness introduced by Molodtsov. This is a parameterized family of subsets defined over a universal set associated with a set of parameters. In this paper, we define membership function for fuzzy soft sets. Like the soft sets, fuzzy soft set is a notion which allows fuzziness over a soft set model. So far, more than one attempt has been made to define this concept. Maji et al. defined fuzzy soft sets and several operations on them. In this paper we followed the definition of soft sets provided by Tripathy et al. through characteristic functions in 2015. Many related concepts like complement of a fuzzy soft set, null fuzzy soft set, absolute fuzzy soft set, intersection of fuzzy soft sets and union of fuzzy soft sets are redefined. We provide an application of fuzzy soft sets in decision making which substantially improve and is more realistic than the algorithm proposed earlier by Maji et al. © Springer India 2016.

Advances in Intelligent Systems and Computing Computational Intelligence in Data Mining—Volume 2

A New Approach to Fuzzy Soft Set Theory and Its Application in Decision Making

Fulltext

International Journal of Advanced Information Technology

An Efficient Algorithm for Anonymization of Set-Valued Data and Representation Using Fp-Tree

Use of published organizational data for a variety of purposes has the chance of violation of leakage of individual secret information. Though this is taken care by the organizations by removal or encryption of explicit identifiers, valuable information may still be leaked by quasi identifiers in the released data. The concept of k-anonymity was introduced and several algorithms in this direction have been proposed by different researchers [1, 2, 3, 4, 5, 6, 7, 8, 11] to handle this problem. But the notion of k-anonymity is susceptible to two types of attacks which necessitated the requirement of a better privacy preserving notion leading to the proposal of l- diversity [6]. In [14] a third phase is added to the two phase clustering-based k-anonymisation algorithm OKA [4] to achieve l-diversity. Recently, the clustering stage of the algorithm has been improved in [14] and the diversity stage algorithm is improved in [16] to come up with a fast l-diversity algorithm which deals with a single sensitive attribute in a relational table. Our main contribution in this paper is to develop an l-diversity algorithm to handle multi-sensitive attributes in databases. Also, we shall improve the adjustment stage algorithm so that it becomes more efficient. We also analyse and provide enough reasons to show that though the second and third stages of the algorithm are not necessary in most of the cases, we cannot avoid using these two stages in some cases. © 2011 IEEE.

2011 IEEE Recent Advances in Intelligent Computational Systems

A fast p-sensitive l-diversity Anonymisation algorithm

A fuzzy algorithm is presented for image segmentation of 2D gray scale images whose quality have been degraded by various kinds of noise. Traditional Fuzzy C Means (FCM) algorithm is very sensitive to noise and does not give good results. To overcome this problem, a new fuzzy c means algorithm was introduced [1] that incorporated spatial information. The spatial function is the sum of all the membership functions within the neighborhood of the pixel under consideration. The results showed that this approach was not as sensitive to noise as compared to the traditional FCM algorithm and yielded better results. The algorithm we have proposed adds an intuitionistic approach in the membership function of the existing spatial FCM (sFCM). Intuitionistic refers to the degree of hesitation that arises as a consequence of lack of information and knowledge. Proposed method is comparatively less hampered by noise and performs better than existing algorithms. © 2014 IEEE.

2014 IEEE International Conference on Computational Intelligence and Computing Research

Image segmentation using spatial intuitionistic fuzzy C means clustering

Several data clustering techniques have been developed in literature. It has been observed that the algorithms developed by using imprecise models like rough sets, fuzzy sets and intuitionistic fuzzy sets have been better than the crisp algorithms. Also, the hybrid models provide far better clustering algorithms than the individual models. Several such models have been developed by using a combination of fuzzy set introduced by Zadeh, the rough set introduced by Pawlak and the intuitionistic fuzzy introduced by Atanassov. Notable among them being the Rough Fuzzy C-Means (RFCM) introduced by Mitra et al and the rough intuitionistic fuzzy c-means algorithm (RIFCM) introduced and studied by Tripathy et al Krishnapuram and Keller observed that the basic clustering algorithms have the probabilistic flavour; for example due to the presence of the constraint on the memberships used in the fuzzy C-Means (FCM) algorithm. So, they introduced the concept of possibilistic approach and developed a possibilistic fuzzy C-means (PFCM) algorithm. Another approach to PFCM is due to Pal et al. In this paper, we improve a possibilistic rough C-Means (PRCM) algorithm introduced by Anuradha et, al. and introduce a new algorithm, which we call as possibilistic rough fuzzy C-Means (PRFCM) and compare its efficiency with the improved PRCM and the basic PRFCM algorithm to establish experimentally that this algorithm is comparatively better than PRCM and the corresponding RCM algorithm. We perform the experimental analysis by taking different types of numerical datasets and images as inputs and using standard accuracy measures like the DB and the D-index. © 2014 IEEE.

Possibilistic rough fuzzy C-means algorithm in data clustering and image segmentation

Purpose: The purpose of this paper is to provide a way to analyze satellite images using various clustering algorithms and refined bitplane methods with other supporting techniques to prove the superiority of RIFCM. Design/methodology/approach: A comparative study has been carried out using RIFCM with other related algorithms from their suitability in analysis of satellite images with other supporting techniques which segments the images for further process for the benefit of societal problems. Four images were selected dealing with hills, freshwater, freshwatervally and drought satellite images. Findings: The superiority of the proposed algorithm, RIFCM with refined bitplane towards other clustering techniques with other supporting methods clustering, has been found and as such the comparison, has been made by applying four metrics (Otsu (Max-Min), PSNR and RMSE (40%-60%-Min-Max), histogram analysis (Max-Max), DB index and D index (Max-Min)) and proved that the RIFCM algorithm with refined bitplane yielded robust results with efficient performance, reduction in the metrics and time complexity of depth computation of satellite images for further process of an image. Practical implications: For better clustering of satellite images like lands, hills, freshwater, freshwatervalley, drought, etc. of satellite images is an achievement. Originality/value: The existing system extends the novel framework to provide a more explicit way to analyze an image by removing distortions with refined bitplane slicing using the proposed algorithm of rough intuitionistic fuzzy c-means to show the superiority of RIFCM. © Emerald Group Publishing Limited.

Kybernetes

A comparative study of RIFCM with other related algorithms from their suitability in analysis of satellite images using other supporting techniques

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

Data clustering algorithms are used in many fields like anonymisation of databases, image processing, analysis of satellite images and medical data analysis. There are several C-Means clustering algorithms in the literature. Besides the hard C-Means, there are uncertainty based C-Means algorithms like the Fuzzy C-Means algorithm and its variants, the Rough C-Means algorithm, the Intuitionistic Fuzzy C- Means algorithm and the hybrid C-Means algorithms (Rough Fuzzy C-Means algorithm). In this paper we propose a new hybrid clustering algorithm called Rough Intuitionistic Fuzzy C-Means and evaluate its performance in comparison to the other algorithms mentioned above. We have applied these algorithms on numerical as well as image data of two different types and used some benchmarking indexes for the evaluation of their performance. The results show that the proposed algorithm outperforms the existing algorithms in almost all cases. © 2013 ACM.

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