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Proceedings ArticleDOI

Rough intuitionistic fuzzy C-means algorithm and a comparative analysis

22 Aug 2013-pp 23
TL;DR: This paper proposes a new hybrid clustering algorithm called Rough Intuitionistic Fuzzy C-Means and evaluates its performance in comparison to the other algorithms mentioned above.
Abstract: 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.
Citations
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Proceedings ArticleDOI
01 Dec 2014
TL;DR: The algorithm proposed adds an intuitionistic approach in the membership function of the existing spatial FCM (sFCM) that is comparatively less hampered by noise and performs better than existing algorithms.
Abstract: 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.

42 citations

Journal ArticleDOI
TL;DR: To mitigate adverse effects of imbalanced clusters and decrease the computational cost, an interval type-2 fuzzy local measure for the RKM clustering is proposed, on the basis of which, a novel RKm clustering algorithm has been developed that specifically gives due consideration to im balanced clusters.
Abstract: Rough K-Means (RKM) is an efficient clustering algorithm for overlapping datasets, and has captured increasing attention in recent years. RKM algorithms are the main focus on the further description of uncertain objects located in boundary regions in order to improve the performance. However, most available RKM algorithms fail to pay attention to the influence of imbalanced clusters, together with imbalanced spatial distributions (i.e., the cluster density) and differing cluster sizes (i.e., the number of object ratios). This paper seeks to address this deficiency and examines in detail some adverse effects caused by imbalanced clusters. To mitigate adverse effects of imbalanced clusters and decrease the computational cost, an interval type-2 fuzzy local measure for the RKM clustering is proposed, on the basis of which, a novel RKM clustering algorithm has been developed that specifically gives due consideration to imbalanced clusters. The effectiveness and superiority of this algorithm are demonstrated through simulation and experimental analysis.

34 citations


Additional excerpts

  • ...[24], developed a novel rough intuitionistic fuzzy k-means algorithm (RIFKM) accommodates graded nonmembership of objects in clusters and the uncertainty through the boundary regions....

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Journal ArticleDOI
01 Sep 2016
TL;DR: The 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.
Abstract: 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 Apacheź 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 (ź), 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).

28 citations

Journal ArticleDOI
02 Jan 2020
TL;DR: It is found that the proposed initialization algorithm has performed better than the existing initialization algorithms with Peters refined rough k-means clustering algorithm on different datasets with varying zeta values.
Abstract: A new initialization algorithm is proposed in this study to address the issue of random initialization in the rough k-means clustering algorithm refined by Peters. A new means to choose appropriate zeta values in Peters algorithm is proposed. Also, a new performance measure S/O [within-variance (S)/total-variance (O)] index has been introduced for the rough clustering algorithm. The performance criteria such as root-mean-square standard deviation, S/O index, and running time complexity are used to validate the performance of the proposed and random initialization with that of Peters. In addition, other popular initialization algorithms like k-means++, Peters Π, Bradley, and Ioannis are also herein compared. It is found that our proposed initialization algorithm has performed better than the existing initialization algorithms with Peters refined rough k-means clustering algorithm on different datasets with varying zeta values.

19 citations

Journal ArticleDOI
27 Oct 2017-Entropy
TL;DR: A new formulation of the MRI segmentation problem as a kernel-based intuitionistic fuzzy C-means (KIFCM) clustering problem is introduced and a new DNA-based genetic algorithm is proposed to obtain the optimal KIFCM clustering.
Abstract: MRI segmentation is critically important for clinical study and diagnosis. Existing methods based on soft clustering have several drawbacks, including low accuracy in the presence of image noise and artifacts, and high computational cost. In this paper, we introduce a new formulation of the MRI segmentation problem as a kernel-based intuitionistic fuzzy C-means (KIFCM) clustering problem and propose a new DNA-based genetic algorithm to obtain the optimal KIFCM clustering. While this algorithm searches the solution space for the optimal model parameters, it also obtains the optimal clustering, therefore the optimal MRI segmentation. We perform empirical study by comparing our method with six state-of-the-art soft clustering methods using a set of UCI (University of California, Irvine) datasets and a set of synthetic and clinic MRI datasets. The preliminary results show that our method outperforms other methods in both the clustering metrics and the computational efficiency.

17 citations

References
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Book
31 Jul 1981
TL;DR: Books, as a source that may involve the facts, opinion, literature, religion, and many others are the great friends to join with, becomes what you need to get.
Abstract: New updated! The latest book from a very famous author finally comes out. Book of pattern recognition with fuzzy objective function algorithms, as an amazing reference becomes what you need to get. What's for is this book? Are you still thinking for what the book is? Well, this is what you probably will get. You should have made proper choices for your better life. Book, as a source that may involve the facts, opinion, literature, religion, and many others are the great friends to join with.

15,662 citations


"Rough intuitionistic fuzzy C-means ..." refers methods in this paper

  • ...Several modifications to HCM framework led to the development of various uncertainty based C-Means algorithms such as Rough C-Means (RCM) [7], Fuzzy C-Means (FCM) [2], Rough-Fuzzy C-Means (RFCM) [8, 9, 10, 11] and Intuitionistic Fuzzy CMeans (IFCM) [4]....

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  • ...2 Fuzzy C-Means In 1981 Bezdek developed an extremely powerful method to classify fuzzy data known as fuzzy c-means [2] by using the concept of objective function....

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Journal ArticleDOI
TL;DR: Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.

13,376 citations

Journal ArticleDOI
TL;DR: This approach seems to be of fundamental importance to artificial intelligence (AI) and cognitive sciences, especially in the areas of machine learning, knowledge acquisition, decision analysis, knowledge discovery from databases, expert systems, decision support systems, inductive reasoning, and pattern recognition.
Abstract: Rough set theory, introduced by Zdzislaw Pawlak in the early 1980s [11, 12], is a new mathematical tool to deal with vagueness and uncertainty. This approach seems to be of fundamental importance to artificial intelligence (AI) and cognitive sciences, especially in the areas of machine learning, knowledge acquisition, decision analysis, knowledge discovery from databases, expert systems, decision support systems, inductive reasoning, and pattern recognition.

7,185 citations

Journal ArticleDOI
TL;DR: A measure is presented which indicates the similarity of clusters which are assumed to have a data density which is a decreasing function of distance from a vector characteristic of the cluster which can be used to infer the appropriateness of data partitions.
Abstract: A measure is presented which indicates the similarity of clusters which are assumed to have a data density which is a decreasing function of distance from a vector characteristic of the cluster. The measure can be used to infer the appropriateness of data partitions and can therefore be used to compare relative appropriateness of various divisions of the data. The measure does not depend on either the number of clusters analyzed nor the method of partitioning of the data and can be used to guide a cluster seeking algorithm.

6,757 citations


"Rough intuitionistic fuzzy C-means ..." refers background or methods in this paper

  • ...The Davies-Bouldin (DB) [5] and Dunn (D) indexes [3] are a well-known bench mark for performance analysis of clustering algorithms....

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  • ...But, it was shown by Dubois and Prade [5] that in fact they complement each other and introduced hybrid models of rough fuzzy set and fuzzy sough set which are better models than the individual ones....

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  • ...PERFORMANCE INDEXES The Davis-Bouldin (DB) [5] and Dunn (D) indexes [3] are two of the most basic performance analysis indexes....

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  • ...As mentioned in ([5], abstract) the DB measure does not depend on neither the number of clusters analysed nor the method of partitioning of the data and can be used to guide a cluster seeking algorithm....

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Book
01 Jan 1974
TL;DR: The present work gives an account of basic principles and available techniques for the analysis and design of pattern processing and recognition systems.
Abstract: The present work gives an account of basic principles and available techniques for the analysis and design of pattern processing and recognition systems. Areas covered include decision functions, pattern classification by distance functions, pattern classification by likelihood functions, the perceptron and the potential function approaches to trainable pattern classifiers, statistical approach to trainable classifiers, pattern preprocessing and feature selection, and syntactic pattern recognition.

3,237 citations