Possibilistic rough fuzzy C-means algorithm in data clustering and image segmentation
01 Dec 2014-pp 1-6
TL;DR: This paper improves a possibilistic rough C-Means (PRCM) algorithm introduced by Anuradha et, al. and introduces a new algorithm, which is called as possibileistic rough fuzzy C-means (PFCM), which is compared with the improved PRCM and the basic PRFCM algorithm to establish experimentally that this algorithm is comparatively better than PR CM and the corresponding RCM algorithm.
Abstract: 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.
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01 Jan 1979
TL;DR: This special issue aims at gathering the recent advances in learning with shared information methods and their applications in computer vision and multimedia analysis and addressing interesting real-world computer Vision and multimedia applications.
Abstract: In the real world, a realistic setting for computer vision or multimedia recognition problems is that we have some classes containing lots of training data and many classes contain a small amount of training data. Therefore, how to use frequent classes to help learning rare classes for which it is harder to collect the training data is an open question. Learning with Shared Information is an emerging topic in machine learning, computer vision and multimedia analysis. There are different level of components that can be shared during concept modeling and machine learning stages, such as sharing generic object parts, sharing attributes, sharing transformations, sharing regularization parameters and sharing training examples, etc. Regarding the specific methods, multi-task learning, transfer learning and deep learning can be seen as using different strategies to share information. These learning with shared information methods are very effective in solving real-world large-scale problems. This special issue aims at gathering the recent advances in learning with shared information methods and their applications in computer vision and multimedia analysis. Both state-of-the-art works, as well as literature reviews, are welcome for submission. Papers addressing interesting real-world computer vision and multimedia applications are especially encouraged. Topics of interest include, but are not limited to: • Multi-task learning or transfer learning for large-scale computer vision and multimedia analysis • Deep learning for large-scale computer vision and multimedia analysis • Multi-modal approach for large-scale computer vision and multimedia analysis • Different sharing strategies, e.g., sharing generic object parts, sharing attributes, sharing transformations, sharing regularization parameters and sharing training examples, • Real-world computer vision and multimedia applications based on learning with shared information, e.g., event detection, object recognition, object detection, action recognition, human head pose estimation, object tracking, location-based services, semantic indexing. • New datasets and metrics to evaluate the benefit of the proposed sharing ability for the specific computer vision or multimedia problem. • Survey papers regarding the topic of learning with shared information. Authors who are unsure whether their planned submission is in scope may contact the guest editors prior to the submission deadline with an abstract, in order to receive feedback.
1,758 citations
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
01 Jan 2016
TL;DR: An application of fuzzy soft sets in decision making is provided which substantially improve and is more realistic than the algorithm proposed earlier by Maji et al.
Abstract: 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.
24 citations
01 Jan 2016
TL;DR: This chapter discusses on several applications of rough set theory in medical diagnosis that can be utilized as a supporting tool to the medical practitioner, mainly country like India with vast rural areas and absolute shortage of physicians.
Abstract: Modeling intelligent system in the field of medical diagnosis is still a challenging work. Intelligent systems in medical diagnosis can be utilized as a supporting tool to the medical practitioner, mainly country like India with vast rural areas and absolute shortage of physicians. Intelligent systems in the field of medical diagnosis can also able to reduce cost and problems for the diagnosis like dynamic perturbations, shortage of physicians, etc. An intelligent system may be considered as an information system that provides answer to queries relating to the information stored in the Knowledge Base (KB), which is a repository of human knowledge. Rough set theory is an efficient model to capture uncertainty in data and the processing of data using rough set techniques is easy and convincing. Rule generation is an inherent component in rough set analysis. So, medical systems which have uncertainty inherent can be handled in a better way using rough sets and its variants. The objective of this chapter is to discuss on several such applications of rough set theory in medical diagnosis.
8 citations
01 Jan 2021
TL;DR: Data mining is a technique to derive hidden patterns from data to classify, predict, and find relationships among the data to inform patients and doctors about the future risk of illness thereby guiding medical experts to determine proper treatment.
Abstract: Data mining is a technique to derive hidden patterns from data to classify, predict, and find relationships among the data. The healthcare industry is growing exponentially with the help of advanced technology and methods to save the lives of people at risk. Classification techniques in healthcare are used to classify the type or category of disease that is affecting the patient. Another dimension of healthcare is prediction of disease, where the patient can be treated earlier before the disease progresses and becomes more severe. Prediction plays a major role as it is directly involved in the success of treatment. Accurate predictive models can inform patients and doctors about the future risk of illness thereby guiding medical experts to determine proper treatment. Both the classification and predictive models can be validated to assess accuracy based on different test cases.
7 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
"Possibilistic rough fuzzy C-means a..." refers methods in this paper
...The corresponding algorithms are the fuzzy c-means (FCM) [5, 6], rough c-means (RCM) [7] and the intuitionistic fuzzy c-means (IFCM) [8]....
[...]
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
"Possibilistic rough fuzzy C-means a..." refers methods in this paper
...The imprecise models used for this purpose are fuzzy set introduced by Zadeh [2], rough set by Pawlak [3], intuitionistic fuzzy set by Atanassov [4]....
[...]
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
"Possibilistic rough fuzzy C-means a..." refers methods in this paper
...Two of the performance indices, which are widely used are the Davis-Bouldin (DB) [14] and Dunn (D) indexes [15]....
[...]
...As far as the accuracy measures are concerned we have taken the two well known indices of the Davis and Bouldin (DB) index [14] and the Dunn (D) index [15]....
[...]
...It has been mentioned in [14] that the number of clusters and the partitioning method methods used do not affect the DB measure....
[...]
...For the experimentation part we take different datasets and images as inputs and use the two measuring indices, the DB-index [14] and the D-index [15]....
[...]
...They have used efficiency measuring indices like the DaviesBouldin (DB) [14] and Dunn (D) indexes [15] to compare the accuracy of performance of these algorithms by using different types of images and datasets for the purpose....
[...]
01 Jan 1973
TL;DR: Two fuzzy versions of the k-means optimal, least squared error partitioning problem are formulated for finite subsets X of a general inner product space; in both cases, the extremizing solutions are shown to be fixed points of a certain operator T on the class of fuzzy, k-partitions of X, and simple iteration of T provides an algorithm which has the descent property relative to the least squarederror criterion function.
Abstract: Two fuzzy versions of the k-means optimal, least squared error partitioning problem are formulated for finite subsets X of a general inner product space. In both cases, the extremizing solutions are shown to be fixed points of a certain operator T on the class of fuzzy, k-partitions of X, and simple iteration of T provides an algorithm which has the descent property relative to the least squared error criterion function. In the first case, the range of T consists largely of ordinary (i.e. non-fuzzy) partitions of X and the associated iteration scheme is essentially the well known ISODATA process of Ball and Hall. However, in the second case, the range of T consists mainly of fuzzy partitions and the associated algorithm is new; when X consists of k compact well separated (CWS) clusters, Xi , this algorithm generates a limiting partition with membership functions which closely approximate the characteristic functions of the clusters Xi . However, when X is not the union of k CWS clusters, the limi...
5,787 citations
"Possibilistic rough fuzzy C-means a..." refers methods in this paper
...They have used efficiency measuring indices like the DaviesBouldin (DB) [14] and Dunn (D) indexes [15] to compare the accuracy of performance of these algorithms by using different types of images and datasets for the purpose....
[...]
...As far as the accuracy measures are concerned we have taken the two well known indices of the Davis and Bouldin (DB) index [14] and the Dunn (D) index [15]....
[...]
...Two of the performance indices, which are widely used are the Davis-Bouldin (DB) [14] and Dunn (D) indexes [15]....
[...]
...For the experimentation part we take different datasets and images as inputs and use the two measuring indices, the DB-index [14] and the D-index [15]....
[...]
01 Jan 1973
TL;DR: In this paper, two fuzzy versions of the k-means optimal, least squared error partitioning problem are formulated for finite subsets X of a general inner product space, and the extremizing solutions are shown to be fixed points of a certain operator T on the class of fuzzy, k-partitions of X, and simple iteration of T provides an algorithm which has the descent property relative to the LSE criterion function.
Abstract: Two fuzzy versions of the k-means optimal, least squared error partitioning problem are formulated for finite subsets X of a general inner product space. In both cases, the extremizing solutions are shown to be fixed points of a certain operator T on the class of fuzzy, k-partitions of X, and simple iteration of T provides an algorithm which has the descent property relative to the least squared error criterion function. In the first case, the range of T consists largely of ordinary (i.e. non-fuzzy) partitions of X and the associated iteration scheme is essentially the well known ISODATA process of Ball and Hall. However, in the second case, the range of T consists mainly of fuzzy partitions and the associated algorithm is new; when X consists of k compact well separated (CWS) clusters, Xi , this algorithm generates a limiting partition with membership functions which closely approximate the characteristic functions of the clusters Xi . However, when X is not the union of k CWS clusters, the limi...
5,254 citations