Efficiency analysis of kernel functions in uncertainty based c-means algorithms
28 Sep 2015-pp 807-813
TL;DR: A comparative analysis is performed over the Gaussian, hyper tangent and radial basis kernel functions by their application on various vague clustering approaches, revealing that for small sized datasets Gaussian kernel produces more accurate clustering than radial basis andhyper tangent kernel functions however for the datasets which are considerably large hyper tangents kernel is superior to other kernel functions.
Abstract: Application of clustering algorithms for investigating real life data has concerned many researchers and vague approaches or their hybridization with other analogous approaches has gained special attention due to their great effectiveness. Recently, rough intuitionistic fuzzy c-means algorithm has been proposed by Tripathy et al [3] and they established its supremacy over all other algorithms contained in the same set. Replacing the Euclidean distance metric with kernel induced metric makes it possible to cluster the objects which are linearly inseparable in the original space. In this paper a comparative analysis is performed over the Gaussian, hyper tangent and radial basis kernel functions by their application on various vague clustering approaches like rough c-means (RCM), intuitionistic fuzzy c-means (IFCM), rough fuzzy c-means (RFCM) and rough intuitionistic fuzzy c-means (RIFCM). All clustering algorithms have been tested on synthetic, user knowledge modeling and human activity recognition datasets taken from UCI repository against the standard accuracy indexes for clustering. The results reveal that for small sized datasets Gaussian kernel produces more accurate clustering than radial basis and hyper tangent kernel functions however for the datasets which are considerably large hyper tangent kernel is superior to other kernel functions. All experiments have been carried out using C language and python libraries have been used for statistical plotting.
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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 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
TL;DR: In this article , two algorithms named jointly fuzzy C-Means and vaguely quantified nearest neighbor (VQNN) imputation (JFCM-VQNI) and jointly fuzzy c-means and fitted VQNN imputation was proposed by considering clustering conception and sufficient extraction of uncertain information.
Abstract: In real cases, missing values tend to contain meaningful information that should be acquired or should be analyzed before the incomplete dataset is used for machine learning tasks. In this work, two algorithms named jointly fuzzy C-Means and vaguely quantified nearest neighbor (VQNN) imputation (JFCM-VQNNI) and jointly fuzzy C-Means and fitted VQNN imputation (JFCM-FVQNNI) have been proposed by considering clustering conception and sufficient extraction of uncertain information. In the proposed JFCM-VQNNI and JFCM-FVQNNI algorithm, the missing value is regarded as a decision feature, and then, the prediction is generated for the objects that contain at least one missing value. Specially, as for JFCM-VQNNI algorithm, indistinguishable matrixes, tolerance relations, and fuzzy membership relations are adopted to identify the potential closest filled values based on corresponding similar objects and related clusters. On the basis of JFCM-VQNNI algorithm, JFCM-FVQNNI algorithm synthetic analyzes the fuzzy membership of the dependent features for instances with each cluster. In order to fill the missing values more accurately, JFCM-FVQNNI algorithm performs fuzzy decision membership adjustment in each object with respect to the related clusters by considering highly relevant decision attributes. The experiments have been carried out on five datasets. Based on the analysis of root-mean-square error, mean absolute error, comparison of imputation values with actual values, and classification accuracy results analysis, we can draw the conclusion that the proposed JFCM-FVQNNI and JFCM-VQNNI algorithms yields sufficient and reasonable imputation performance results by comparing with fuzzy C-Means parameter-based imputation algorithm and fuzzy C-Means rough parameter-based imputation algorithm.
8 citations
TL;DR: It is observed that there is an enhancement in the classification accuracy by using NC and NCH, and it has identified that NCH gives better results.
Abstract: The classification accuracy and the computational complexity are degraded by the occurrence of nonlinear data and mixed pixels present in satellite images. Therefore, the kernel-based fuzzy classifiers are required for the separation of linear and nonlinear data. This paper presents two classifiers for handling the nonlinear separable data and mixed pixels. The classifiers, noise clustering (NC) and NC with hypertangent kernels (NCH), are used for handling these problems in the satellite images. In this study, a comparative study between NC and NCH has been carried out. The membership values of KFCM are obtained to produce the final result. It is found that the proposed classifiers achieved good accuracy. It is observed that there is an enhancement in the classification accuracy by using NC and NCH. The maximum accuracy achieved for NC and NCH is 75% at δ = 0.7, δ = 0.5, respectively. After comparing both the results, it has identified that NCH gives better results. The classification of Formosat-2 data is done by obtaining optimized values of m and δ to generate the fractional outputs. The classification accuracy is performed by using the error matrix with the incorporation of hard classifier and α-cut.
5 citations
Additional excerpts
...It has been clearly seen that the hypertangent kernel performs better than other kernels when applied to a large dataset (Mittal and Tripathy 2015). x; við Þ ¼ 1 tanh jjx vijj2 r2 ð4Þ...
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TL;DR: A new approach of handling mixed pixel problem present in remote sensing data and nonlinearity between class boundaries through incorporating the kernel functions with noise classifier (NC) is presented.
Abstract: Remote sensing data have been used for effective recognition and classification of land use and land cover features on Earth surface. This paper presents a new approach of handling mixed pixel problem present in remote sensing data and nonlinearity between class boundaries through incorporating the kernel functions with noise classifier (NC). Kernel functions have been combined with conventional noise clustering without entropy, classification method (KNC) to classify data obtained from Landsat-8 and Formosat-2 satellites. Simulated image technique has been introduced and used to handle mixed pixel problem and to assess the results of adopted classification method (KNC). The procedure includes optimization of parameters for nine different kernels, finding the best performing kernel, and image to image accuracy assessment using fuzzy error matrix. A comparative analysis of kernel-based noise classifier over conventional NC classifier has also been included in this paper.
4 citations
References
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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
"Efficiency analysis of kernel funct..." refers background or methods in this paper
...The dataset for experimentation was gathered from UCI machine learning repository, evaluations have been performed over synthetic, user modeling and human 807978-1-4799-8792-4/15/$31.00 c©2015 IEEE activity recognition datasets....
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...It is given by following formula = ≠ )(max ),( minmin ll ki iki mS mmd Dunn (7) where 1 i, k, l C C denotes the total number of clusters, m denotes the centroid and S(mi) denotes the within cluster distance that can be found independently for each algorithm....
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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
"Efficiency analysis of kernel funct..." refers background or methods in this paper
...The dataset for experimentation was gathered from UCI machine learning repository, evaluations have been performed over synthetic, user modeling and human 807978-1-4799-8792-4/15/$31.00 c©2015 IEEE activity recognition datasets....
[...]
...It is given by following formula = ≠ )(max ),( minmin ll ki iki mS mmd Dunn (7) where 1 i, k, l C C denotes the total number of clusters, m denotes the centroid and S(mi) denotes the within cluster distance that can be found independently for each algorithm....
[...]
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
TL;DR: It is argued that both notions of a rough set and a fuzzy set aim to different purposes, and it is more natural to try to combine the two models of uncertainty (vagueness and coarseness) rather than to have them compete on the same problems.
Abstract: The notion of a rough set introduced by Pawlak has often been compared to that of a fuzzy set, sometimes with a view to prove that one is more general, or, more useful than the other. In this paper we argue that both notions aim to different purposes. Seen this way, it is more natural to try to combine the two models of uncertainty (vagueness and coarseness) rather than to have them compete on the same problems. First, one may think of deriving the upper and lower approximations of a fuzzy set, when a reference scale is coarsened by means of an equivalence relation. We then come close to Caianiello's C-calculus. Shafer's concept of coarsened belief functions also belongs to the same line of thought. Another idea is to turn the equivalence relation into a fuzzy similarity relation, for the modeling of coarseness, as already proposed by Farinas del Cerro and Prade. Instead of using a similarity relation, we can start with fuzzy granules which make a fuzzy partition of the reference scale. The main contribut...
2,452 citations