A New Rough-Fuzzy Clustering Algorithm and its Applications
01 Jan 2014-pp 1245-1251
TL;DR: A robust rough-fuzzy clustering algorithm is applied here to identify clusters having similar objects and it can find overlapping and vaguely defined clusters with arbitrary shapes in noisy environment.
Abstract: Cluster analysis is a technique that divides a given data set into a set of clusters in such a way that two objects from the same cluster are as similar as possible and the objects from different clusters are as dissimilar as possible. A robust rough-fuzzy \(c\)-means clustering algorithm is applied here to identify clusters having similar objects. Each cluster of the robust rough-fuzzy clustering algorithm is represented by a set of three parameters, namely, cluster prototype, a possibilistic fuzzy lower approximation, and a probabilistic fuzzy boundary. The possibilistic lower approximation helps in discovering clusters of various shapes. The cluster prototype depends on the weighting average of the possibilistic lower approximation and probabilistic boundary. The reported algorithm is robust in the sense that it can find overlapping and vaguely defined clusters with arbitrary shapes in noisy environment. The effectiveness of the clustering algorithm, along with a comparison with other clustering algorithms, is demonstrated on synthetic as well as coding and non-coding RNA expression data sets using some cluster validity indices.
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01 Jan 2014
TL;DR: This dissertation aims to provide a history of web exceptionalism from 1989 to 2002, a period chosen in order to explore its roots as well as specific cases up to and including the year in which descriptions of “Web 2.0” began to circulate.
Abstract: Data mining techniques have been used widely in many areas such as business, science, engineering and medicine The techniques allow a vast amount of data to be explored in order to extract useful information from the data One of the foci in the health area is finding interesting biomarkers from biomedical data Mass throughput data generated from microarrays and mass spectrometry from biological samples are high dimensional and is small in sample size Examples include DNA microarray datasets with up to 500,000 genes and mass spectrometry data with 300,000 m/z values While the availability of such datasets can aid in the development of techniques/drugs to improve diagnosis and treatment of diseases, a major challenge involves its analysis to extract useful and meaningful information The aims of this project are: 1) to investigate and develop feature selection algorithms that incorporate various evolutionary strategies, 2) using the developed algorithms to find the “most relevant” biomarkers contained in biological datasets and 3) and evaluate the goodness of extracted feature subsets for relevance (examined in terms of existing biomedical domain knowledge and from classification accuracy obtained using different classifiers) The project aims to generate good predictive models for classifying diseased samples from control
4 citations
Journal Article•
TL;DR: This paper proposes Fuzzy to Rough FuzzY Link Element (FRFLE) which is used as an important factor to conceptualize the rough fuzzy clustering from the fuzzy clusters result and shows that proposed RFCM algorithm using FRFLE deals with less computation time than the traditional RFCM algorithms.
Abstract: Clustering is a standard approach in analysis of data and construction of separated similar groups. The most widely used robust soft clustering methods are fuzzy, rough and rough fuzzy clustering. The prominent feature of soft clustering leads to combine the rough and fuzzy sets. The Rough Fuzzy C-Means (RFCM) includes the lower and boundary estimation of rough sets, and fuzzy membership of fuzzy sets into c-means algorithm, the widespread RFCM needs more computation. To avoid this, this paper proposes Fuzzy to Rough Fuzzy Link Element (FRFLE) which is used as an important factor to conceptualize the rough fuzzy clustering from the fuzzy clustering result. Experiments with synthetic, standard and the different benchmark dataset shows the automation process of the FRFLE value, then the comparison between the results of general RFCM and RFCM using FRFLE is observed. Moreover, the performance analysis result shows that proposed RFCM algorithm using FRFLE deals with less computation time than the traditional RFCM algorithms.
3 citations
Cites methods from "A New Rough-Fuzzy Clustering Algori..."
...RFCM algorithm has been widely used inmany applications [10,12,13,5]....
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22 Oct 2021
TL;DR: Zhang et al. as discussed by the authors proposed a new rough k-means algorithm to measure the weight of boundary objects, which considers the distance from boundary objects to their neighbor points and the number of neighbor points together to dynamically calculate the weights of boundary object to clusters that may belong to.
Abstract: Rough k-means algorithm can effectively deal with the problem of the fuzzy boundaries. But traditional rough k-means algorithm set unified weight for boundary object, ignoring the differences between individual objects. Membership degree method of rough fuzzy k-means algorithm is used to measure the membership degree of boundary object to the clusters that they may belong to, ignoring the distribution of neighbor points of the boundary object. So, according to the distribution of neighbor points of the boundary object, we put forward a new rough k-means algorithm to measure the weight of boundary objects. The proposed algorithm considers the distance from boundary objects to their neighbor points and the number of neighbor points of boundary objects together to dynamically calculate the weights of boundary object to clusters that may belong to. Simulation and experiment, through examples verify the effectiveness of the proposed method.
References
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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
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: An appropriate objective function whose minimum will characterize a good possibilistic partition of the data is constructed, and the membership and prototype update equations are derived from necessary conditions for minimization of the criterion function.
Abstract: The clustering problem is cast in the framework of possibility theory. The approach differs from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values can be interpreted as degrees of possibility of the points belonging to the classes, i.e., the compatibilities of the points with the class prototypes. An appropriate objective function whose minimum will characterize a good possibilistic partition of the data is constructed, and the membership and prototype update equations are derived from necessary conditions for minimization of the criterion function. The advantages of the resulting family of possibilistic algorithms are illustrated by several examples. >
2,388 citations
TL;DR: In this paper, the authors considered the problem of decomposition of the probability density function of the original set into the weighted sum of the component fuzzy set densities, which is done by optimization of some functional defined over all possible fuzzy classifications.
561 citations
Book•
01 Aug 1996
TL;DR: A general framework for the treatment of pattern-recognition problems is discussed, including the notion of a 'fuzzy' set and how this may be employed in a sequential experimental procedure to ascertain whether a symbol is a member of a particular set or not.
Abstract: : This is a preliminary paper in which the authors discuss a general framework for the treatment of pattern-recognition problems. They make precise the notion of a 'fuzzy' set. Then they show how this may be employed in a sequential experimental procedure to ascertain whether a symbol is a member of a particular set or not. The close relation between the problem of pattern recognition and interpolation is stressed. (Author)
378 citations