Book•
Pattern Recognition with Fuzzy Objective Function Algorithms
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.
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08 Sep 2000TL;DR: This book presents dozens of algorithms and implementation examples, all in pseudo-code and suitable for use in real-world, large-scale data mining projects, and provides a comprehensive, practical look at the concepts and techniques you need to get the most out of real business data.
Abstract: The increasing volume of data in modern business and science calls for more complex and sophisticated tools. Although advances in data mining technology have made extensive data collection much easier, it's still always evolving and there is a constant need for new techniques and tools that can help us transform this data into useful information and knowledge. Since the previous edition's publication, great advances have been made in the field of data mining. Not only does the third of edition of Data Mining: Concepts and Techniques continue the tradition of equipping you with an understanding and application of the theory and practice of discovering patterns hidden in large data sets, it also focuses on new, important topics in the field: data warehouses and data cube technology, mining stream, mining social networks, and mining spatial, multimedia and other complex data. Each chapter is a stand-alone guide to a critical topic, presenting proven algorithms and sound implementations ready to be used directly or with strategic modification against live data. This is the resource you need if you want to apply today's most powerful data mining techniques to meet real business challenges. * Presents dozens of algorithms and implementation examples, all in pseudo-code and suitable for use in real-world, large-scale data mining projects. * Addresses advanced topics such as mining object-relational databases, spatial databases, multimedia databases, time-series databases, text databases, the World Wide Web, and applications in several fields. *Provides a comprehensive, practical look at the concepts and techniques you need to get the most out of real business data
23,600 citations
TL;DR: An overview of pattern clustering methods from a statistical pattern recognition perspective is presented, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners.
Abstract: Clustering is the unsupervised classification of patterns (observations, data items, or feature vectors) into groups (clusters). The clustering problem has been addressed in many contexts and by researchers in many disciplines; this reflects its broad appeal and usefulness as one of the steps in exploratory data analysis. However, clustering is a difficult problem combinatorially, and differences in assumptions and contexts in different communities has made the transfer of useful generic concepts and methodologies slow to occur. This paper presents an overview of pattern clustering methods from a statistical pattern recognition perspective, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners. We present a taxonomy of clustering techniques, and identify cross-cutting themes and recent advances. We also describe some important applications of clustering algorithms such as image segmentation, object recognition, and information retrieval.
14,054 citations
Cites background or methods from "Pattern Recognition with Fuzzy Obje..."
...A generalization of the FCM algorithm was proposed by Bezdek [1981] through a family of...
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...The book by Bezdek [1981] is a good source for material on fuzzy clustering....
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TL;DR: A thorough exposition of community structure, or clustering, is attempted, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists.
Abstract: The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.
9,057 citations
Cites methods from "Pattern Recognition with Fuzzy Obje..."
...Another popular technique, similar in spirit to k-means clustering, is fuzzy k-means clustering (Bezdek, 1981; Dunn, 1974)....
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...Another popular technique, similar in spirit to k-means clustering, is fuzzy k-means clustering (Bezdek, 1981; Dunn, 1973)....
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...In the second step, the vertex points are associated to nc clusters by using fuzzy k-means clustering (Bezdek, 1981; Dunn, 1973) (Section IV....
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TL;DR: A thorough exposition of the main elements of the clustering problem can be found in this paper, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.
8,432 citations
01 Jun 2010
TL;DR: A brief overview of clustering is provided, well known clustering methods are summarized, the major challenges and key issues in designing clustering algorithms are discussed, and some of the emerging and useful research directions are pointed out.
Abstract: Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms into a system of ranked taxa: domain, kingdom, phylum, class, etc. Cluster analysis is the formal study of methods and algorithms for grouping, or clustering, objects according to measured or perceived intrinsic characteristics or similarity. Cluster analysis does not use category labels that tag objects with prior identifiers, i.e., class labels. The absence of category information distinguishes data clustering (unsupervised learning) from classification or discriminant analysis (supervised learning). The aim of clustering is to find structure in data and is therefore exploratory in nature. Clustering has a long and rich history in a variety of scientific fields. One of the most popular and simple clustering algorithms, K-means, was first published in 1955. In spite of the fact that K-means was proposed over 50 years ago and thousands of clustering algorithms have been published since then, K-means is still widely used. This speaks to the difficulty in designing a general purpose clustering algorithm and the ill-posed problem of clustering. We provide a brief overview of clustering, summarize well known clustering methods, discuss the major challenges and key issues in designing clustering algorithms, and point out some of the emerging and useful research directions, including semi-supervised clustering, ensemble clustering, simultaneous feature selection during data clustering, and large scale data clustering.
6,601 citations
References
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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
"Pattern Recognition with Fuzzy Obje..." refers background in this paper
...Prove that each of the sets described is convex: (i) {(x, y) E 1R21x2 + y2 < 9} = B(9, 3) (ii) {(x, y) E 1R21x 2 + y2,,; 9} = B(9, 3) (iii) {(x, y) E 1R211xl + Iyl,,; 9} (iv) {x E W Illxll,,; r} = 11(9, r) H6....
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...X = {(4, 1), (2,1), (3,5), (2, 2)} u {(6, 6), (8,6), (7,5), (9, 9)} C 1R2 is a labeled sample of size 8 from the mixture F(x; w) = Pln(J1t....
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...For example, vector xi = (0,0); xi7 = (9,9)....
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...• , xn} is bounded in [RP, then for any initial (U(°l, ViOl) E M fc x [conv(X)r x [8B(9, 1)r', the ....
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...i341 Fuzzy sets as a basis for clustering were first suggested by Bellman, Kalaba, and Zadeh.(9) Shortly thereafter, some initial attempts were reported by Wee, (114) Flake and Turner,(39) and Gitman and Levine....
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Book•
01 Jan 1972
TL;DR: Republication of this book provides social science and mathematics students with a text that is the analogue of mathematical methods textbooks used in the study of the physical sciences and engineering.
Abstract: As the need for more substantial mathematical training has increased among social science students, the lack of any adequate textbook between the very elementary and the very advanced levels has become crutial. The authors, long-time experts in this field, have answered the need with this volume, and the MIT Press has repsonded by bringing it into renewed circulation.Mathematical Models in the Social Sciences investigates and teaches the formation and analysis of mathematical models with detailed interpretations of the results. These models are self-contained, with the necessary mathematics included in each chapter. A vast range of topics in the social sciences and a wide variety of mathematical techniques are covered by the models. Ample opportunity is also provided for the students to form their own models. Republication of this book provides social science and mathematics students with a text that is the analogue of mathematical methods textbooks used in the study of the physical sciences and engineering. Prerequisites are kept to a minimum; a course in finite mathematics and a semester of calculus are all that is necessary.The chapters cover these main topics (and employ the mathematical approach parenthetically indicated): methodology; preference rankings (an axiomatic approach); ecology (two dynamic models); market stability (a dynamic model); a Markov chain model in sociology; stabilization of money flow (an application of discrete potential theory); branching processes; organization theory (applications of graph theory); and optimal scheduling (a problem in dynamic programming).
367 citations
"Pattern Recognition with Fuzzy Obje..." refers background in this paper
...Several of these aspects are analyzed in Kemeny and Snell, (63) a particularly readable classic introduction to some of the issues raised in this section....
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TL;DR: An algorithm is described for generating fuzzy partitions which extremize a fuzzy extension of the k-means squared-error criterion function on finite data sets X, and the behavior of the algorithm is compared with that of the ordinary ISODATA clustering process and the maximum likelihood method.
Abstract: An algorithm is described for generating fuzzy partitions which extremize a fuzzy extension of the k-means squared-error criterion function on finite data sets X. It is shown how this algorithm may be applied to the problem of estimating the parameters (a priori probabilities, means, and covariances) of mixture of multivariate normal densities, given a finite sample X drawn from the mixture. The behavior of the algorithm is compared with that of the ordinary ISODATA clustering process and the maximum likelihood method, for a specific bivariate mixture.
236 citations
"Pattern Recognition with Fuzzy Obje..." refers background or methods or result in this paper
...(18) In view of the fact that fuzzy c-means prototypes {v;} always lie in [conv(X)Y [as in the proof of (T12....
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...The proof is quite straightforward, using classical unconstrained second-order conditions on the Hessian of !/I at v*, and is again left to (18)....
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...2 are discussed in greater detail in (18), where it was suggested that liB - 011 and Iitli - vdl ~ 0 as n ~ 00, that is, that FCM may converge (stochastically) to the same asymptotic (ML) estimates as (A26....
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...There are various ways to compare these estimates, several of which are discussed in (18)....
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...14 (18,0) 2 3 4 4 5 15 (18, 1) 2 3 4 4 5 16 (18,2) 2 [0....
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TL;DR: This work generalizes the straight line prototype of a cluster developed in Part I to any r-dimensional linear variety of $R^s ,( 0\leqq r < s)$ and considers a distance functional which utilizes convex combinations of the distance functionals developed here and in Part II.
Abstract: In Part I [SIAM J. Appl. Math., 40 (1981), pp. 339–357], Fuzzy c-Lines was introduced as an algorithm for detection and characterization of linearly clustered data. In Part II, we address two extensions of the theory in Part I. Specifically, we will first generalize the straight line prototype of a cluster developed in Part I to any r-dimensional linear variety of $R^s ,( 0\leqq r < s)$; secondly, we will consider a distance functional which utilizes convex combinations of the distance functionals developed here and in Part I. All of the notation and symbols used here are unchanged from Part I.
196 citations
"Pattern Recognition with Fuzzy Obje..." refers background or methods in this paper
...Detailed proof of this fact is given in (17), where it is shown that every sequence generated by (A24....
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...1), we present the proof for r = 1; (17) contains details in the general case....
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...It is shown in (17) that Trm is closed if and only if the extraction of principal components of each S~~ is closed....
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...S); its proof can be found in detail in (17)....
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...algorithms ensue, using necessary conditions delineated in (17)....
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TL;DR: Several experiments reported in here show that the proposed performance measure puts an order on different partitions of the same data which is consistent with the error rate of a classifier designed on the basis of the obtained cluster labelings.
Abstract: Clustering is primarily used to uncover the true underlying structure of a given data set and, for this purpose, it is desirable to subject the same data to several different clustering algorithms. This paper attempts to put an order on the various partitions of a data set obtained from different clustering algorithms. The goodness of each partition is expressed by means of a performance measure based on a fuzzy set decomposition of the data set under consideration. Several experiments reported in here show that the proposed performance measure puts an order on different partitions of the same data which is consistent with the error rate of a classifier designed on the basis of the obtained cluster labelings.
192 citations
"Pattern Recognition with Fuzzy Obje..." refers background in this paper
...Finally, a recent paper by Backer and Jain(6) attempts to compare the utility of various hard clustering algorithms using B (U ; c) and the induced fuzzy partition approach....
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...X = {(4, 1), (2,1), (3,5), (2, 2)} u {(6, 6), (8,6), (7,5), (9, 9)} C 1R2 is a labeled sample of size 8 from the mixture F(x; w) = Pln(J1t....
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