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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.
Citations
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Book
Jiawei Han1, Micheline Kamber2, Jian Pei2Institutions (2)
08 Sep 2000-
TL;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

23,590 citations


Journal ArticleDOI
Anil K. Jain1, M. N. Murty2, Patrick J. Flynn3Institutions (3)
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.

13,346 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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Journal ArticleDOI
Santo Fortunato1Institutions (1)
01 Feb 2010-Physics Reports
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.

8,432 citations


Journal ArticleDOI
Santo Fortunato1Institutions (1)
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.

7,999 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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Journal ArticleDOI
TL;DR: The objective of this review paper is to summarize and compare some of the well-known methods used in various stages of a pattern recognition system and identify research topics and applications which are at the forefront of this exciting and challenging field.
Abstract: The primary goal of pattern recognition is supervised or unsupervised classification. Among the various frameworks in which pattern recognition has been traditionally formulated, the statistical approach has been most intensively studied and used in practice. More recently, neural network techniques and methods imported from statistical learning theory have been receiving increasing attention. The design of a recognition system requires careful attention to the following issues: definition of pattern classes, sensing environment, pattern representation, feature extraction and selection, cluster analysis, classifier design and learning, selection of training and test samples, and performance evaluation. In spite of almost 50 years of research and development in this field, the general problem of recognizing complex patterns with arbitrary orientation, location, and scale remains unsolved. New and emerging applications, such as data mining, web searching, retrieval of multimedia data, face recognition, and cursive handwriting recognition, require robust and efficient pattern recognition techniques. The objective of this review paper is to summarize and compare some of the well-known methods used in various stages of a pattern recognition system and identify research topics and applications which are at the forefront of this exciting and challenging field.

6,278 citations


Cites background from "Pattern Recognition with Fuzzy Obje..."

  • ...In syntactic pattern recognition, a formal analogy is drawn between the structure of patterns and the syntax of a language....

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References
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Journal ArticleDOI

12,936 citations


"Pattern Recognition with Fuzzy Obje..." refers methods in this paper

  • ...Fisher(38) first used it to exemplify linear discriminant analysis....

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  • ...The Iris data have been used as a test set by at least a dozen authors, including Fisher, (38) Kendall, (64) Friedman and Rubin,'40) Wolfe,(117) Scott and Symons,<95) and Backer....

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Book
01 Jan 1972-
TL;DR: This completely revised second edition presents an introduction to statistical pattern recognition, which is appropriate as a text for introductory courses in pattern recognition and as a reference book for workers in the field.
Abstract: This completely revised second edition presents an introduction to statistical pattern recognition Pattern recognition in general covers a wide range of problems: it is applied to engineering problems, such as character readers and wave form analysis as well as to brain modeling in biology and psychology Statistical decision and estimation, which are the main subjects of this book, are regarded as fundamental to the study of pattern recognition This book is appropriate as a text for introductory courses in pattern recognition and as a reference book for workers in the field Each chapter contains computer projects as well as exercises

10,516 citations


"Pattern Recognition with Fuzzy Obje..." refers background in this paper

  • ...(42) Texts on general pattern recognition include those of Bongard,(2S) Patrick,IH1) Tou and Wilcox,(04) Tou and Gonzalez,(l03) and Duda and Hart....

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Journal ArticleDOI
Thomas M. Cover1, Peter E. Hart2Institutions (2)
TL;DR: The nearest neighbor decision rule assigns to an unclassified sample point the classification of the nearest of a set of previously classified points, so it may be said that half the classification information in an infinite sample set is contained in the nearest neighbor.
Abstract: The nearest neighbor decision rule assigns to an unclassified sample point the classification of the nearest of a set of previously classified points. This rule is independent of the underlying joint distribution on the sample points and their classifications, and hence the probability of error R of such a rule must be at least as great as the Bayes probability of error R^{\ast} --the minimum probability of error over all decision rules taking underlying probability structure into account. However, in a large sample analysis, we will show in the M -category case that R^{\ast} \leq R \leq R^{\ast}(2 --MR^{\ast}/(M-1)) , where these bounds are the tightest possible, for all suitably smooth underlying distributions. Thus for any number of categories, the probability of error of the nearest neighbor rule is bounded above by twice the Bayes probability of error. In this sense, it may be said that half the classification information in an infinite sample set is contained in the nearest neighbor.

10,453 citations


"Pattern Recognition with Fuzzy Obje..." refers background or methods in this paper

  • ...In fact, the efficiency of the 1-NN classifier is asymptotically less than twice the theoretically optimal Bayes risk: Cover and Hart showed in (29) that...

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  • ...4) can be improved: the tighter upper bound derived in (29) is...

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  • ...In particular, no analysis such as Cover and Hart's(29) has been formulated for fuzzy classifier designs; whether fuzzy classifiers such as {hb}PCM in (S26) and {!Jh-NP in (S27) have nice asymptotic relations to {fjb} or others remains to be discovered....

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01 Jan 1973-
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


Book
01 Dec 1973-

5,132 citations


"Pattern Recognition with Fuzzy Obje..." refers background or methods in this paper

  • ...1e) is quite involved; and sizes of local error (el), loop error (ed, and a measure of closeness for matrices in Ven (1IU(1+1) - u(1)11> must be chosen....

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  • ...Clustering, for example, is ably represented by the books of Anderberg,(1) Tryon and Bailey,(I09) and Hartigan....

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  • ...l that groups together (1,3) and (10, 3) and minimizes Iw( U, v)....

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  • ...X = {(1, 1), (1, 3), (10, 1), (10, 3), (5, 2)}....

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  • ...[Answer {(1, 1), (1, 3)} u {(5, 2)} u {(la, 1), (10, 3))....

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Network Information
Related Papers (5)
01 Aug 1996

Lotfi A. Zadeh

01 Sep 1999, ACM Computing Surveys

Anil K. Jain, M. N. Murty +1 more

01 Jan 1988

Anil K. Jain, Richard C. Dubes

Performance
Metrics
No. of citations received by the Paper in previous years
YearCitations
202211
2021462
2020535
2019577
2018639
2017687