There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

/pdf/data-mining-concepts-and-techniques-4dtvdfkvmi.pdf

Data Mining: Concepts and Techniques

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.

Pattern Recognition with Fuzzy Objective Function Algorithms

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.

/pdf/data-clustering-a-review-4c452f5cab.pdf

Data clustering: a review

Data Mining - Concepts and Techniques.

This paper reports the results of a numerical comparison of two versions of the fuzzy c-means (FCM) clustering algorithms. In particular, we propose and exemplify an approximate fuzzy c-means (AFCM) implementation based upon replacing the necessary ``exact'' variates in the FCM equation with integer-valued or real-valued estimates. This approximation enables AFCM to exploit a lookup table approach for computing Euclidean distances and for exponentiation. The net effect of the proposed implementation is that CPU time during each iteration is reduced to approximately one sixth of the time required for a literal implementation of the algorithm, while apparently preserving the overall quality of terminal clusters produced. The two implementations are tested numerically on a nine-band digital image, and a pseudocode subroutine is given for the convenience of applications-oriented readers. Our results suggest that AFCM may be used to accelerate FCM processing whenever the feature space is comprised of tuples having a finite number of integer-valued coordinates.

Efficient Implementation of the Fuzzy c-Means Clustering Algorithms

A recently developed fuzzy clustering technique is utilized to analyze the substructure of a well known set of 4-dimensional botanical data. A solution obtained without prior knowledge of labelled pattern structure is offered in support of our contention that the technique proposed affords a comparatively reliable criterion for a posteriori evaluation of cluster validity.

Numerical taxonomy with fuzzy sets

A family of objective functions called fuzzy c-regression models, which can be used too fit switching regression models to certain types of mixed data, is presented. Minimization of particular objective functions in the family yields simultaneous estimates for the parameters of c regression models, together with a fuzzy c-partitioning of the data. A general optimization approach for the family of objective functions is given and corresponding theoretical convergence results are discussed. The approach is illustrated by two numerical examples that show how it can be used to fit mixed data to coupled linear and nonlinear models. >

Switching regression models and fuzzy clustering

Fuzzy models for pattern recognition : methods that search for structures in data

A counterexample to the original incorrect convergence theorem for the fuzzy c-means (FCM) clustering algorithms (see J.C. Bezdak, IEEE Trans. Pattern Anal. and Math. Intell., vol.PAMI-2, no.1, pp.1-8, 1980) is provided. This counterexample establishes the existence of saddle points of the FCM objective function at locations other than the geometric centroid of fuzzy c-partition space. Counterexamples previously discussed by W.T. Tucker (1987) are summarized. The correct theorem is stated without proof: every FCM iterate sequence converges, at least along a subsequence, to either a local minimum or saddle point of the FCM objective function. Although Tucker's counterexamples and the corrected theory appear elsewhere, they are restated as a caution not to further propagate the original incorrect convergence statement.

James C. Bezdek

Papers

Efficient Implementation of the Fuzzy c-Means Clustering Algorithms

Numerical taxonomy with fuzzy sets

Switching regression models and fuzzy clustering

Fuzzy models for pattern recognition : methods that search for structures in data

Convergence theory for fuzzy c-means: Counterexamples and repairs