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

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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.

We discuss topological preservation under feature extraction transformations. Transformations that preserve the order of all distances in any neighborhood of vectors in p-space are defined as metric topology preserving (MTP) transformations. We give a necessary and sufficient condition for this property in terms of Spearman's rank correlation coefficient. A modification of Kohonen's self-organizing feature map algorithm that extracts vectors in q-space from data in p-space is given. Three methods are empirically compared: principal components analysis; Sammon's algorithm; and our extension of the self-organizing feature map algorithm. Our MTP index shows that the first two methods preserve distance ranks on six data sets much more effectively than extended SOFM.

An index of topological preservation and its application to self-organizing feature maps

Statistical features (mean and variance) are considered for region-based image segmentation. These features contain self similar structures which we interpret as fractal objects. Ellipsoidal attractors are transformed to approximately linear structures which are well separated and enable a robust segmentation. We identify class locations using fuzzy c-elliptotypes. The clustering results then yield segmentation using maximum membership defuzzification or, equivalently, a nearest prototype classifier. The method is applied to the digital mammograms from the Mammographic Image Analysis Society and produces reasonable segmentation in all cases.

http://ieeexplore.ieee.org/iel3/4864/13484/00619747.pdf

Image segmentation using fuzzy clustering with fractal features

A Knowledge-Based System Approach to Document Retrieval.

Clustering aims to identify groups of similar objects. To evaluate the results of cluster algorithms, an investigator uses cluster-validity indices. While the theory of cluster validity is well established for vector object data, little effort has been made to extend it to relationship-based data. As such, this paper proposes a theory of reformulation for object-data validity indices so that they can be used to rank the results produced by the relational -means clustering algorithms. More specifically, we create a class of relational validity indices, which is called dual-relational indices, that are guaranteed under certain, but easily met, constraints to produce the same results and, hence, the same cluster counts, as their object-data counterparts.

Relational Duals of Cluster-Validity Functions for the $c$ -Means Family

The authors introduce two new general classes of measures of fuzziness, called the additive and multiplicative classes. Usually three axioms are required for fuzziness measures. The classes not only satisfy these three basic axioms, but also two other desirable axioms. The multiplicative class is based on nonnegative, monotone increasing concave functions. The additive class requires only nonnegative concave functions. Constructing a measure of fuzziness under each of these classes is simple, as the required functional form does not have restrictions. It is demonstrated that several existing measures of fuzziness are special cases of these new classes. >

http://ieeexplore.ieee.org/iel2/1022/7759/00327390.pdf

James C. Bezdek

Papers

An index of topological preservation and its application to self-organizing feature maps

Image segmentation using fuzzy clustering with fractal features

A Knowledge-Based System Approach to Document Retrieval.

Relational Duals of Cluster-Validity Functions for the $c$ -Means Family

Several new classes of measures of fuzziness