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.

Clustering is an important family of unsupervised machine learning methods. Cluster validity indices are widely used to assess the quality of obtained clustering results. The C index is one of the most popular cluster validity indices. This paper shows that the C index can be used not only to validate but also to actually find clusters. This leads to difficult discrete optimization problems which can be approximately solved by a canonical genetic algorithm. Numerical experiments compare this novel approach to the well-known c-means and single linkage clustering algorithms. For all five considered popular real-world benchmark data sets the proposed method yields a better C index than any of the other (pure) clustering methods.

Optimizing the C Index Using a Canonical Genetic Algorithm

A knowledge-based system approach is applied to the design of a document retrieval system for online retrieval of bibliographic material. The main components of the system are a language interface that understands user queries in pseudo natural language (i.e. queries that are restricted to subject domain concepts), a retrieval component that combines the expertise of subject-domain and retrieval experts, a help system that aids users in formulating and reformulating queries, and a user model builder that infers specific user characteristics. A comprehensive mathematical model based on fuzzy sets and fuzzy relations has been defined for the thesaurus and the retrieval mechanism and a prototypical system has been implemented in a modular fashion to test system response to changes in model parameters.

A knowledge-based approach to online document retrieval system design

Summary form only given, as follows. Let x be a real-valued scalar field, partitioned into t subsets of non-overlapping variables X/sub i/ (i=1, ..., t). Alternating optimization (AO) is an iterative procedure for minimizing (or maximizing) the function f(x)= f(X/sub 1/, X/sub 2/, ..., X/sub t/) jointly over all variables by alternating restricted minimizations (or maximizations) over the individual subsets of variables X/sub 1/, ..., X/sub t/. AO is the basis for the c-means clustering algorithm (t=2), many forms of vector quantization (t = 2, 3 and 4) and the expectation maximization algorithm (t=4) for normal mixture decomposition. First we review where and how AO fits into the overall optimization landscape. Then we state (without proofs) two new theorems that give very general local and global convergence and rate-of-convergence results which hold for all partitionings of x. Finally, we discuss the important problem of choosing a "best" partitioning of the input variables for the AO approach. We show that the number of possible AO iteration schemes is larger than the number of standard partitions of the input variables. Two numerical examples are given to illustrate that the selection of the t subsets of x has an important effect on the rate of convergence of the corresponding AO algorithm to a solution.

Partitioning the variables for alternating optimization of real-valued scalar fields

An iterative procedure for minimizing a generalized sum-of-squared-errors clustering criterion

The human genome project and its related research bring the promise of a revolution in our knowledge of the function of genes and their interactions with environmental factors across multiple species. However, there is a huge amount of information related to these genes that is located in multiple knowledge sources available on the Internet, with much of the data changing rapidly. High density microarray technologies and newer proteomics techniques allow for the analyses of thousands of genes. In clustering and subsequent knowledge discovery on unknown gene products, the primary features to date are the gene sequence and expression values found following a microarray experiment. One major goal is to determine the function of this gene product and its similarity in function or structure to other up-regulated or down-regulated gene products. Many measures have been proposed to calculate closeness of sequences. However, for many gene products, additional information comes from the set of gene ontology (GO) annotations and the set of journal abstracts related to the gene product. For these genes, it is reasonable to include similarity measures based on the terms found in the GO and/or the index term sets of the related documents (MeSH annotations). In both cases we deal with comparing two sets of terms coming from a taxonomy (GO or MeSH.). In this talk we propose ordered weighted average (OWA) measures for computing the similarity of two sets of terms found in a taxonomy (and hence, the two gene products annotated with terms from the taxonomy). The operators we identify are also known as linear combinations of order statistics (LOS), special cases of the Choquet integral, and qualify as OWA operators because the weights are defined by linguistic quantifiers. Using them, we build similarity measures based on the collection of pairwise term "associations" found using an information theoretic approach. The advantage of the OWA operators is the fact that they are simply built out of pairwise coefficients of association and the measures for the integral fusion can be tailored to produce "linguistic" combinations, e.g., "at least two terms must support the connection". We present examples and comparisons and show the use of our GO approach for knowledge discovery, annotation verification, visualization and clustering.

James C. Bezdek

Papers

Optimizing the C Index Using a Canonical Genetic Algorithm

A knowledge-based approach to online document retrieval system design

Partitioning the variables for alternating optimization of real-valued scalar fields

An iterative procedure for minimizing a generalized sum-of-squared-errors clustering criterion

LevenshteinOWA operators for gene product similarity, clustering, and knowledge discovery