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.

This paper utilizes a flat, convex set of fuzzy relations to provide a physically realistic and mathematically tractable model for small group decision theory. Measures of individual preference, group consensus, and distance to consensus are defined, and a number of theoretical results about them are given. Various decision-oriented goals are characterized, and the theory is illustrated numerically using data from a small group communication experiment.

Fuzzy measures of preference and consensus in group decision-making

This paper extends some of the work presented in Redner and Walker [I9841 on the maximum likelihood estimate of parameters in a mixture model to a Bayesian modal estimate. The problem of determining the mode of the joint posterior distribution is discussed. Necessary conditions are given for a choice of parameters to be the mode and a numerical scheme based on the EM algorithm is presented. Some theoretical remarks on the resulting iterative scheme and simulation results are also given.

Estimating the parameters of mixture models with modal estimators

We extend the nearest prototype classifier to a generalized nearest prototype classifier (GNPC). The GNPC uses "soft" labeling of the prototypes in the classes, thereby encompassing a variety of classifiers. Based on how the prototypes are found we distinguish between presupervised and post-supervised GNPC designs. We derive the conditions for optimality of two designs where prototypes represent: 1) the components of class-conditional mixture densities (presupervised design); or 2) the components of the unconditional mixture density (post-supervised design). An artificial data set and the "satimage" data set from the database ELENA are used to experimentally study the two approaches. A radial basis function network is used as a representative of each GNPC type. Neither the theoretical nor the experimental results indicate clear reasons to prefer one of the approaches. The post-supervised GNPC design tends to be more robust and less accurate than the presupervised one.

Presupervised and post-supervised prototype classifier design

his paper describes a computer program developed at the University of South Carolina to simulate the evolution of carbonate geometries and their facies responding to: (1 ) varying rates of accumulation; (2) eustatic sea-level variation; and (3) tectonic movement of the crust, The simulation creates two-dimensional plots of synchronous depositional sequences within sediment bodies. Rates of carbonate accumulation are modeled as a function of water depth and lateral position across the shelf. Carbonate accumulation includes in situ organic production and transport by hydrodynamic processes. Influx of clastic sediments is modeled to cause an exponential decrease in the rate of carbonate accumulation. Rates of carbonate accumulation can be further diminished with a user-defined depth-controlled wave-damping function. Eustatic variation is modeled by a fourth-order linear change in sea level over time (as described by Vail and others, 1977), with a higher order sinusoidal oscillation of sea level superimposed upon it. Reef margin and interior lagoonal facies on platforms and shelves are predicted. Modeling of these facies zones includes aggradation, progradation, backstepping, shoal development, and drowning. The Devonian Judy Creek reef complex of the western Canada Alberta basin was used both as an aid in constructing the carbonate simulation model and as an example on which to test the completed program. The Judy Creek model was constructed by the fourth co-author (J.C.W.) from the study of 100 cores and the correlation of a systematic grid of wireline log-core cross sections. Judy Creek consists of five overall shoaling-upward depositional cycles. Superimposed upon each cycle are several subcycles. Marine hardgrounds locally cap the first three cycles at the margin of the buildup. The top of the fourth cycle is a subaerial cemented surface. The top of the upper cycle is a widespread marine hardground. Subcycles consist of minor shoaling-upward sequences of lagoonal facies. The results of two versions of the carbonate model include: (1) a site-specific version of the Judy Creek area, which shows the facies location and movement within Judy Creek; and (2) a more generalized carbonate model. Both versions use similar inputs. The geometry and facies distributions of Judy Creek are simulated using a stairlike fourth-order eustatic sea-level curve (as described by Vail and others, 1977) and a low-amplitude higher order sea-level oscillation with a varying period in which sea-level fall is matched by tectonic subsidence. Maximum rates of accumulation average around 3.0 to 5.0 m/10 ka. The fourth-order sea-level variation consists of a rapid 3.5-5.0 m/10 ka rise followed by a gradual rise of 0.7-1.5 m/10 ka, followed by another rapid rise of the same magnitude, followed by another gradual rise. The higher order sea-level oscillation consists of 0.5 to 1.5-m amplitudes with periods ranging from 20 to 40 ka. Tectonic subsidence averages between 0.5 and 1.0 m/10 ka.

Judy Creek: A Case Study for a Two-Dimensional Sediment Deposition Simulation

Alternating cluster estimation (ACE) is a generalized clustering model. Relational ACE is a modification of ACE that can be used to cluster data which do not possess a clear numerical representation, but for which a meaningful relation matrix can be defined. For text data sets we define (pairwise) relation matrices based on the Levenshtein string distance (1966). Relational ACE with Levenshtein distances is applied to four different texts. The cluster centers represent typical words in the texts, so this algorithm can be used to automatically determine keywords.

James C. Bezdek

Papers

Fuzzy measures of preference and consensus in group decision-making

Estimating the parameters of mixture models with modal estimators

Presupervised and post-supervised prototype classifier design

Judy Creek: A Case Study for a Two-Dimensional Sediment Deposition Simulation

Automatic keyword extraction with relational clustering and Levenshtein distances