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.

Anomaly detection is an important challenge for tasks such as fault diagnosis and intrusion detection in energy constrained wireless sensor networks. A key problem is how to minimise the communication overhead in the network while performing in-network computation when detecting anomalies. Our approach to this problem is based on a formulation that uses distributed, one-class quarter-sphere support vector machines to identify anomalous measurements in the data. We demonstrate using sensor data from the Great Duck Island Project that our distributed approach is energy efficient in terms of communication overhead while achieving comparable accuracy to a centralised scheme.

Quarter Sphere Based Distributed Anomaly Detection in Wireless Sensor Networks

Many clustering models define good clusters as extrema of objective functions. Optimization of these models is often done using an alternating optimization (AO) algorithm driven by necessary conditions for local extrema. We abandon the objective function model in favor of a generalized model called alternating cluster estimation (ACE). ACE uses an alternating iteration architecture, but membership and prototype functions are selected directly by the user. Virtually every clustering model can be realized as an instance of ACE. Out of a large variety of possible instances of non-AO models, we present two examples: 1) an algorithm with a dynamically changing prototype function that extracts representative data and 2) a computationally efficient algorithm with hyperconic membership functions that allows easy extraction of membership functions. We illustrate these non-AO instances on three problems: a) simple clustering of plane data where we show that creating an unmatched ACE algorithm overcomes some problems of fuzzy c-means (FCM-AO) and possibilistic c-means (PCM-AO); b) functional approximation by clustering on a simple artificial data set; and c) functional approximation on a 12 input 1 output real world data set. ACE models work pretty well in all three cases.

Alternating cluster estimation: a new tool for clustering and function approximation

An extension of the hard and fuzzy c-means (HCM/FCM) clustering algorithms is described. Specifically, these models are extended to admit the case where the (dis)similarity measure on pairs of numerical vectors includes two members of the Minkowski or p-norm family, viz., the p=1 and p= infinity norms. In the absence of theoretically necessary conditions to guide a numerical solution of the nonlinear constrained optimization problem associated with this case, it is shown that a certain basis exchange algorithm can be used to find approximate critical points of the new objective functions. This method broadens the applications horizon of the FCM family by enabling users to match discontinuous multidimensional numerical data structures with similarity measures that have nonhyperelliptical topologies. >

c-means clustering with the l/sub l/ and l/sub infinity / norms

Derives an interpretation for a family of competitive learning algorithms and investigates their relationship to fuzzy c-means and fuzzy learning vector quantization. These algorithms map a set of feature vectors into a set of prototypes associated with a competitive network that performs unsupervised learning. Derivation of the new algorithms is accomplished by minimizing an average generalized distance between the feature vectors and prototypes using gradient descent. A close relationship between the resulting algorithms and fuzzy c-means is revealed by investigating the functionals involved. It is also shown that the fuzzy c-means and fuzzy learning vector quantization algorithms are related to the proposed algorithms if the learning rate at each iteration is selected to satisfy a certain condition.

An integrated approach to fuzzy learning vector quantization and fuzzy c-means clustering

Anomaly detection in wireless sensor networks is an important challenge for tasks such as intrusion detection and monitoring applications. This paper proposes two approaches to detecting anomalies from measurements from sensor networks. The first approach is a linear programming-based hyperellipsoidal formulation, which is called a centered hyperellipsoidal support vector machine (CESVM). While this CESVM approach has advantages in terms of its flexibility in the selection of parameters and the computational complexity, it has limited scope for distributed implementation in sensor networks. In our second approach, we propose a distributed anomaly detection algorithm for sensor networks using a one-class quarter-sphere support vector machine (QSSVM). Here a hypersphere is found that captures normal data vectors in a higher dimensional space for each sensor node. Then summary information about the hyperspheres is communicated among the nodes to arrive at a global hypersphere, which is used by the sensors to identify any anomalies in their measurements. We show that the CESVM and QSSVM formulations can both achieve high detection accuracies on a variety of real and synthetic data sets. Our evaluation of the distributed algorithm using QSSVM reveals that it detects anomalies with comparable accuracy and less communication overhead than a centralized approach.

James C. Bezdek

Papers

Quarter Sphere Based Distributed Anomaly Detection in Wireless Sensor Networks

Alternating cluster estimation: a new tool for clustering and function approximation

c-means clustering with the l/sub l/ and l/sub infinity / norms

An integrated approach to fuzzy learning vector quantization and fuzzy c-means clustering

Centered Hyperspherical and Hyperellipsoidal One-Class Support Vector Machines for Anomaly Detection in Sensor Networks