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.

Random projection is a popular method for dimensionality reduction due to its simplicity and efficiency. In the past few years, random projection and fuzzy c-means based cluster ensemble approaches have been developed for high-dimensional data clustering. However, they require large amounts of space for storing a big affinity matrix, and incur large computation time while clustering in this affinity matrix. In this paper, we propose a new random projection, fuzzy c-means based cluster ensemble framework for high-dimensional data. Our framework uses cumulative agreement to aggregate fuzzy partitions. Fuzzy partitions of random projections are ranked using external and internal cluster validity indices. The best partition in the ranked queue is the core (or base) partition. Remaining partitions then provide cumulative inputs to the core, thus, arriving at a consensus best overall partition built from the ensemble. Experimental results with Gaussian mixture datasets and a variety of real datasets demonstrate that our approach outperforms three state-of-the-art methods in terms of accuracy and space-time complexity. Our algorithm runs one to two orders of magnitude faster than other state-of-the-arts algorithms.

Ensemble Fuzzy Clustering Using Cumulative Aggregation on Random Projections

Optimality tests for fixed points of the fuzzy c -means algorithm

http://ccc.inaoep.mx/~ariel/Approximate%20pairwise%20clustering%20for%20large%20data%20sets%20via%20sampling%20plus%20extension.pdf

Approximate pairwise clustering for large data sets via sampling plus extension

Numerous computational schemes have arisen over the years that attempt to learn information about objects based upon the similarity or dissimilarity of one object to another. One such scheme, clustering, looks for self-similar groups of objects. To use clustering algorithms, an investigator must often have a priori knowledge of the number of clusters, i.e., c, to search for in the data. Moreover, it is often convenient to have ways to rank the returned results, either for a single value of c, a range of c's different clustering methods, or any combination thereof. However, the task of assessing the quality of the results, so that c may be determined objectively, is currently ill-defined for object-object relationships. To bridge this gap, we generalize three well-known validity indices: the modified Hubert's Gamma, Xie-Beni, and the generalized Dunn's indices, to relational data. In doing so, we develop a framework to convert many other validity indices to a relational form. Numerical examples on 12 datasets (samples from four normal mixtures, four real-world object datasets, and four real-world “pure relational” datasets) using the relational duals of the hard, fuzzy, and possibilistic c-means cluster algorithms are offered to illustrate and evaluate the new indices.

Relational Generalizations of Cluster Validity Indices

In current deep learning models, centralized architecture forces participants to pool their data to the central Cloud to train a global model, while distributed architecture requires a parameter server to mediate the training process. However, privacy issues, response delays, and computation and communication bottlenecks prevent these architectures from working well at the scale of Internet of Things devices. To counter these problems, in this paper we build a Fog-embedded privacy-preserving deep learning framework (FPPDL), which moves computation from the centralized Cloud to Fog nodes near the end devices. The experimental results on benchmark image datasets under different settings demonstrate that FPPDL achieves comparable accuracy to the centralized stochastic gradient descent (SGD) framework, and delivers better accuracy than the standalone SGD framework. Our evaluations also show that both computation and communication cost are greatly reduced by FPPDL, hence achieving the desired tradeoff between privacy and performance.

James C. Bezdek

Papers

Ensemble Fuzzy Clustering Using Cumulative Aggregation on Random Projections

Optimality tests for fixed points of the fuzzy c -means algorithm

Approximate pairwise clustering for large data sets via sampling plus extension

Relational Generalizations of Cluster Validity Indices

Fog-Embedded Deep Learning for the Internet of Things