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.

The widespread use of Internet-of-Things (IoT) technologies, smartphones, and social media services generates huge amounts of data streaming at high velocity. Automatic interpretation of these rapidly arriving data streams is required for the timely detection of interesting events that usually emerge in the form of clusters. This article proposes a new relative of the visual assessment of the cluster tendency (VAT) model, which produces a record of structural evolution in the data stream by building a cluster heat map of the entire processing history in the stream. The existing VAT-based algorithms for streaming data, called inc-VAT/inc-iVAT and dec-VAT/dec-iVAT, are not suitable for high-velocity and high-volume streaming data because of high memory requirements and slower processing speed as the accumulated data increases. The scalable iVAT (siVAT) algorithm can handle big batch data, but for streaming data, it needs to be (re)applied everytime a new datapoint arrives, which is not feasible due to the associated computation complexities. To address this problem, we propose an incremental siVAT algorithm, called inc-siVAT, which deals with the streaming data in chunks. It first extracts a small size smart sample using an intelligent sampling scheme, called maximin random sampling (MMRS), then incrementally updates the smart sample points on the fly, using our novel incremental MMRS (inc-MMRS) algorithm, to reflect changes in the data stream after each chunk is processed, and finally, produces an incrementally built iVAT image of the updated smart sample, using the inc-VAT/inc-iVAT and dec-VAT/dec-iVAT algorithms. These images can be used to visualize the evolving cluster structure and for anomaly detection in streaming data. Our method is illustrated with one synthetic and four real datasets, two of which evolve significantly over time. Our numerical experiments demonstrate the algorithm's ability to successfully identify anomalies and visualize changing cluster structure in streaming data.

Visual Structural Assessment and Anomaly Detection for High-Velocity Data Streams.

Clustering waveform data is used in applications ranging from healthcare to economics and entertainment. In this paper, we present a study on clustering gestures enacted by subjects while wearing wrist-worn accelerometer sensors through different dissimilarity measures between individual components of multi-variate waveform data. We show how dissimilarity measures between different components of a multi-variate waveform database can measure the similarity, or the lack of it, between the motion of two hands in order to differentiate between different gestures, for applications in assistive technology and smart health-care. In doing so, we exploit a hierarchical clustering architecture and visualize it through single-linkage dendrograms and visual assessment of cluster tendency. Using annotations of the gestures, we describe the physical significance behind the formation of the hierarchy. We also discuss combining different dissimilarity measures by convex combination to improve clustering.

Experiments with Dissimilarity Measures for Clustering Waveform Data from Wearable Sensors

This paper presents the design and development of a prototype document retrieval system using a knowledge-based systems approach. Both the domain-specific knowledge base and the inferencing schemes are based on a fuzzy set theoretic framework. A query in natural language represents a request to retrieve a relevant subset of documents from a document base. Such a query, which can include both fuzzy terms and fuzzy relational operators, is converted into an unambiguous intermediate form by a natural language interface. Concepts that describe domain topics and the relationships between concepts, such as the synonym relation and the implication relation between a general concept and more specific concepts, have been captured in a knowledge base. The knowledge base enables the system to emulate the reasoning process followed by an expert, such as a librarian, in understanding and reformulating user queries. The retrieval mechanism processes the query in two steps. First it produces a pruned list of documents pertinent to the query. Second, it uses an evidence combination scheme to compute a degree of support between the query and individual documents produced in step one. The front-end component of the system then presents a set of document citations to the user in ranked order as an answer to the information request.

Document Retrieval Using A Fuzzy Knowledge-Based System

The existence of large volumes of time series data in many applications has motivated data miners to investigate specialized methods for mining time series data. Clustering is a popular data mining method due to its powerful exploratory nature and its usefulness as a preprocessing step for other data mining techniques. This article develops two novel clustering algorithms for time series data that are extensions of a crisp c-shapes algorithm. The two new algorithms are heuristic derivatives of fuzzy c-means (FCM). Fuzzy c-Shapes plus (FCS+) replaces the inner product norm in the FCM model with a shape-based distance function. Fuzzy c-Shapes double plus (FCS++) uses the shape-based distance, and also replaces the FCM cluster centers with shape-extracted prototypes. Numerical experiments on 48 real time series data sets show that the two new algorithms outperform state-of-the-art shape-based clustering algorithms in terms of accuracy and efficiency. Four external cluster validity indices (the Rand index, Adjusted Rand Index, Variation of Information, and Normalized Mutual Information) are used to match candidate partitions generated by each of the studied algorithms. All four indices agree that for these finite waveform data sets, FCS++ gives a small improvement over FCS+, and in turn, FCS+ is better than the original crisp c-shapes method. Finally, we apply two tests of statistical significance to the three algorithms. The Wilcoxon and Friedman statistics both rank the three algorithms in exactly the same way as the four cluster validity indices.

Fuzzy c-Shape: A new algorithm for clustering finite time series waveforms

Figure 2.1 portrays cluster analysis. This field comprises three problems: tendency assessment, clustering and validation. Given an unlabeled data set, ① is there substructure in the data? This is clustering tendency — should you look for clusters at all? Very few methods — fuzzy or otherwise — address this problem. Panayirci and Dubes (1983), Smith and Jain (1984), Jain and Dubes (1988), Tukey (1977) and Everitt (1978) discuss statistical and informal graphical methods (visual displays) for deciding what — if any — substructure is in unlabeled data.

James C. Bezdek

Papers

Visual Structural Assessment and Anomaly Detection for High-Velocity Data Streams.

Experiments with Dissimilarity Measures for Clustering Waveform Data from Wearable Sensors

Document Retrieval Using A Fuzzy Knowledge-Based System

Fuzzy c-Shape: A new algorithm for clustering finite time series waveforms

Cluster Analysis for Object Data