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.

Sorting spikes from extracellular recording into clusters associated with distinct single units (putative neurons) is a fundamental step in analyzing neuronal populations. Such spike sorting is intrinsically unsupervised, as the number of neurons are not known a priori. Therefor, any spike sorting is an unsupervised learning problem that requires either of the two approaches: specification of a fixed value k for the number of clusters to seek, or generation of candidate partitions for several possible values of c, followed by selection of a best candidate based on various post-clustering validation criteria. In this paper, we investigate the first approach and evaluate the utility of several methods for providing lower dimensional visualization of the cluster structure and on subsequent spike clustering. We also introduce a visualization technique called improved visual assessment of cluster tendency (iVAT) to estimate possible cluster structures in data without the need for dimensionality reduction. Experimental results are conducted on two datasets with ground truth labels. In data with a relatively small number of clusters, iVAT is beneficial in estimating the number of clusters to inform the initialization of clustering algorithms. With larger numbers of clusters, iVAT gives a useful estimate of the coarse cluster structure but sometimes fails to indicate the presumptive number of clusters. We show that noise associated with recording extracellular neuronal potentials can disrupt computational clustering schemes, highlighting the benefit of probabilistic clustering models. Our results show that t-Distributed Stochastic Neighbor Embedding (t-SNE) provides representations of the data that yield more accurate visualization of potential cluster structure to inform the clustering stage. Moreover, The clusters obtained using t-SNE features were more reliable than the clusters obtained using the other methods, which indicates that t-SNE can potentially be used for both visualization and to extract features to be used by any clustering algorithm.

/pdf/cluster-tendency-assessment-in-neuronal-spike-data-4h63dzs0hw.pdf

Cluster tendency assessment in neuronal spike data.

Dunn's internal cluster validity index is used to assess partition quality and identify a “best” crisp c-partition of n objects built from static data sets. This index is quite sensitive to inliers and outliers in the input data, so a subsequent study developed a family of 17 generalized Dunn's indices that extend and improve the original measure in various ways. This paper presents online versions of two modified generalized Dunn's indices that can be used for the dynamic evaluation of an evolving (cluster) structure in streaming data. We argue that this method is a good way to monitor the ongoing performance of streaming clustering algorithms, and we illustrate several types of inferences that can be drawn from such indices. Streaming clustering algorithms are incremental, process incoming data points only once and then discard them, adapt as the data stream evolves, flag outliers, and most importantly, spawn new emerging structures. We compare the two new indices to the incremental Xie-Beni and Davies-Boudin indices, which to our knowledge offer the only comparable approach, with numerical examples on a variety of synthetic and real datasets.

Evaluating Evolving Structure in Streaming Data With Modified Dunn's Indices

While various ensemble algorithms have been proposed for supervised ensembles or clustering ensembles, there are few ensemble based approaches for outlier detection. The main challenge in this context is the lack of knowledge about the accuracy of the outlier detectors. Hence, none of the proposed approaches focused on sequential boosting techniques. In this paper for the first time we propose a novel boosting algorithm for outlier detection called BSS, where we sequentially improve the accuracy of each ensemble detector in an unsupervised manner. We discuss the effectiveness of our approach in terms of bias-variance trade-off. Furthermore, an extended version of BSS (called DBSS) is proposed to introduce a novel source of diversity in outlier ensemble modeling. DBSS is used to analyze the effect of changing the input parameter of BSS on its detection accuracy. Our experimental results on both synthetic and real data sets demonstrate that our approaches outperform the two state-of-the-art outlier ensemble algorithms and benefit from bias reduction. In addition, our BSS approach is robust with respect to the changing input parameter. Since each detector in our proposed BSS/DBSS is only a subset of the whole dataset, our both techniques are well suited to application environments with limited memory processors (e.g., wireless sensor networks).

Smart sampling: a novel unsupervised boosting approach for outlier detection

This paper presents cluster validity for kernel fuzzy clustering. First, we describe existing cluster validity indices that can be directly applied to partitions obtained by kernel fuzzy clustering algorithms. Second, we show how validity indices that take dissimilarity (or relational) data D as input can be applied to kernel fuzzy clustering. Third, we present four propositions that allow other existing cluster validity indices to be adapted to kernel fuzzy partitions. As an example of how these propositions are used, five well-known indices are formulated.We demonstrate several indices for kernel fuzzy c-means (kFCM) partitions of both synthetic and real data.

Cluster validity for kernel fuzzy clustering

Fuzzy c-means (FCM) is a well-known algorithm for clustering data, but for large datasets termination takes significant time. As a result, a number of scalable algorithms based on FCM have been developed. In this paper, four scalable variants of FCM are compared to the base algorithm. Runtime and three quality metrics are calculated. Experimental results using five data sets are analyzed. We show that the scalable algorithms are consistent with regard to speedup, but less consistent when quality is considered. The three quality measures are shown to have little correlation and vary in magnitude across datasets. Selection of a scalable algorithm must consider a tradeoff between the quality of results and speed. Of the variants, single pass FCM (SPFCM) is fastest with good fidelity to FCM, and extensible fast FCM (eFFCM) is almost as fast as SPFCM (as implemented) with very good fidelity to FCM. Random FCM is the fastest overall and often close in quality to FCM. The results showed that scalable algorithms occasionally produce better optimized results than FCM.

James C. Bezdek

Papers

Cluster tendency assessment in neuronal spike data.

Evaluating Evolving Structure in Streaming Data With Modified Dunn's Indices

Smart sampling: a novel unsupervised boosting approach for outlier detection

Cluster validity for kernel fuzzy clustering

Comparison of scalable fuzzy clustering methods