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

We discuss the following problem given a random sample X = (X 1, X 2,…, X n) from an unknown probability distribution F, estimate the sampling distribution of some prespecified random variable R(X, F), on the basis of the observed data x. (Standard jackknife theory gives an approximate mean and variance in the case R(X, F) = \(\theta \left( {\hat F} \right) - \theta \left( F \right)\), θ some parameter of interest.) A general method, called the “bootstrap”, is introduced, and shown to work satisfactorily on a variety of estimation problems. The jackknife is shown to be a linear approximation method for the bootstrap. The exposition proceeds by a series of examples: variance of the sample median, error rates in a linear discriminant analysis, ratio estimation, estimating regression parameters, etc.

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Bootstrap Methods: Another Look at the Jackknife

Fuzzy sets as a basis for a theory of possibility

We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.

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Monte Carlo Statistical Methods

Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms into a system of ranked taxa: domain, kingdom, phylum, class, etc. Cluster analysis is the formal study of methods and algorithms for grouping, or clustering, objects according to measured or perceived intrinsic characteristics or similarity. Cluster analysis does not use category labels that tag objects with prior identifiers, i.e., class labels. The absence of category information distinguishes data clustering (unsupervised learning) from classification or discriminant analysis (supervised learning). The aim of clustering is to find structure in data and is therefore exploratory in nature. Clustering has a long and rich history in a variety of scientific fields. One of the most popular and simple clustering algorithms, K-means, was first published in 1955. In spite of the fact that K-means was proposed over 50 years ago and thousands of clustering algorithms have been published since then, K-means is still widely used. This speaks to the difficulty in designing a general purpose clustering algorithm and the ill-posed problem of clustering. We provide a brief overview of clustering, summarize well known clustering methods, discuss the major challenges and key issues in designing clustering algorithms, and point out some of the emerging and useful research directions, including semi-supervised clustering, ensemble clustering, simultaneous feature selection during data clustering, and large scale data clustering.

Data clustering: 50 years beyond K-means

Clustering algorithms are now in widespread use for sorting heterogeneous data into homogeneous blocks. If the data consist of a number of variables taking values over a number of cases, these algorithms may be used either to construct clusters of variables (using, say, correlation as a measure of distance between variables) or clusters of cases. This article presents a model, and a technique, for clustering cases and variables simultaneously. The principal advantage in this approach is the direct interpretation of the clusters on the data.

https://www.jstor.org/stable/pdfplus/2284710.pdf

Direct Clustering of a Data Matrix

A sequence of observations undergoes sudden changes at unknown times. We model the process by supposing that there is an underlying sequence of parameters partitioned into contiguous blocks of equal parameter values; the beginning of each block is said to be a change point. Observations are then assumed to be independent in different blocks given the sequence of parameters. In a Bayesian analysis it is necessary to give probability distributions to both the change points and the parameters. We use product partition models (Barry and Hartigan 1992), which assume that the probability of any partition is proportional to a product of prior cohesions, one for each block in the partition, and that given the blocks the parameters in different blocks have independent prior distributions. Given the observations a new product partition model holds, with posterior cohesions for the blocks and new independent block posterior distributions for parameters. The product model thus provides a convenient machinery for allo...

A Bayesian Analysis for Change Point Problems

Product partition models assume that observations in different components of a random partition of the data are independent. If the probability distribution of random partitions is in a certain product form prior to making the observations, it is also in product form given the observations. The product model thus provides a convenient machinery for allowing the data to weight the partitions likely to hold; and inference about particular future observations may then be made by first conditioning on the partition and then averaging over all partitions. These models apply with special computational simplicity to change point problems, where the partitions divide the sequence of observations into components within which different regimes hold. We show, with appropriate selection of prior product models, that the observations can eventually determine approximately the true partition.

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Product Partition Models for Change Point Problems

Suppose given a set of similarities (or dissimilarities) between pairs of of objects from some set of objects, such as animal species, books, colours. We wish to construct from this similarity matrix a tree, or nested set of clusterings of the objects; graphs of trees provide a striking visual display of similarity groupings of the objects. The construction requires (1) a definition specifying when a similarity matrix has exact tree structure, (2) a measure of distance between any two similarity matrices, which yields (when combined with (1)) a measure of distance between any similarity matrix and any tree, (3) a family of local operations on a tree, which can be used to search out trees which best fit a given similarity matrix. The construction technique is applied to voting behaviour of the 50 United States in the last 13 presidential elections, giving a tree clustering of the states.

https://www.jstor.org/stable/pdfplus/2283766.pdf

Representation of similarity matrices by trees

The core data of molecular biology consists of DNA sequences. We will show how DNA sequences may be used to infer the evolution of the primates, human, chimpanzee, ape, orangutan and gibbon. The underlying probability models are taken to be Markov processes on trees. Some dependencies along the sequence due to the genetic code are also considered.

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J. A. Hartigan

Papers

Direct Clustering of a Data Matrix

A Bayesian Analysis for Change Point Problems

Product Partition Models for Change Point Problems

Representation of similarity matrices by trees

Statistical Analysis of Hominoid Molecular Evolution