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

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

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Community detection in graphs

We define a most specific generalization of a fuzzy set of topics assigned to leaves of the rooted tree of a domain taxonomy. This generalization lifts the set to its “head subject” node in the higher ranks of the taxonomy tree. The head subject is supposed to “tightly” cover the query set, possibly bringing in some errors referred to as “gaps” and “offshoots”. Our method, ParGenFS, globally minimizes a penalty function combining the numbers of head subjects and gaps and offshoots, differently weighted. Two applications are considered: (1) analysis of tendencies of research in Data Science; (2) audience extending for programmatic targeted advertising online. The former involves a taxonomy of Data Science derived from the celebrated ACM Computing Classification System 2012. Based on a collection of research papers published by Springer 1998–2017, and applying in-house methods for text analysis and fuzzy clustering, we derive fuzzy clusters of leaf topics in learning, retrieval and clustering. The head subjects of these clusters inform us of some general tendencies of the research. The latter involves publicly available IAB Tech Lab Content Taxonomy. Each of about 25 mln users is assigned with a fuzzy profile within this taxonomy, which is generalized offline using ParGenFS. Our experiments show that these head subjects effectively extend the size of targeted audiences at least twice without loosing quality.

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Computational Generalization in Taxonomies Applied to: (1) Analyze Tendencies of Research and (2) Extend User Audiences

This chapter describes the method of principal components (PCA) as a method for fitting a data-driven data summarization model. The model proposes that the data entries, up to the errors, are products of hidden factor scores and feature loadings. This, together with the least-squares fitting criterion, appears to be equivalent to finding what is known in mathematics as part of the singular value decomposition (SVD) of a rectangular matrix. Three applications of the method are described: (1) scoring hidden aggregate factors, (2) visualization of the data, and (3) feature space reduction. Unlike the conventional formulation of PCA, also described, our presentation derives the property that the principal components are linear combinations of features rather than postulates it. Two more distant applications of PCA, Latent semantic analysis (for disambiguation in document retrieval) and Correspondence analysis (for visualization of contingency tables), are explained too. The issue of data standardization in data summarization problems, remaining unsolved, is discussed at length.

Principal Component Analysis and SVD

In this paper, we develop a model reference adaptive control scheme for a class of multi-input multi-output nonlinearly perturbed dynamic systems with unknown time-varying state delays which is also robust with respect to an external disturbance with unknown bounds. The output feedback adaptive control scheme uses feedback actions only, and thus does not require a direct measurement of the command or disturbance signals. A suitable Lyapunov–Krasovskii type functional is introduced to design the adaptation algorithms and to prove stability.

Multivariable output feedback robust adaptive tracking control design for a class of delayed systems

A method for structural clustering is proposed based on information about entity-to-set interactions that can be easily collected in digitalized images. The method is based on the multiscale structure of the problem of maximization of a so-called bottleneck link function, which can be globally solved with a greedy-wise algorithm. Extension of the construction to clusters consisting of "hard" cores and dispersed "shells" is proposed.

http://ieeexplore.ieee.org/iel5/6450/17254/00796655.pdf

Link and bottleneck link set functions and multiresolution structural clusters

An outline of a few methods in an emerging field of data analysis, ”data interpretation”, is given as pertaining to medical informatics and being parts of a general interpretation issue. Specifically, the following subjects are covered: measuring correlation between categories, conceptual clustering, and generalization and interpretation of empirically derived concepts in taxonomies. It will be shown that all of these can be put as parts of the same inquiry.

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Boris Mirkin

Papers

Computational Generalization in Taxonomies Applied to: (1) Analyze Tendencies of Research and (2) Extend User Audiences

Principal Component Analysis and SVD

Multivariable output feedback robust adaptive tracking control design for a class of delayed systems

Link and bottleneck link set functions and multiresolution structural clusters

Methods for interpretation of data in medical informatics