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

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

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

The architecture and learning procedure underlying ANFIS (adaptive-network-based fuzzy inference system) is presented, which is a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an input-output mapping based on both human knowledge (in the form of fuzzy if-then rules) and stipulated input-output data pairs. In the simulation, the ANFIS architecture is employed to model nonlinear functions, identify nonlinear components on-line in a control system, and predict a chaotic time series, all yielding remarkable results. Comparisons with artificial neural networks and earlier work on fuzzy modeling are listed and discussed. Other extensions of the proposed ANFIS and promising applications to automatic control and signal processing are also suggested. >

ANFIS: adaptive-network-based fuzzy inference system

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

In this study, we are concerned with the role of information granulation in data mining in databases. By their nature, data mining pursuits are very much oriented towards end-users and imply that any results need to be easily interpretable. Granulation of information promotes this interpretability and channels all pursuits of data mining (that are otherwise computationally intensive and thus highly prohibitive) towards more efficient and feasible processing. First, we discuss the essence of information granulation and afterwards elaborate on the main approaches to the design of information granules. We distinguish between user-driven, data-driven and hybrid methods of information granulation. Several main classes of membership functions of information granules-fuzzy sets are investigated and contrasted in terms of some selection criteria such as parametric flexibility and sensitivity of the ensuing information granules. We propose two fundamental concepts in data mining: associations and rules. Associations are direction-free constructs that capture the most essential components of the overall structure in database. The relevance of associations is expressed by the cardinality of the data embraced by the Cartesian products of the information granules contributing to the construction of the associations. The proposed methodology of data mining comprises two phases. First, associations are built and the most essential (relevant) ones are collected in the form of a data mining agenda. Second, some associations can be converted into direction-driven constructs (rules). The idea of consistency of the rules is discussed in detail.

Granular computing in data mining

Association rules mining is another key unsupervised data mining method, after clustering, that finds interesting associations (relationships, dependencies) in large sets of data items. The items are stored in the form of transactions that can be generated by an external process, or extracted from relational databases or data warehouses. Due to good scalability characteristics of the association rules algorithms and the ever-growing size of the accumulated data, association rules are an essential data mining tool for extracting knowledge from data. The discovery of interesting associations provides a source of information often used by businesses for decision making. Some application areas of association rules are market-basket data analysis, cross-marketing, catalog design, loss-leader analysis, clustering, data preprocessing, genomics, etc. Interesting examples are personalization and recommendation systems for browsing web pages (such as Amazon’s recommendations of related/associated books) and the analysis of genomic data. Market-basket analysis, one of the most intuitive applications of association rules, strives to analyze customer buying patterns by finding associations between items that customers put into their baskets. For instance, one can discover that customers buy milk and bread together, and even that some particular brands of milk are more often bought with certain brands of bread, e.g., multigrain bread and soy milk. These and other more interesting (and previously unknown) rules can be used to maximize profits by helping to design successful marketing campaigns, and by customizing store layout. In the case of the milk and bread example, the retailer may not offer discounts for both at the same time, but just for one; the milk can be put at the opposite end of the store with respect to bread, to increase customer traffic so that customers may possibly buy more products. A number of interesting associations can be found in the market basket data, as illustrated in Figure 10.1. This Chapter provides background and explains which data are suitable for association rule mining, what kinds of association rules can be generated, how to generate association rules, and which rules are the most interesting. The explanations are supported by easy-to-understand examples. Upon finishing this Chapter, the reader will know how to generate and interpret association rules.

Unsupervised Learning: Association Rules

https://doi.org/10.1016/j.cie.2022.107970

Optimizing deep neural networks to predict the effect of social distancing on COVID-19 spread

An error correction prediction model based on three-way decision and ensemble learning

Fuzzy sets membership functions are numeric constructs. In spite of the underlying semantics of fuzzy sets which is inherently linked with the higher level of abstraction, the membership grades and processing of fuzzy sets themselves emphasize the numeric facets of all pursuits stressing the numeric nature of membership grades and in this way reducing the interpretability and transparency of results. In this study, we advocate an idea of a granular description of membership functions where instead of numeric membership grades, introduced are more interpretable granular descriptors say, low, high membership, etc.. Granular descriptors are formalized with the aid of various formal schemes available in Granular Computing, especially sets intervals, fuzzy sets, and shadowed sets. We formulate a problem of a design of granular descriptors as a certain optimization task, elaborate on the solutions and highlight some areas of applications.

Witold Pedrycz

Papers

Granular computing in data mining

Unsupervised Learning: Association Rules

Optimizing deep neural networks to predict the effect of social distancing on COVID-19 spread

An error correction prediction model based on three-way decision and ensemble learning

From Numeric to Granular Description and Interpretation of Information Granules