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Titlebook: Mathematical Foundations of Big Data Analytics; Vladimir Shikhman,David Müller Textbook 2021 Springer-Verlag GmbH Germany, part of Springe

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发表于 2025-3-21 19:58:44 | 显示全部楼层 |阅读模式
书目名称Mathematical Foundations of Big Data Analytics
编辑Vladimir Shikhman,David Müller
视频video
概述Covers all relevant techniques commonly used in Big Data Analytics?.Standardized structure and size of the chapters: motivation, results, case-study, exercises.Recommended and developed for university
图书封面Titlebook: Mathematical Foundations of Big Data Analytics;  Vladimir Shikhman,David Müller Textbook 2021 Springer-Verlag GmbH Germany, part of Springe
描述In this textbook, basic mathematical models used in Big Data Analytics are presented and application-oriented references to relevant practical issues are made. Necessary mathematical tools are examined and applied to current problems of data analysis, such as brand loyalty, portfolio selection, credit investigation, quality control, product clustering, asset pricing etc. – mainly in an economic context. In addition, we discuss interdisciplinary applications to biology, linguistics, sociology, electrical engineering, computer science and artificial intelligence. For the models, we make use of a wide range of mathematics – from basic disciplines of numerical linear algebra, statistics and optimization to more specialized game, graph and even complexity theories. By doing so, we cover all relevant techniques commonly used in Big Data Analytics..Each chapter starts with a concrete practical problem whose primary aim is to motivate the study of a particular Big Data Analytics technique. Next, mathematical results follow – including important definitions, auxiliary statements and conclusions arising. Case-studies help to deepen the acquired knowledge by applying it in an interdisciplinar
出版日期Textbook 2021
关键词Mathematical Models for Big Data Analytics; Analysis of Big Data; Economic Applications of Big Data An
版次1
doihttps://doi.org/10.1007/978-3-662-62521-7
isbn_softcover978-3-662-62520-0
isbn_ebook978-3-662-62521-7
copyrightSpringer-Verlag GmbH Germany, part of Springer Nature 2021
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nique. Next, mathematical results follow – including important definitions, auxiliary statements and conclusions arising. Case-studies help to deepen the acquired knowledge by applying it in an interdisciplinar978-3-662-62520-0978-3-662-62521-7
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Ranking,e, to the definition of a ranking as the leading . of a corresponding stochastic matrix. In this chapter we explain the mathematics behind ranking. First, we focus on the existence of a ranking by using the duality of linear programming. This leads to . from linear algebra. Second, a dynamic procedu
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Recommendation Systems, and the . algorithm is described. The model-based approach uses a linear-algebraic technique of .. Singular value decomposition allows to reveal hidden patterns of users’ choice behavior. After imposing a low-rank model on the latter, the prediction becomes optimization-driven. For solving the corr
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Classification,of linear classifiers are discussed. First, we introduce the statistically motivated .. The latter maximizes the sample variance between the classes and minimizes the variance of data within the classes. The computation of Fisher’s discriminant leads to a nicely structured eigenvalue problem. Second
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Clustering,enters are recalculated by minimizing the dissimilarity within the clusters. The .-means algorithm is specified for the Euclidean setup, where centers turn out to be clusters’ sample means. Additionally, we discuss the modifications of .-means with respect to other dissimilarity measures. They inclu
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Linear Regression,ied whether some exogenous variables may have no linear relationship with the endogenous variable at all, or identified which subsets of exogenous variables may contain redundant information about the endogenous variable. In this chapter, we discuss the meanwhile classical technique of . for linear
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