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

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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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