Titlebook: Matrix and Tensor Factorization Techniques for Recommender Systems; Panagiotis Symeonidis,Andreas Zioupos Book 2016 The Editor(s) (if appl

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HOSVD on Tensors and Its Extensions(i.e., user–item–tag). The main factorization method that will be presented in this chapter is higher order SVD (HOSVD), which is an extended version of the Singular Value Decomposition (SVD) method. In this chapter, we will present a step-by-step implementation of HOSVD in our toy example. Then we

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Experimental Evaluation on Tensor Decomposition Methodsuss the criteria that we will set for testing all algorithms and the experimental protocol we will follow. Moreover, we will discuss the metrics that we will use (i.e., Precision, Recall, root-mean-square error, etc.). Our goal is to present the main factors that influence the effectiveness of algor

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en nach bestimmten Glattheitsforderungen verheftet sind. Die Bezeichnung Spline-Funktionen (Spline Functions) geht auf I. J. Schoenberg [1946]zurück. Die so bezeichneten Funktionen waren jedoch schon früher immer wieder bei verschiedenen Aufgabenstellungen benutzt worden. So kann man etwa bereits da

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Related Work on Matrix Factorizationmethod is CUR decomposition, which confronts the problem of high density in factorized matrices (a problem that is faced when using the SVD method). This chapter concludes with a description of other state-of-the-art matrix decomposition techniques.

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HOSVD on Tensors and Its Extensionsr methods for leveraging the quality of recommendations. Finally, we will study limitations of HOSVD and discuss in detail the problem of non-unique tensor decomposition results and how we can deal with this problem. We also discuss other problems in tensor decomposition, e.g., actualization and scalability.

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Introductionnsor decomposition methods (also known as factorization methods). In this chapter, we provide some basic definitions and preliminary concepts on dimensionality reduction methods of matrices and tensors. Gradient descent and alternating least squares methods are also discussed. Finally, we present the book outline and the goals of each chapter.

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