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What is Singular Value Decomposition (SVD)

Chapter 32
Handbook of Research on Text and Web Mining Technologies
A linear algebra method of decomposing an arbitrary matrix into three matrices, two of which are orthonormal (the columns, the left and right singular vectors, respectively, are orthogonal and have length1) and the third is a diagonal matrix whose diagonal values are the singular values of the matrix
Published in Chapter:
Latent Semantic Analysis and Beyond
Anne Kao (The Boeing Phantom Works, USA)
Copyright: © 2009 |Pages: 25
DOI: 10.4018/978-1-59904-990-8.ch032
Abstract
Latent Semantic Analysis (LSA) or Latent Semantic Indexing (LSI), when applied to information retrieval, has been a major analysis approach in text mining. It is an extension of the vector space method in information retrieval, representing documents as numerical vectors but using a more sophisticated mathematical approach to characterize the essential features of the documents and reduce the number of features in the search space. This chapter summarizes several major approaches to this dimensionality reduction, each of which has strengths and weaknesses, and it describes recent breakthroughs and advances. It shows how the constructs and products of LSA applications can be made user-interpretable and reviews applications of LSA beyond information retrieval, in particular, to text information visualization.
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Chapter 12
Immunocomputing for Spatio-Temporal Forecast
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Chapter 153
Context-Aware Approach for Restaurant Recommender Systems
One of the matrix factorization methods to decompose a matrix to the product of two orthogonal matrices and one diagonal matrix.
Published in Chapter: Context-Aware Approach for Restaurant Recommender Systems; From: Encyclopedia of Information Science and Technology, Fourth Edition
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Chapter 75
Hybrid Artificially Intelligent Multi-Layer Blockchain and Bitcoin Cryptology (AI-MLBBC): Anti-Crime-Theft Smart Wall Defense
A factorization mathematical algorithm of matrices used in diverse application such as signal processing, communication, and imagery.
Published in Chapter: Hybrid Artificially Intelligent Multi-Layer Blockchain and Bitcoin Cryptology (AI-MLBBC): Anti-Crime-Theft Smart Wall Defense; From: Encyclopedia of Criminal Activities and the Deep Web
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Chapter 122
Image Inpainting as an Evolving Topic in Image Engineering
A factorization of a real or complex matrix in linear algebra. It was originally developed by differential geometers, who wished to determine whether a real bilinear form could be made equal to another by independent orthogonal transformations of the two spaces it acts on. It is closely related to the eigen-decomposition, and has found many applications recently in image engineering (IE).
Published in Chapter: Image Inpainting as an Evolving Topic in Image Engineering; From: Encyclopedia of Information Science and Technology, Third Edition
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