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What is Singular Value Decomposition

Handbook of Research on Hybrid Learning Models: Advanced Tools, Technologies, and Applications
In linear algebra, the singular value decomposition (SVD) is an important factorization of a rectangular real or complex matrix, with several applications in signal processing and statistics. Applications which employ the SVD include computing the pseudoinverse, least squares fitting of data, matrix approximation, and determining the rank, range and null space of a matrix.
Published in Chapter:
The Clustering of Large Scale E-Learning Resources
Fei Wu (Zhejiang University, China), Wenhua Wang (Zhejiang University, China), Hanwang Zhang (Zhejiang University, China), and Yueting Zhuang (Zhejiang University, China)
DOI: 10.4018/978-1-60566-380-7.ch006
Abstract
E-learning resources increase vastly with the pervasion of the Internet. Thus, the retrieval of e-learning resources becomes more and more important. This chapter introduces an approach to retrieve e-learning resources from large-scale dataset. The basic idea behind that method is, the authors cluster the whole resources into topics first, and only search from those clusters which are the most tightly relevant to the query. To make the clustering feasible to large-scale dataset, the authors adapt affinity propagation in MapReduce framework and therefore the so called parallel affinity propagation is proposed. The proposed approach could improve the retrieval of e-learning resources by understanding users’ underlying intentions.
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Principal Component Analysis of Hydrological Data
A method of linear algebra for the decomposition of m x n data matrix into three matrices: m x r matrix, r x r matrix of singular values, and r x n matrix.
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Digital Watermarking Techniques for Images: Survey
SVD is applied on matrices to identify the most variant data points of it and order the dimension.
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System Theory: From Classical State Space to Variable Selection and Model Identification
Algorithm able to compute the eigenvalues and eigenvectors of a matrix, also used to make principal components analysis.
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Automated Essay Scoring Systems
A statistical technique for grouping terms in a document according to meaning.
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Machine Learning Through Data Mining
Algorithm able to compute the eigenvalues and eigenvectors of a matrix; also used to make principal components analysis.
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Foundational Recommender Systems for Business
SVD involves factorization of a matrix into two matrices U and L, such that requires U and L to be orthogonal.
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Video Steganography Using Two-Level SWT and SVD
It is used to find the factorization of the matrix or image.
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