Analysis and Linear Algebra: The Singular Value Decomposition and Applications

2021 ◽  
Author(s):  
James Bisgard
Keyword(s):  
Singular Value Decomposition ◽  
Linear Algebra ◽  
Singular Value ◽  
Value Decomposition

scholarly journals Using SVD on Clusters to Improve Precision of Interdocument Similarity Measure

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Wen Zhang ◽  
Fan Xiao ◽  
Bin Li ◽  
Siguang Zhang
Keyword(s):  
Singular Value Decomposition ◽  
Linear Algebra ◽  
Similarity Measure ◽  
Latent Semantic Indexing ◽  
Singular Value ◽  
Semantic Indexing ◽  
Discriminative Power ◽  
Good Representative ◽  
Value Decomposition ◽  
Dimension Expansion

Recently, LSI (Latent Semantic Indexing) based on SVD (Singular Value Decomposition) is proposed to overcome the problems of polysemy and homonym in traditional lexical matching. However, it is usually criticized as with low discriminative power for representing documents although it has been validated as with good representative quality. In this paper, SVD on clusters is proposed to improve the discriminative power of LSI. The contribution of this paper is three manifolds. Firstly, we make a survey of existing linear algebra methods for LSI, including both SVD based methods and non-SVD based methods. Secondly, we propose SVD on clusters for LSI and theoretically explain that dimension expansion of document vectors and dimension projection using SVD are the two manipulations involved in SVD on clusters. Moreover, we develop updating processes to fold in new documents and terms in a decomposed matrix by SVD on clusters. Thirdly, two corpora, a Chinese corpus and an English corpus, are used to evaluate the performances of the proposed methods. Experiments demonstrate that, to some extent, SVD on clusters can improve the precision of interdocument similarity measure in comparison with other SVD based LSI methods.

scholarly journals Truncated singular value decomposition in ripped photo recovery

2021 ◽  
Vol 36 ◽  
pp. 04008
Author(s):  
Kong Hoong Lem
Keyword(s):  
Singular Value Decomposition ◽  
Linear Algebra ◽  
Singular Value ◽  
Frobenius Norm ◽  
Truncated Singular Value Decomposition ◽  
Matrix Decompositions ◽  
Truncated Svd ◽  
Value Decomposition

Singular value decomposition (SVD) is one of the most useful matrix decompositions in linear algebra. Here, a novel application of SVD in recovering ripped photos was exploited. Recovery was done by applying truncated SVD iteratively. Performance was evaluated using the Frobenius norm. Results from a few experimental photos were decent.

scholarly journals Cache Servers Placement Based on Important Switches for SDN-Based ICN

Electronics ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 39 ◽  
Author(s):  
Jan Badshah ◽  
Majed Mohaia Alhaisoni ◽  
Nadir Shah ◽  
Muhammad Kamran
Keyword(s):  
Energy Consumption ◽  
Singular Value Decomposition ◽  
Linear Algebra ◽  
Optimization Problem ◽  
Computation Time ◽  
Singular Value ◽  
Qr Factorization ◽  
Traffic Matrix ◽  
Column Pivoting ◽  
Value Decomposition

In centralized cache management for SDN-based ICN, it is an optimization problem to compute the location of cache servers and takes a longer time. We solve this problem by proposing to use singular-value-decomposition (SVD) and QR-factorization with column pivoting methods of linear algebra as follows. The traffic matrix of the network is lower-rank. Therefore, we compute the most important switches in the network by using SVD and QR-factorization with column pivoting methods. By using real network traces, the results show that our proposed approach reduces the computation time significantly, and also decreases the traffic overhead and energy consumption as compared to the existing approach.

Improving TF-IDF with Singular Value Decomposition (SVD) for Feature Extraction on Twitter

2017 ◽  
Author(s):  
Ammar Ismael Kadhim ◽  
Yu-N Cheah ◽  
Inaam Abbas Hieder ◽  
Rawaa Ahmed Ali
Keyword(s):  
Feature Extraction ◽  
Singular Value Decomposition ◽  
Singular Value ◽  
Value Decomposition
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