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.

Calculation of Fourth-Order Tensor Product Expansion by Power Method and Comparison of it with Higher-Order Singular Value Decomposition

2013 ◽  
Vol 444-445 ◽  
pp. 703-711
Author(s):  
Akio Ishida ◽  
Takumi Noda ◽  
Jun Murakami ◽  
Naoki Yamamoto ◽  
Chiharu Okuma
Keyword(s):  
Singular Value Decomposition ◽  
Tensor Product ◽  
Fourth Order ◽  
Computation Time ◽  
Higher Order ◽  
Singular Value ◽  
Multidimensional Data ◽  
Power Method ◽  
Order Tensor ◽  
Value Decomposition

Higher-order singular value decomposition (HOSVD) is known as an effective technique to reduce the dimension of multidimensional data. We have proposed a method to perform third-order tensor product expansion (3OTPE) by using the power method for the same purpose as HOSVD, and showed that our method had a better accuracy property than HOSVD, and furthermore, required fewer computation time than that. Since our method could not be applied to the tensors of fourth-order (or more) in spite of having those useful properties, we extend our algorithm of 3OTPE calculation to forth-order tensors in this paper. The results of newly developed method are compared to those obtained by HOSVD. We show that the results follow the same trend as the case of 3OTPE.

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 Optimal Attitude Determination from Vector Sensors Using Fast Analytical Singular Value Decomposition

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Zhuohua Liu ◽  
Wei Liu ◽  
Xiangyang Gong ◽  
Jin Wu
Keyword(s):  
Singular Value Decomposition ◽  
Attitude Determination ◽  
Computation Time ◽  
Singular Value ◽  
Simulation Experiments ◽  
Vector Sensors ◽  
Vector Observation ◽  
Wahba Problem ◽  
Analytic Singular Value Decomposition ◽  
Value Decomposition

A novel algorithm is proposed in this paper to solve the optimal attitude determination formulation from vector observation pairs, that is, the Wahba problem. We propose here a fast analytic singular value decomposition (SVD) approach to obtain the optimal attitude matrix. The derivations and mandatory proofs are presented to clarify the theory and support its feasibility. Through simulation experiments, the proposed algorithm is validated. The results show that it maintains the same attitude determination accuracy and robustness with conventional methodologies but significantly reduces the computation time.

Design Optimization Problem Reformulation Using Singular Value Decomposition

2009 ◽  
Vol 131 (8) ◽  
Author(s):  
Somwrita Sarkar ◽  
Andy Dong ◽  
John S. Gero
Keyword(s):  
Singular Value Decomposition ◽  
Design Optimization ◽  
Optimization Problem ◽  
Singular Value ◽  
Unsupervised Clustering ◽  
Problem Representation ◽  
Case Identification ◽  
Single Method ◽  
Problem Reformulation ◽  
Value Decomposition

This paper presents a design optimization problem reformulation method based on singular value decomposition, dimensionality reduction, and unsupervised clustering. The method calculates linear approximations of associative patterns of symbol co-occurrences in a design problem representation to induce implicit coupling strengths between variables and constraints. Unsupervised clustering of these approximations is used to heuristically identify useful reformulations. In contrast to knowledge-rich Artificial Intelligence methods, this method derives from a knowledge-lean, unsupervised pattern recognition perspective. We explain the method on an analytically formulated decomposition problem, and apply it to various analytic and nonanalytic problem forms to demonstrate design decomposition and design “case” identification. A single method is used to demonstrate multiple design reformulation tasks. The results show that the method can be used to infer multiple well-formed reformulations starting from a single problem representation in a knowledge-lean manner.

scholarly journals Continuous analogues of matrix factorizations

2015 ◽  
Vol 471 (2173) ◽  
pp. 20140585 ◽  
Author(s):  
Alex Townsend ◽  
Lloyd N. Trefethen
Keyword(s):  
Singular Value Decomposition ◽  
Infinite Series ◽  
Singular Value ◽  
Matrix Factorizations ◽  
One Dimension ◽  
Continuous Variables ◽  
Triangular Structure ◽  
Column Pivoting ◽  
Value Decomposition ◽  
Cholesky Factorizations

Analogues of singular value decomposition (SVD), QR, LU and Cholesky factorizations are presented for problems in which the usual discrete matrix is replaced by a ‘quasimatrix’, continuous in one dimension, or a ‘cmatrix’, continuous in both dimensions. Two challenges arise: the generalization of the notions of triangular structure and row and column pivoting to continuous variables (required in all cases except the SVD, and far from obvious), and the convergence of the infinite series that define the cmatrix factorizations. Our generalizations of triangularity and pivoting are based on a new notion of a ‘triangular quasimatrix’. Concerning convergence of the series, we prove theorems asserting convergence provided the functions involved are sufficiently smooth.

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