Computation of the Singular Value Decomposition

Cline, Alan; Dhillon, Inderjit S.

doi:10.1201/9781420010572-45

Cited by 40 publications

(33 citation statements)

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“…Their idea is to modify the second step of SVD computation using other eigenvalue algorithms. The state-of-the-art review with more SVD algorithms tailored for specific matrices can be found in [30].…”

Section: Computing Pseudoinverse Using Singular Value Decomposition (mentioning

confidence: 99%

On Moore‐Penrose Pseudoinverse Computation for Stiffness Matrices Resulting from Higher Order Approximation

Klimczak

Cecot

2019

Mathematical Problems in Engineering

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Computing the pseudoinverse of a matrix is an essential component of many computational methods. It arises in statistics, graphics, robotics, numerical modeling, and many more areas. Therefore, it is desirable to select reliable algorithms that can perform this operation efficiently and robustly. A demanding benchmark test for the pseudoinverse computation was introduced. The stiffness matrices for higher order approximation turned out to be such tough problems and therefore can serve as good benchmarks for algorithms of the pseudoinverse computation. It was found out that only one algorithm, out of five known from literature, enabled us to obtain acceptable results for the pseudoinverse of the proposed benchmark test.

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Section: Computing Pseudoinverse Using Singular Value Decomposition (mentioning

confidence: 99%

On Moore‐Penrose Pseudoinverse Computation for Stiffness Matrices Resulting from Higher Order Approximation

Klimczak

Cecot

2019

Mathematical Problems in Engineering

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“…The time complexity for SVD over a matrix with M rows and N columns such that M > N , is O M 2 N + N 3 , with constants defined by the specific algorithm and matrix shape [5]. Equations (2) and (3) represent the relative matrix sizes introduced in Sect. II-A for PCA and MPP, respectively.…”

Section: B Computational Challengesmentioning

confidence: 99%

Scaling Dense Linear Algebra on Multicore and Beyond: A Survey

Viviani¹,

Drocco²,

Aldinucci

2018

2018 26th Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP)

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The present trend in big-data analytics is to exploit algorithms with linear or even sub-linear time complexity, in this sense it is usually worth to investigate if the available techniques can be approximated to reach an affordable complexity. However, there are still problems in data science and engineering that involve algorithms with higher time complexity, like matrix inversion or Singular Value Decomposition (SVD). This work presents the results of a survey that reviews a number of tools meant to perform dense linear algebra at "Big Data" scale: namely, the proposed approach aims first to define a feasibility boundary for the problem size of shared-memory matrix factorizations, then to understand whether it is convenient to employ specific tools meant to scale out such dense linear algebra tasks on distributed platforms. The survey will eventually discuss the presented tools from the point of view of domain experts (data scientist, engineers), hence focusing on the tradeoff between usability and performance.

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“…Note that this decomposition is always possible since D is a non-negative diagonal matrix of node degrees. Additionally, both P and Q can be represented in the square matrices while Σ a rectangular one of n × m size according to the most general decomposition form in [6]. Following this, the combined matrix on the right hand size can be rewritten as:…”

Section: Solving the Functionmentioning

confidence: 99%

Discriminative Subnetworks with Regularized Spectral Learning for Global-State Network Data

Dang

Singh

Bogdanov

et al. 2014

Machine Learning and Knowledge Discovery in Databases

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Data mining practitioners are facing challenges from data with network structure. In this paper, we address a specific class of global-state networks which comprises of a set of network instances sharing a similar structure yet having different values at local nodes. Each instance is associated with a global state which indicates the occurrence of an event. The objective is to uncover a small set of discriminative subnetworks that can optimally classify global network values. Unlike most existing studies which explore an exponential subnetwork space, we address this difficult problem by adopting a space transformation approach. Specifically, we present an algorithm that optimizes a constrained dualobjective function to learn a low-dimensional subspace that is capable of discriminating networks labelled by different global states, while reconciling with common network topology sharing across instances. Our algorithm takes an appealing approach from spectral graph learning and we show that the globally optimum solution can be achieved via matrix eigen-decomposition.

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Computation of the Singular Value Decomposition

Cited by 40 publications

References 0 publications

On Moore‐Penrose Pseudoinverse Computation for Stiffness Matrices Resulting from Higher Order Approximation

On Moore‐Penrose Pseudoinverse Computation for Stiffness Matrices Resulting from Higher Order Approximation

Scaling Dense Linear Algebra on Multicore and Beyond: A Survey

Discriminative Subnetworks with Regularized Spectral Learning for Global-State Network Data

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