A Learning and Inference Mechanism for Design Optimization Problem (Re)-Formulation Using Singular Value Decomposition

2008 ◽  
Author(s):  
Somwrita Sarkar ◽  
Andy Dong ◽  
John S. Gero
Keyword(s):  
Singular Value Decomposition ◽  
Design Optimization ◽  
Design Problem ◽  
Large Scale ◽  
Optimization Problem ◽  
Analytical Form ◽  
Singular Value ◽  
Training Data ◽  
Inference Mechanism ◽  
Value Decomposition

This paper presents a knowledge-lean learning and inference mechanism based on Singular Value Decomposition (SVD) for design optimization problem (re)-formulation at the problem modeling stage. The distinguishing feature of the mechanism is that it requires very few training cases to extract and generalize knowledge for large classes of problems sharing similar characteristics. The genesis of the mechanism is based on viewing problem (re)-formulation as a statistical pattern extraction problem. SVD is applied as a dimensionality reduction tool to extract semantic patterns from a syntactic formulation of the design problem. We explain and evaluate the mechanism on a model-based decomposition problem, a hydraulic cylinder design problem, and a medium-large scale Aircraft Concept Sizing problem. The results show that the method generalizes quickly and can be used to impute relations between variables, parameters, objective functions, and constraints when training data is provided in symbolic analytical form, and is likely to be extensible to forms when the representation is not in analytical functional form.

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 Introduction to Matrix Factorization for Recommender Systems

2021 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Singular Value Decomposition ◽  
Online Education ◽  
Recommender Systems ◽  
Matrix Factorization ◽  
Gradient Descent ◽  
Large Scale ◽  
Singular Value ◽  
Factorization Algorithms ◽  
Value Decomposition ◽  
Interaction History

Recommender systems aim to personalize the experience of user by suggesting items to the user based on the preferences of a user. The preferences are learned from the user’s interaction history or through explicit ratings that the user has given to the items. The system could be part of a retail website, an online bookstore, a movie rental service or an online education portal and so on. In this paper, I will focus on matrix factorization algorithms as applied to recommender systems and discuss the singular value decomposition, gradient descent-based matrix factorization and parallelizing matrix factorization for large scale applications.

scholarly journals Split-and-Combine Singular Value Decomposition for Large-Scale Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jengnan Tzeng
Keyword(s):  
Singular Value Decomposition ◽  
Large Scale ◽  
Semantic Analysis ◽  
Computational Cost ◽  
Matrix Decomposition ◽  
Singular Value ◽  
Fast Method ◽  
The Matrix ◽  
Scale Matrix ◽  
Value Decomposition

The singular value decomposition (SVD) is a fundamental matrix decomposition in linear algebra. It is widely applied in many modern techniques, for example, high- dimensional data visualization, dimension reduction, data mining, latent semantic analysis, and so forth. Although the SVD plays an essential role in these fields, its apparent weakness is the order three computational cost. This order three computational cost makes many modern applications infeasible, especially when the scale of the data is huge and growing. Therefore, it is imperative to develop a fast SVD method in modern era. If the rank of matrix is much smaller than the matrix size, there are already some fast SVD approaches. In this paper, we focus on this case but with the additional condition that the data is considerably huge to be stored as a matrix form. We will demonstrate that this fast SVD result is sufficiently accurate, and most importantly it can be derived immediately. Using this fast method, many infeasible modern techniques based on the SVD will become viable.

A fast algorithm for regularized focused 3D inversion of gravity data using randomized singular-value decomposition

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. G25-G34 ◽  
Author(s):  
Saeed Vatankhah ◽  
Rosemary Anne Renaut ◽  
Vahid Ebrahimzadeh Ardestani
Keyword(s):  
Linear System ◽  
Singular Value Decomposition ◽  
Fast Algorithm ◽  
Large Scale ◽  
Gravity Data ◽  
Singular Values ◽  
Singular Value ◽  
System Matrix ◽  
Large Scale System ◽  
Value Decomposition

We develop a fast algorithm for solving the under-determined 3D linear gravity inverse problem based on randomized singular-value decomposition (RSVD). The algorithm combines an iteratively reweighted approach for [Formula: see text]-norm regularization with the RSVD methodology in which the large-scale linear system at each iteration is replaced with a much smaller linear system. Although the optimal choice for the low-rank approximation of the system matrix with [Formula: see text] rows is [Formula: see text], acceptable results are achievable with [Formula: see text]. In contrast to the use of the iterative LSQR algorithm for the solution of linear systems at each iteration, the singular values generated using RSVD yield a good approximation of the dominant singular values of the large-scale system matrix. Thus, the regularization parameter found for the small system at each iteration is dependent on the dominant singular values of the large-scale system matrix and appropriately regularizes the dominant singular space of the large-scale problem. The results achieved are comparable with those obtained using the LSQR algorithm for solving each linear system, but they are obtained at a reduced computational cost. The method has been tested on synthetic models along with real gravity data from the Morro do Engenho complex in central Brazil.

Reciprocity-Based Singular Value Decomposition for Inverse Kinematic Analysis of the Metamorphic Multifingered Hand

2012 ◽  
Vol 4 (3) ◽  
Author(s):  
Lei Cui ◽  
Jian S. Dai
Keyword(s):  
Singular Value Decomposition ◽  
Degrees Of Freedom ◽  
Singular Values ◽  
Analytical Form ◽  
Inverse Kinematic ◽  
Singular Value ◽  
Robotic Hand ◽  
Value Analysis ◽  
Constraint Equations ◽  
Value Decomposition

With a new type of multifingered hands that raise a new philosophy in the construction and study of a multifingered hand, this paper is a follow-on study of the kinematics of the metamorphic multifingered hand based on finger constraint equations. The finger constraint equations lead to a comprehensive mathematical model of the hand with a reconfigurable palm which integrates all finger motions with the additional palm motion. Singular values of the partitioned Jacobian matrix in their analytical form are derived and applied to obtaining analytical solution to inverse kinematics of a complete robotic hand. The paper for the first time solves this integrated motion and the multifingered hand model with the singular value decomposition and extra degrees of freedom are examined with the singular value analysis to avoid the singularities. The work identifies finger displacement and velocity with effect from the articulated palm and presents a new way of analyzing a multifingered robotic hand.

Implementation of SVD Parallel Algorithm and its Application in Medical Industry

2015 ◽  
Vol 743 ◽  
pp. 515-521 ◽  
Author(s):  
You Wu ◽  
Lei Feng Liu ◽  
Xue Liang Zhao ◽  
Kun Hua Zhong
Keyword(s):  
Singular Value Decomposition ◽  
Large Scale ◽  
Medical Industry ◽  
Singular Value ◽  
Construction Process ◽  
Time Cost ◽  
Scale Matrix ◽  
Value Decomposition ◽  
Speed And Accuracy ◽  
Computing Speed

Singular value decomposition (SVD) is an important part of the numerical calculateion.It is widely used in biology, meteorology, quantum mechanics and other fields. It is discovered that the speed of calculation and accuracy has become the two basic questions of singular value decomposition during the construction process. With the era of big data,there are more and more cases of largescale data analysis using SVD. Singular value decomposition was originally an algorithm for computing resources are consumed, if still using the traditional stand-alone mode, will consume a lot of time cost. In order to improve the computing speed and accuracy, the system implement the parallel SVD algorithm which is based on unilateral jacobi method.It is used to analyze large-scale matrix about medicine for finding similarity of medicine efficacy.

Rotational Speed-Dependent Contact Formulation for Nonlinear Blade Dynamics Prediction

2018 ◽  
Author(s):  
Torsten Heinze ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek ◽  
Andreas Hartung
Keyword(s):  
Singular Value Decomposition ◽  
Rotational Speed ◽  
Large Scale ◽  
Vibrational Analysis ◽  
Harmonic Balance Method ◽  
Singular Value ◽  
Nonlinear Frequency ◽  
Computational Performance ◽  
Contact Situation ◽  
Value Decomposition

Considering rotational speed-dependent stiffness for vibrational analysis of friction-damped bladed disk models has proven to lead to significant improvements in nonlinear frequency response curve computations. The accuracy of the result is driven by a suitable choice of reduction bases. Multi-model reduction combines various bases which are valid for different parameter values. This composition reduces the solution error drastically. The resulting set of equations is typically solved by means of the harmonic balance method. Nonlinear forces are regularized by a Lagrangian approach embedded in an alternating frequency/time domain method providing the Fourier coefficients for the frequency domain solution. The aim of this paper is to expand the multi-model approach to address rotational speed-dependent contact situations. Various reduction bases derived from composing Craig-Bampton, Rubin-Martinez, and hybrid interface methods will be investigated with respect to their applicability to capture the changing contact situation correctly. The methods validity is examined based on small academic examples as well as large-scale industrial blade models. Coherent results show that the multi-model composition works successfully, even if multiple different reduction bases are used per sample point of variable rotational speed. This is an important issue in case that a contact situation for a specific value of the speed is uncertain forcing the algorithm to automatically choose a suitable basis. Additionally, the randomized singular value decomposition is applied to rapidly extract an appropriate multi-model basis. This approach improves the computational performance by orders of magnitude compared to the standard singular value decomposition, while preserving the ability to provide a best rank approximation.

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