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.

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.

scholarly journals A Hybrid Deep Collaborative Filtering Approach for Recommender Systems

2021 ◽  
Author(s):  
Kirubahari R ◽  
Miruna Joe Amali S
Keyword(s):  
Singular Value Decomposition ◽  
Collaborative Filtering ◽  
Recommender Systems ◽  
Cold Start ◽  
Singular Value ◽  
User Preferences ◽  
Boltzmann Machine ◽  
Latent Features ◽  
Value Decomposition ◽  
Cold Start Problem

Abstract Recommender Systems (RS) help the users by showing better products and relevant items efficiently based on their likings and historical interactions with other users and items. Collaborative filtering is one of the most powerful technique of recommender system and provides personalized recommendation for users by prediction rating approach. Many Recommender Systems generally model only based on user implicit feedback, though it is too challenging to build RS. Conventional Collaborative Filtering (CF) techniques such as matrix decomposition, which is a linear combination of user rating for an item with latent features of user preferences, but have limited learning capacity. Additionally, it has been suffering from data sparsity and cold start problem due to insufficient data. In order to overcome these problems, an integration of conventional collaborative filtering with deep neural networks is proposed. A Weighted Parallel Deep Hybrid Collaborative Filtering based on Singular Value Decomposition (SVD) and Restricted Boltzmann Machine (RBM) is proposed for significant improvement. In this approach a user-item relationship matrix with explicit ratings is constructed. The user - item matrix is integrated to Singular Value Decomposition (SVD) that decomposes the matrix into the best lower rank approximation of the original matrix. Secondly the user-item matrix is embedded into deep neural network model called Restricted Boltzmann Machine (RBM) for learning latent features of user- item matrix to predict user preferences. Thus, the Weighted Parallel Deep Hybrid RS uses additional attributes of user - item matrix to alleviate the cold start problem. The proposed method is verified using two different movie lens datasets namely, MovieLens 100K and MovieLens of 1M and evaluated using Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE). The results indicate better prediction compared to other techniques in terms of accuracy.

scholarly journals A Survey of Latent Factor Models for Recommender Systems and Personalization

2021 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Recommender Systems ◽  
Matrix Factorization ◽  
Matrix Completion ◽  
Factor Models ◽  
Singular Value ◽  
Bayesian Personalized Ranking ◽  
Latent Factor Models ◽  
Value Decomposition ◽  
Personalized Ranking ◽  
Non Negative Matrix Factorization

<p>Recommender systems aim to personalize the experience of a user and are critical for businesses like retail portals, e-commerce websites, book sellers, streaming movie websites and so on. The earliest personalized algorithms use matrix factorization or matrix completion using algorithms like the singular value decomposition (SVD). There are other more advanced algorithms, like factorization machines, Bayesian personalized ranking (BPR), and a more recent Hebbian graph embeddings (HGE) algorithm. In this work, we implement BPR and HGE and compare our results with SVD, Non-negative matrix factorization (NMF) using the MovieLens dataset.</p>

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.

Sign in / Sign up

Export Citation Format

Share Document