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.

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 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.

Dynamic Document Clustering Using Singular Value Decomposition

2012 ◽  
Vol 3 (3) ◽  
pp. 27-55
Author(s):  
Rashmi Nadubeediramesh ◽  
Aryya Gangopadhyay
Keyword(s):  
Singular Value Decomposition ◽  
Low Cost ◽  
Cluster Formation ◽  
Document Clustering ◽  
Computational Cost ◽  
Singular Value ◽  
Healthcare Data ◽  
Medical Library ◽  
Initial Cluster ◽  
Value Decomposition

Incremental document clustering is important in many applications, but particularly so in healthcare contexts where text data is found in abundance, ranging from published research in journals to day-to-day healthcare data such as discharge summaries and nursing notes. In such dynamic environments new documents are constantly added to the set of documents that have been used in the initial cluster formation. Hence it is important to be able to incrementally update the clusters at a low computational cost as new documents are added. In this paper the authors describe a novel, low cost approach for incremental document clustering. Their method is based on conducting singular value decomposition (SVD) incrementally. They dynamically fold in new documents into the existing term-document space and dynamically assign these new documents into pre-defined clusters based on intra-cluster similarity. This saves the cost of re-computing SVD on the entire document set every time updates occur. The authors also provide a way to retrieve documents based on different window sizes with high scalability and good clustering accuracy. They have tested their proposed method experimentally with 960 medical abstracts retrieved from the PubMed medical library. The authors’ incremental method is compared with the default situation where complete re-computation of SVD is done when new documents are added to the initial set of documents. The results show minor decreases in the quality of the cluster formation but much larger gains in computational throughput.

scholarly journals A Note on Full-Rank Factorization of Matrix

2019 ◽  
Vol 15 (2) ◽  
pp. 152-154
Author(s):  
Gyan Bahadur Thapa ◽  
J. López-Bonilla ◽  
R. López-Vázquez
Keyword(s):  
Singular Value Decomposition ◽  
Full Rank ◽  
Singular Value ◽  
The Matrix ◽  
Rank Factorization ◽  
Value Decomposition

We exhibit that the Singular Value Decomposition of a matrix Anxm implies a natural full-rank factorization of the matrix.

Fault feature extraction and classification based on WPT and SVD: Application to element bearings with artificially created faults under variable conditions

2016 ◽  
Vol 231 (22) ◽  
pp. 4186-4196 ◽  
Author(s):  
Mourad Kedadouche ◽  
Zhaoheng Liu
Keyword(s):  
Support Vector Machine ◽  
Singular Value Decomposition ◽  
Wavelet Packet ◽  
Rolling Bearing ◽  
Wavelet Packet Transform ◽  
Singular Value ◽  
Support Vector ◽  
Rolling Bearings ◽  
The Matrix ◽  
Value Decomposition

Achieving a precise fault diagnosis for rolling bearings under variable conditions is a problematic challenge. In order to enhance the classification and achieves a higher precision for diagnosing rolling bearing degradation, a hybrid method is proposed. The method combines wavelet packet transform, singular value decomposition and support vector machine. The first step of the method is the decomposition of the signal using wavelet packet transform and then instantaneous amplitudes and energy are computed for each component. The Second step is to apply the singular value decomposition to the matrix constructed by the instantaneous amplitudes and energy in order to reduce the matrix dimension and obtaining the fault feature unaffected by the operating condition. The features extracted by singular value decomposition are then used as an input to the support vector machine in order to recognize the fault mode of rolling bearings. The method is applied to a bearing with faults created using electro-discharge machining under laboratory conditions. Test results show that the proposed methodology is effective to classify rolling bearing faults with high accuracy.

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.

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