scholarly journals USE OF SINGULAR-VALUE DECOMPOSITION IN GRAVITATIONAL-WAVE DATA ANALYSIS

2013 ◽  
Vol 23 ◽  
pp. 99-105
Author(s):  
DREW KEPPEL
Keyword(s):  
Parameter Estimation ◽  
Data Analysis ◽  
Singular Value Decomposition ◽  
Gravitational Wave ◽  
Computational Cost ◽  
Singular Value ◽  
Matched Filtering ◽  
Powerful Technique ◽  
Wave Data ◽  
Value Decomposition

Singular-value decomposition is a powerful technique that has been used in the analysis of matrices in many fields. In this paper, we summarize how it has been applied to the analysis of gravitational-wave data analysis. These include producing basis waveforms for matched filtering, decreasing the computational cost of searching for many waveforms, improving parameter estimation, and providing a method of waveform interpolation.

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 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.

scholarly journals A Unified Scalable Equivalent Formulation for Schatten Quasi-Norms

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1325
Author(s):  
Fanhua Shang ◽  
Yuanyuan Liu ◽  
Fanjie Shang ◽  
Hongying Liu ◽  
Lin Kong ◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Computational Cost ◽  
Singular Value ◽  
Weighted Sum ◽  
Equivalent Formulation ◽  
Norm Minimization ◽  
The Mean ◽  
Value Decomposition ◽  
High Computational Cost ◽  
Theoretical Results

The Schatten quasi-norm is an approximation of the rank, which is tighter than the nuclear norm. However, most Schatten quasi-norm minimization (SQNM) algorithms suffer from high computational cost to compute the singular value decomposition (SVD) of large matrices at each iteration. In this paper, we prove that for any p, p1, p2>0 satisfying 1/p=1/p1+1/p2, the Schatten p-(quasi-)norm of any matrix is equivalent to minimizing the product of the Schatten p1-(quasi-)norm and Schatten p2-(quasi-)norm of its two much smaller factor matrices. Then, we present and prove the equivalence between the product and its weighted sum formulations for two cases: p1=p2 and p1≠p2. In particular, when p>1/2, there is an equivalence between the Schatten p-quasi-norm of any matrix and the Schatten 2p-norms of its two factor matrices. We further extend the theoretical results of two factor matrices to the cases of three and more factor matrices, from which we can see that for any 0<p<1, the Schatten p-quasi-norm of any matrix is the minimization of the mean of the Schatten (⌊1/p⌋+1)p-norms of ⌊1/p⌋+1 factor matrices, where ⌊1/p⌋ denotes the largest integer not exceeding 1/p.

The Inversion Problem for Two Fold Photoelectron Counting Statistics

1975 ◽  
Vol 53 (13) ◽  
pp. 1215-1220 ◽  
Author(s):  
Julian Blake ◽  
Richard Barakat
Keyword(s):  
Parameter Estimation ◽  
Correlation Function ◽  
Singular Value Decomposition ◽  
General Structure ◽  
Coherence Time ◽  
Singular Value ◽  
Spectral Information ◽  
Inversion Problem ◽  
Counting Statistics ◽  
Value Decomposition

The extraction of spectral information from measurements of the full or clipped photoelectron correlation function is treated. Unlike previous treatments, the discussion here is not limited to counting times short compared to the coherence time of the light. The method of singular value decomposition is applied to the case where there is no prior knowledge of the spectrum. Parameter estimation is applied when the general structure of the spectrum is known.

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