Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Matrix resconstruction: Skeleton decomposition versus singular value decomposition
Date
2017-07-12
Author
SEKMEN, ali
ALDROUBİ, Akram
Koku, Ahmet Buğra
HAMM, Keaton
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
225
views
0
downloads
Cite This
In this work, Skeleton Decomposition (SD) and Singular Value Decomposition (SVD) are compared and evaluated for reconstruction of data matrices whose columns come from a union of subspaces. Specifically, an original data matrix is reconstructed from noise-contaminated version of it. First, matrix reconstruction using SD iteratively is introduced and alternative methods for forming SD-based reconstruction are discussed. Then, through exhaustive simulations, effects of process parameters such as noise level, data size, number of subspaces and their dimensions are evaluated for reconstruction performance. It is also shown that SD-based reconstruction is more effective when data is drawn from a union of low dimensional subspaces compared to a single space of the same dimension.
Subject Keywords
Skeleton decomposition
,
SVD
,
Matrix reconstruction
,
Low-tail-noise
,
High-tail-noise
URI
https://hdl.handle.net/11511/46197
DOI
https://doi.org/10.23919/spects.2017.8046777
Collections
Department of Mechanical Engineering, Conference / Seminar
Suggestions
OpenMETU
Core
Similarity matrix framework for data from union of subspaces
Aldroubi, Akram; Sekmen, Ali; Koku, Ahmet Buğra; Cakmak, Ahmet Faruk (2018-09-01)
This paper presents a framework for finding similarity matrices for the segmentation of data W = [w(1)...w(N)] subset of R-D drawn from a union U = boolean OR(M)(i=1) S-i, of independent subspaces {S-i}(i=1)(M), of dimensions {d(i)}(i=1)(M). It is shown that any factorization of W = BP, where columns of B form a basis for data W and they also come from U, can be used to produce a similarity matrix Xi w. In other words, Xi w(i, j) not equal 0, when the columns w(i) and w(j) of W come from the same subspace, ...
Skeleton Decomposition Analysis for Subspace Clustering
Sekmen, Ali; Aldroubi, Akram; Koku, Ahmet Buğra (2016-12-08)
This paper provides a comprehensive analysis of skeleton decomposition used for segmentation of data W = [w(1) center dot center dot center dot w(N)] subset of R-D drawn from a union u = U-i=1(M) S-i of linearly independent subspaces {Si}(M)(i=1) of dimensionsof {di}(M)(i=1). Our previous work developed a generalized theoretical framework for computing similarity matrices by matrix factorization. Skeleton decomposition is a special case of this general theory. First, a square sub-matrix A is an element of R...
PATH-INTEGRAL FOR SPIN - A NEW APPROACH
Alıyev, Tahmasıb; PAK, NK (1994-10-31)
The path integral representation for the propagator of a Dirac particle in an external electromagnetic field is derived using the functional derivative formalism with the help of Weyl symbol representation for the Grassmann vector part of the variables. The proposed method simplifies the proof of the path integral representation starting from the equation for the Green function significantly and automatically leads to a precise and unambiguous set of boundary conditions for the anticommuting variables and p...
Reduced order optimal control of the convective FitzHugh-Nagumo equations
Karasözen, Bülent; KÜÇÜKSEYHAN, TUĞBA (2020-02-15)
In this paper, we compare three model order reduction methods: the proper orthogonal decomposition (POD), discrete empirical interpolation method (DEIM) and dynamic mode decomposition (DMD) for the optimal control of the convective FitzHugh-Nagumo (FHN) equations. The convective FHN equations consist of the semi-linear activator and the linear inhibitor equations, modeling blood coagulation in moving excitable media. The semilinear activator equation leads to a non-convex optimal control problem (OCP). The ...
Refining technique for multilevel graph k-partitioning and its application on domain decomposition non overlapping Schwarz technique for urban acoustic pollution
Faucard, B.; Sorguç, Arzu; F., Magoules; I., Hagiwara (2009-06-01)
It is known that convergence rate of Domain Decomposition Method for finite element analysis depends on the mesh decomposition quality. In this study, a new approach for refinement algorithm to be employed in mesh segmentation is presented Method is based on multilevel quadrisection and octasection graph partitioning. In this method, the connection is guaranteed first by detecting the disconnected parts and then through the algorithm, assigning them to the domain which mostly contain the mesh of interest. H...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
a. SEKMEN, A. ALDROUBİ, A. B. Koku, and K. HAMM, “Matrix resconstruction: Skeleton decomposition versus singular value decomposition,” 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46197.