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Bounded Matrix Low Rank Approximation

2012
*
2012 IEEE 12th International Conference on Data Mining
*

In this paper, we propose a new

doi:10.1109/icdm.2012.131
dblp:conf/icdm/KannanIP12
fatcat:bt2i6dfhwjcnvioc6fmgo4k4xu
*matrix*lower*rank**approximation*called*Bounded**Matrix**Low**Rank**Approximation*(BMA) which imposes a lower and an upper*bound*on every element of a lower*rank**matrix*that ... BMA is different from NMF as it imposes*bounds*on the*approximation*itself rather than on each of the*low**rank*factors. ...*Matrix**Low**Rank**Approximation*(BMA) Figure 1 : 1 Block*Bounded**Matrix**Low**Rank**Approximation*the ground truth. ...##
###
Bounded Matrix Low Rank Approximation
[chapter]

2015
*
Signals and Communication Technology
*

In this paper, we propose a new

doi:10.1007/978-3-662-48331-2_4
fatcat:wxtdcaqrqza6fkvut3ynmcbtu4
*matrix*lower*rank**approximation*called*Bounded**Matrix**Low**Rank**Approximation*(BMA) which imposes a lower and an upper*bound*on every element of a lower*rank**matrix*that ... BMA is different from NMF as it imposes*bounds*on the*approximation*itself rather than on each of the*low**rank*factors. ...*Matrix**Low**Rank**Approximation*(BMA) Figure 1 : 1 Block*Bounded**Matrix**Low**Rank**Approximation*the ground truth. ...##
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Low Rank Matrix-Valued Chernoff Bounds and Approximate Matrix Multiplication
[article]

2010
*
arXiv
*
pre-print

To handle similar

arXiv:1005.2724v3
fatcat:wk2qxpcpsjgd3p7wv6cm45wawe
*bounds*for row sampling, we develop a novel*matrix*-valued Chernoff*bound*inequality which we call*low**rank**matrix*-valued Chernoff*bound*. ... In this paper we develop algorithms for*approximating**matrix*multiplication with respect to the spectral norm. Let A∈^n× m and B∈^n × p be two matrices and >0. ... , ℓ 2 -regression, and*low**rank**matrix**approximation*. ...##
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Lower bounds for the low-rank matrix approximation

2017
*
Journal of Inequalities and Applications
*

*Low*-

*rank*

*matrix*recovery is an active topic drawing the attention of many researchers. It addresses the problem of

*approximating*the observed data

*matrix*by an unknown

*low*-

*rank*

*matrix*. ... Suppose that A is a

*low*-

*rank*

*matrix*

*approximation*of D, where D and A are m × n matrices. ... There are some reasons for the study of lower

*bound*of a

*low*-

*rank*

*matrix*

*approximation*problem. ...

##
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Low Rank Matrix-valued Chernoff Bounds and Approximate Matrix Multiplication
[chapter]

2011
*
Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms
*

Second we give improved

doi:10.1137/1.9781611973082.109
dblp:conf/soda/MagenZ11
fatcat:nkiq6xfprvc7vg77ihrz7bndbq
*approximation*algorithms for the*low**rank**matrix**approximation*problem with respect to the spectral norm. ... To handle similar*bounds*for row sampling, we develop a novel*matrix*-valued Chernoff*bound*inequality which we call*low**rank*matrixvalued Chernoff*bound*. ... , 2 -regression, and*low**rank**matrix**approximation*. ...##
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Least upper bound of truncation error of low-rank matrix approximation algorithm using QR decomposition with pivoting

2021
*
Japan journal of industrial and applied mathematics
*

AbstractLow-

doi:10.1007/s13160-021-00459-x
fatcat:jhqosv7c5bf6lp4i4fagxuhoka
*rank**approximation*by QR decomposition with pivoting (pivoted QR) is known to be less accurate than singular value decomposition (SVD); however, the calculation amount is smaller than that ... The least upper*bound*of the ratio of the truncation error, defined by $$\Vert A-BC\Vert _2$$ ‖ A - B C ‖ 2 , using pivoted QR to that using SVD is proved to be $$\sqrt{\frac{4^k-1}{3}(n-k)+1}$$ 4 k - ... Introduction*Low*-*rank**approximation**Low*-*rank**matrix**approximation*involves*approximating*a*matrix*by a*matrix*whose*rank*is less than that of the original*matrix*. ...##
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Bilateral Random Projections
[article]

2011
*
arXiv
*
pre-print

In this paper, we show a dense

arXiv:1112.5215v1
fatcat:aqnc33djofelrkylotjaehq7bq
*matrix*X's*low*-*rank**approximation*can be rapidly built from its left and right random projections Y_1=XA_1 and Y_2=X^TA_2, or bilateral random projection (BRP). ... The effectiveness and the efficiency of BRP based*low*-*rank**approximation*is empirically verified on both artificial and real datasets. ...*Approximation*error*bounds*We analyze the error*bounds*of the BRP based*low*-*rank**approximation*(1) and its power scheme modification (5) . ...##
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Bilateral random projections

2012
*
2012 IEEE International Symposium on Information Theory Proceedings
*

In this paper, we show a dense

doi:10.1109/isit.2012.6283064
dblp:conf/isit/ZhouT12
fatcat:j2dm3ucd3bglfivskt3ze2cacy
*matrix*X's*low*-*rank**approximation*can be rapidly built from its left and right random projections Y 1 = XA 1 and Y 2 = X T A 2 , or bilateral random projection (BRP). ... The effectiveness and the efficiency of BRP based*low*-*rank**approximation*is empirically verified on both artificial and real datasets. ...*APPROXIMATION*ERROR*BOUNDS*We analyze the error*bounds*of the BRP based*low*-*rank**approximation*(1) and its power scheme modification (5) . ...##
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Why are Big Data Matrices Approximately Low Rank?
[article]

2018
*
arXiv
*
pre-print

Hence any sufficiently large

arXiv:1705.07474v2
fatcat:hqwyluzpf5hd3faxmfuq6lmjzi
*matrix*from such a latent variable model can be*approximated*, up to a small entrywise error, by a*low**rank**matrix*. ... However, we show that we can*approximate*every entry of an m × n*matrix*drawn from this model to within a fixed absolute error by a*low**rank**matrix*whose*rank*grows as O((m + n)). ... It is useful to know when a dataset can be*approximated*by a*low**rank**matrix*. A*low**rank**approximation*can be used to make filtering and statistics either computationally feasible or more efficient. ...##
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Matrix Coherence and the Nystrom Method
[article]

2010
*
arXiv
*
pre-print

The Nystrom method is an efficient technique to speed up large-scale learning applications by generating

arXiv:1004.2008v1
fatcat:bojflagkffaijf2mdjcra4txse
*low*-*rank**approximations*. ... Making use of related work in the compressed sensing and the*matrix*completion literature, we derive novel coherence-based*bounds*for the Nystrom method in the*low*-*rank*setting. ... a*low*-*rank**approximation*. ...##
###
Matrix Coherence and the Nystrom Method
[article]

2014
*
arXiv
*
pre-print

Making use of related work in the compressed sensing and the

arXiv:1408.2044v1
fatcat:qnhwnoqcsreghbrp2hvzuvky2y
*matrix*completion literature, we derive novel coherence-based*bounds*for the Nystrom method in the*low*-*rank*setting. ... The Nystrom method is an efficient technique used to speed up large-scale learning applications by generating*low*-*rank**approximations*. ... This is done by generating*low*-*rank**approximations*of G using a subset of the columns of the*matrix*. ...##
###
Practical Sketching Algorithms for Low-Rank Matrix Approximation

2017
*
SIAM Journal on Matrix Analysis and Applications
*

This paper describes a suite of algorithms for constructing

doi:10.1137/17m1111590
fatcat:nnntlyw3nray5c3cha5ay452gi
*low*-*rank**approximations*of an input*matrix*from a random linear image of the*matrix*, called a sketch. ... These methods can preserve structural properties of the input*matrix*, such as positive-semidefiniteness, and they can produce*approximations*with a user-specified*rank*. ... Proof of Theorem 4.2: Spectral Error*Bound*. In this section, we establish a spectral-norm error*bound*for the*low*-*rank**approximation*(4.3). ...##
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Clustered low rank approximation of graphs in information science applications
[chapter]

2011
*
Proceedings of the 2011 SIAM International Conference on Data Mining
*

In this paper we present a fast and accurate procedure called clustered

doi:10.1137/1.9781611972818.15
dblp:conf/sdm/SavasD11
fatcat:stqgahy4zrdv7i3agofx6al4bi
*low**rank**matrix**approximation*for massive graphs. ... Further, we generalize stochastic algorithms to the clustered*low**rank**approximation*framework and present theoretical*bounds*for the*approximation*error. ... Contributions Clustered*low**rank**matrix**approximation*. We are interested in a*low**rank**approximation*of a given*matrix*A arising from a graph. ...##
###
Robust and Sample Optimal Algorithms for PSD Low-Rank Approximation
[article]

2021
*
arXiv
*
pre-print

Bakshi and Woodruff (NeurIPS, 2018) showed a bi-criteria, relative-error

arXiv:1912.04177v5
fatcat:746322w7njalrlc2a2p2huhub4
*low*-*rank**approximation*which queries O(nk/ϵ^2.5) entries and outputs a*rank*-(k+4)*matrix*. ... Recently, Musco and Woodruff (FOCS, 2017) showed that given an n × n positive semidefinite (PSD)*matrix*A, it is possible to compute a (1+ϵ)-*approximate*relative-error*low*-*rank**approximation*to A by querying ... Lower*Bound*for Robust PSD*Low*-*Rank**Approximation*In this subsection, we show a query lower*bound*of Ω( 2 2 / 2 ) = Ω( 2 max / ) for any algorithm that outputs a*low**rank**approximation*up to additive-error ...##
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Computing Structured Singular Values for Sturm-Liouville Problems

2019
*
International Journal of Analysis and Applications
*

The

doi:10.28924/2291-8639-17-2019-879
fatcat:yvvzi3r6indoxa3cfiqsqtq7fu
*low**rank*ODE's based technique is used for the*approximation*of the*bounds*of SSV. The lower*bounds*of SSV discuss the instability analysis of linear system in system theory. ... The numerical experimentation show the comparison of*bounds*of SSV computed by*low**rank*ODE'S technique with the well-known MATLAB routine mussv available in MATLAB Control Toolbox. ... routine mussv is very fast compare to*Low**rank*ODE's based technique. • The MATLAB routine mussv additionally*approximate*an upper*bounds*of SSV which is not possible while making use of*Low**rank*ODE's ...
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