A Note on Alternating Minimization Algorithm for the Matrix Completion Problem

Gamarnik, David; Misra, Sidhant

doi:10.1109/LSP.2016.2576979

Title: A Note on Alternating Minimization Algorithm for the Matrix Completion Problem

Full Record
Other Related Research

Abstract

Here, we consider the problem of reconstructing a low-rank matrix from a subset of its entries and analyze two variants of the so-called alternating minimization algorithm, which has been proposed in the past.We establish that when the underlying matrix has rank one, has positive bounded entries, and the graph underlying the revealed entries has diameter which is logarithmic in the size of the matrix, both algorithms succeed in reconstructing the matrix approximately in polynomial time starting from an arbitrary initialization.We further provide simulation results which suggest that the second variant which is based on the message passing type updates performs significantly better.

Authors:

Gamarnik, David ^[1];

^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: Mon Jun 06 00:00:00 EDT 2016

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Laboratory Directed Research and Development (LDRD) Program; National Science Foundation of China

OSTI Identifier:: 1361478

Report Number(s):: LA-UR-16-23854
Journal ID: ISSN 1070-9908; TRN: US1702183

Grant/Contract Number:: AC52-06NA25396; CMMI-1335155

Resource Type:: Accepted Manuscript

Journal Name:: IEEE Signal Processing Letters

Additional Journal Information:: Journal Volume: 23; Journal Issue: 10; Journal ID: ISSN 1070-9908

Publisher:: IEEE Signal Processing Society

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Mathematics; Alternating minimization; compressive sensing; low-rank matrix completion

Citation Formats


                    Gamarnik, David, and Misra, Sidhant. A Note on Alternating Minimization Algorithm for the Matrix Completion Problem.  United States: N. p., 2016. 
Web.  doi:10.1109/LSP.2016.2576979.

Copy to clipboard


                    Gamarnik, David, & Misra, Sidhant. A Note on Alternating Minimization Algorithm for the Matrix Completion Problem.  United States.  https://doi.org/10.1109/LSP.2016.2576979

Copy to clipboard


                    Gamarnik, David, and Misra, Sidhant. Mon .  
"A Note on Alternating Minimization Algorithm for the Matrix Completion Problem".  United States.  https://doi.org/10.1109/LSP.2016.2576979.  https://www.osti.gov/servlets/purl/1361478.

Copy to clipboard


                    
@article{osti_1361478,

  title        = {A Note on Alternating Minimization Algorithm for the Matrix Completion Problem},

  author       = {Gamarnik, David and Misra, Sidhant},

  abstractNote = {Here, we consider the problem of reconstructing a low-rank matrix from a subset of its entries and analyze two variants of the so-called alternating minimization algorithm, which has been proposed in the past.We establish that when the underlying matrix has rank one, has positive bounded entries, and the graph underlying the revealed entries has diameter which is logarithmic in the size of the matrix, both algorithms succeed in reconstructing the matrix approximately in polynomial time starting from an arbitrary initialization.We further provide simulation results which suggest that the second variant which is based on the message passing type updates performs significantly better.},

  doi          = {10.1109/LSP.2016.2576979},

  journal      = {IEEE Signal Processing Letters},

  number       = 10,

  volume       = 23,

  place        = {United States},

  year         = {Mon Jun 06 00:00:00 EDT 2016},

  month        = {Mon Jun 06 00:00:00 EDT 2016}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1109/LSP.2016.2576979

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 11 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Similar Records in DOE PAGES and OSTI.GOV collections:

Predecessor and permutation existence problems for sequential dynamical systems

Conference Barrett, C L ; Hunt, H B ; Marathe, M V ; ...

A class of finite discrete dynamical systems, called Sequential Dynamical Systems (SDSs), was introduced in BMR99, BR991 as a formal model for analyzing simulation systems. An SDS S is a triple (G, F,n ),w here (i) G(V,E ) is an undirected graph with n nodes with each node having a state, (ii) F = (fi, fi, . . ., fn), with fi denoting a function associated with node ui E V and (iii) A is a permutation of (or total order on) the nodes in V, A configuration of an SDS is an n-vector ( b l, bz, . .more »« less
https://doi.org/10.46298/dmtcs.2314

Full Text Available
The price of privately releasing contingency tables, and the spectra of random matrices with correlated rows

Conference Kasiviswanathan, Shiva ; Rudelson, Mark ; Smith, Adam

Contingency tables are the method of choice of government agencies for releasing statistical summaries of categorical data. In this paper, we consider lower bounds on how much distortion (noise) is necessary in these tables to provide privacy guarantees when the data being summarized is sensitive. We extend a line of recent work on lower bounds on noise for private data analysis [10, 13. 14, 15] to a natural and important class of functionalities. Our investigation also leads to new results on the spectra of random matrices with correlated rows. Consider a database D consisting of n rows (one per individual),more »« less
https://doi.org/10.1145/1806689.1806795

Full Text Available
Adaptive Runtime Features For Distributed Graph Algorithms

Conference Firoz, Jesun S. ; Zalewski, Marcin J. ; Suetterlein, Joshua D. ; ...

Performance of distributed graph algorithms can benefit greatly by forming rapport between algorithmic abstraction and the underlying runtime system that is responsible for scheduling work and exchanging messages. However, due to their dynamic and irregular nature of computation, distributed graph algorithms written in different programming models impose varying degree of workload pressure on the runtime. To cope with such vastly different workload characteristics, a runtime has to make several trade-offs. One such trade-off arises, for example, when the runtime scheduler has to choose among alternatives such as whether to execute algorithmic work, or progress the network by probing network buffers,more »« less
https://doi.org/10.1109/HiPC.2018.00018
Incremental nonnegative matrix factorization based on correlation and graph regularization for matrix completion

Journal Article Zhang, Xiaoxia ; Chen, Degang ; Wu, Kesheng - International Journal of Machine Learning and Cybernetics

Matrix factorization is widely used in recommendation systems, text mining, face recognition and computer vision. As one of the most popular methods, nonnegative matrix factorization and its incremental variants have attracted much attention. The existing incremental algorithms are established based on the assumption of samples are independent and only update the new latent variable of weighting coefficient matrix when the new sample comes, which may lead to inferior solutions. To address this issue, we investigate a novel incremental nonnegative matrix factorization algorithm based on correlation and graph regularizer (ICGNMF). The correlation is mainly used for finding out those correlated rowsmore »« less
https://doi.org/10.1007/s13042-018-0808-7
A matrix completion algorithm for efficient calculation of quantum and variational effects in chemical reactions

Journal Article Bac, Selin ; Quiton, Stephen Jon Du ; Kron, Kareesa J. ; ... - Journal of Chemical Physics

This work examines the viability of matrix completion methods as cost-effective alternatives to full nuclear Hessians for calculating quantum and variational effects in chemical reactions. The harmonic variety-based matrix completion (HVMC) algorithm, developed in a previous study [S. J. Quiton et al., J. Chem. Phys. 153, 054122 (2020)], exploits the low-rank character of the polynomial expansion of potential energy to recover vibrational frequencies (square roots of eigenvalues of nuclear Hessians) constituting the reaction path using a small sample of its entities. These frequencies are essential for calculating rate coefficients using variational transition state theory with multidimensional tunneling (VTST-MT). HVMC performancemore »« less
https://doi.org/10.1063/5.0091155

Full Text Available

Similar Records