On an optimization model for Approximate Nonnegative Matrix Factorization

Authors

Abstract

Image and video signal processing have a various
number of tasks to be performed in order to obtain an efficient
and low-dimensional encoding for transmission. Studies have
shown that Nonnegative Factorization of the data Matrix (NFM)
is a suitable tool for obtaining ranking reduction and sparse coding.
Thus, developing efficient optimization algorithmic methods
for video/image encoding presents a key technical challenge in
the effort to minimize distortion and obtain good quality reduced
encodings. In this paper, we propose a discrete optimization
framework where NMF is formulated as a nonlinear programming
optimization problem, and apply an Spectral Projected
Gradient (SPG) algorithm to this problem. The computational
experience reported shows that the proposed approach can in
fact produce good quality local minima.

Keywords

Nonnegative Matrix Factorization, Constrained Large Scale Optimization, Image Signal Processing

Subject

Combinatorial Optimization, Feature extraction, Image Signal Processing

Conference

ISCIES - International Symposium on Computational Intelligence for Engineering System, November 2011

Cited by

Year 2015 : 3 citations

Ecem Edisa, Inês Flores-Colenb, Jorge de Brito. "Quasi-quantitative infrared thermographic detection of moisture variation in facades with adhered ceramic cladding using principal component analysis". Building and Environment, Volume 94, Part 1, December 2015, Pages 97–108. doi:10.1016/j.buildenv.2015.07.027

A. M. Tomé , R. Schachtner, V. Vigneron, C. G. Puntonet, E. W. LangA logistic non-negative matrix factorization approach to binary data sets. Multidimensional Systems and Signal Processing, January 2015, Volume 26, Issue 1, pp 125-143. (First online: 25 June 2013)

Ecem Edis , Inês Flores-Colen, Jorge De Brito. Time-Dependent Passive Building Thermography for Detecting Delamination of Adhered Ceramic Cladding. Journal of Nondestructive Evaluation (Available on-line: July 2015).

Year 2013 : 1 citations

Torkestani, J.A., International Journal of Foundations of Computer Science, ”A Learning Automata-based algorithm to the Stochastic Min-Degree Constrained Minimum Spanning Tree Problem”. 24(03):329-348, 2013.(DOI: 10.1142/S012905411350007X)

Year 2012 : 2 citations

Torlestani, J.L., ”Mobility-based Backbone Formation in Wireless Mobile Ad-hoc Networks”. Wireless Personal Communications, Springer US, 2012, 7422:237-248, 2012.(DOI: 10.1007/s1277-012-0955-1)

L. C. Martinez e A. S. da Cunha, ”A Parallel Lagrangian Relaxation Algorithm for the Min-Degree Constrained Minimum Spanning Tree Problem”. Combinatorial Optimization, 7422:237-248, 2012.