# Accelerated image factorization based on improved NMF algorithm

Accelerated image factorization based on improved NMF algorithm Non-negative matrix factorization (NMF) is widely used in feature extraction and dimension reduction fields. Essentially, it is an optimization problem to determine two non-negative low rank matrices $$W_{m \times k}$$ W m × k and $$H_{k \times n}$$ H k × n for a given matrix $$A_{m \times n}$$ A m × n , satisfying $$A_{m \times n} \approx W_{m \times k}H_{k \times n}$$ A m × n ≈ W m × k H k × n . In this paper, a novel approach to improve the image decomposing and reconstruction effects by introducing the Singular Value Decomposing (SVD)-based initialization scheme of factor matrices W and H, and another measure called choosing rule to determine the optimum value of factor rank k, are proposed. The input image is first decomposed using SVD to get its singular values and corresponding eigenvectors. Then, the number of main components as the rank value k is extracted. Then, the singular values and corresponding eigenvectors are used to initialize W and H based on selected rank k. Finally, convergent results are obtained using multiplicative and additive update rules. However, iterative NMF algorithms’ convergence is very slow on most platforms limiting its practicality. To this end, a parallel implementation frame of described improved NMF algorithm using CUDA, a tool for algorithms parallelization on massively parallel processors, i.e., many-core graphics processors, is presented. Experimental results show that our approach can get better decomposing effect than traditional NMF implementations and dramatic accelerate rate comparing to serial schemes as well as existing distributed-system implementations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Real-Time Image Processing Springer Journals

# Accelerated image factorization based on improved NMF algorithm

, Volume 15 (1) – May 15, 2018
13 pages

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Computer Science; Image Processing and Computer Vision; Multimedia Information Systems; Computer Graphics; Pattern Recognition; Signal,Image and Speech Processing
ISSN
1861-8200
eISSN
1861-8219
D.O.I.
10.1007/s11554-018-0785-9
Publisher site
See Article on Publisher Site

### Abstract

Non-negative matrix factorization (NMF) is widely used in feature extraction and dimension reduction fields. Essentially, it is an optimization problem to determine two non-negative low rank matrices $$W_{m \times k}$$ W m × k and $$H_{k \times n}$$ H k × n for a given matrix $$A_{m \times n}$$ A m × n , satisfying $$A_{m \times n} \approx W_{m \times k}H_{k \times n}$$ A m × n ≈ W m × k H k × n . In this paper, a novel approach to improve the image decomposing and reconstruction effects by introducing the Singular Value Decomposing (SVD)-based initialization scheme of factor matrices W and H, and another measure called choosing rule to determine the optimum value of factor rank k, are proposed. The input image is first decomposed using SVD to get its singular values and corresponding eigenvectors. Then, the number of main components as the rank value k is extracted. Then, the singular values and corresponding eigenvectors are used to initialize W and H based on selected rank k. Finally, convergent results are obtained using multiplicative and additive update rules. However, iterative NMF algorithms’ convergence is very slow on most platforms limiting its practicality. To this end, a parallel implementation frame of described improved NMF algorithm using CUDA, a tool for algorithms parallelization on massively parallel processors, i.e., many-core graphics processors, is presented. Experimental results show that our approach can get better decomposing effect than traditional NMF implementations and dramatic accelerate rate comparing to serial schemes as well as existing distributed-system implementations.

### Journal

Journal of Real-Time Image ProcessingSpringer Journals

Published: May 15, 2018

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