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Non-negative Matrix Factorization Algorithm Based on Method of Least Square and Its Applications

Author: XuTaiYan
Tutor: GaoZunHai
School: Wuhan Polytechnic University
Course: Mechanical and Electronic Engineering
Keywords: NMF The method of least squares Full rank decomposition Program implementation Image decomposition
CLC: O151.21
Type: Master's thesis
Year: 2010
Downloads: 395
Quote: 1
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Abstract

Scientific research, in order to analyze and process large-scale data, the data matrix in a different sense, different ways of decomposition, matrix factorization, low-rank approximation can get the original matrix, thereby greatly reducing the dimension of the data to save storage space and computing resources. Non-negative matrix factorization (NMF) is a new matrix decomposition method, which is in the \non-negative matrices, to reflect the potential linear structure of the data. And traditional matrix factorization algorithm is simple, fast, decomposition results can be explained, small storage space and many other advantages, was put forth to the scientific community. In the original non-negative matrix decomposition based on the theory put forward a traditional non-negative matrix decomposition algorithm optimization algorithm, which is based on the method of least squares non-negative matrix decomposition algorithm, the program implementation of the algorithm, and applied to the image Processing. The main tasks are as follows: First, summarized the traditional non-negative matrix factorization theory and its application. Second, the proposed non-negative matrix decomposition algorithm based on the method of least squares. Euclid distance metric non-negative matrix factorization approximation, to be translated into the least squares method for the optimization problem to some extent reduce the complexity. Two improved algorithms and gives the algorithm, the computing speed and accuracy of the algorithm to achieve varying degrees of improvement last examples are given to verify the effectiveness of this algorithm. Third, combined with a matrix of full rank decomposition theory, from the point of view of pure mathematical theory proposed decomposition algorithm based on the method of least squares non-negative matrix of full rank. To discuss the nature of the algorithm, citing the advantages and disadvantages of the algorithm, and accompanied by examples of verification. Fourth, the combination of the LINGO VC theory, the program implementation of the algorithm. The program by calling the VC, multiple cycles of operation, greatly improve processing speed. In the subsequent image processing applications to achieve a direct calls and image processing, quick and easy. Fifth, the least squares method based on the non-negative matrix decomposition algorithm used in image processing, including processing on a single three-dimensional graphics and a smaller resolution image processing. The study presents a new non-negative matrix least-squares method based on the decomposition decomposition algorithm, and applied image processing, use program fast cycle operation for further study of the non-negative matrix decomposition theory and its application to provide a reference.

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