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Nonnegative Matrix Factorization with Sparseness Constraint

Author: ZhangYuFei
Tutor: ChengMingSong
School: Dalian University of Technology
Course: Computational Mathematics
Keywords: Non - negative matrix factorization The steepest descent method Auxiliary function Sparsity Constraint KKT conditions Image storage
CLC: O151.21
Type: Master's thesis
Year: 2010
Downloads: 207
Quote: 1
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Abstract


Non- negative matrix factorization (Nonnegative Matrix Factorization, NMF) is a matrix decomposition method recently proposed international . Compared with other matrix factorization , NMF special about its by the introduction of non- negative constraint matrix decomposition process , this constraint original data will be based on the part of the representation , in order to better reflect the local features of the original data . Due to a large number of experimental data in the real world are non- negative expression , which makes the presence of a wide range of applications , such as blind source separation and non negative signal analysis , pattern recognition , text knowledge mining , digital image watermark as well as facial expression recognition [16 - 21] and other fields . Depending on the application , the decomposition of the matrix elements can have different interpretations . For example , the method described by Lee and Seung [ '] is to face image decomposed into portions ( such as the lips , eyes , nose , ears, etc. ). The first part of this paper describes the background of non- negative matrix factorization , the description of the problem , and Research , NMF problem there described the shortcomings and difficulties . The second part first introduced this article related to prior knowledge , the next listed some of the NMF algorithm , and its details , making you a more in-depth understanding of the NMF method . The third part of the core of this article : plus the sparse constraint of non- negative matrix decomposition algorithm , the algorithm is an improvement of the previous NMF algorithm . NMF 's purpose is to the original non- negative matrix V ∈ Rm × n decomposed into the product of the new non - negative matrix W ∈ Rm × r and H ∈ Rr x n : V ≈ WH , wherein r satisfies : ( Mn ) r lt ; Mn and the decomposition error as small as possible . Our goal is to ensure on the basis of the non - negative constraint conditions and the decomposition of accuracy by sparse constraint conditions on the increase in the objective function , obtained in the decomposition matrix as sparse as possible , to save storage space more . The fourth part is the numerical experiments , the use of numerical examples to verify the effectiveness of the correctness of the conclusions in the paper as well as solving methods , and by different methods to verify the algorithm does have a fast convergence rate and good sparsity .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Theory of algebraic equations,linear algebra > Linear Algebra > Matrix theory
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