NMF-matlab

Hello everyone , I meet you again , I'm your friend, Quan Jun .

matlab Practice the program （ Nonnegative matrix decomposition ）

　　 The algorithm is Lee and Seung stay 1999 Years published in nature In the magazine . See the specific paper here ：http://www.seas.upenn.edu/~ddlee/Papers/nmf.pdf.

　　 It doesn't matter if you don't understand English , You can see this introduction in Chinese ：http://wenku.baidu.com/view/94c8af0bf78a6529647d5331.html.

　　 The principle of the above two articles has been very clear , I'm introducing it according to my own understanding .

　　 Usually, matrix decomposition is as follows svd Or any other decomposition will decompose the matrix into positive and negative matrices , And his decomposition method completely decomposes the matrix into a matrix with only positive numbers , Because in the real world, such as images , Negative numbers are meaningless , So this decomposition method that only decomposes into positive matrix is very meaningful , Otherwise, it will not be sent in nature Such a cow B In my magazine .

　　 Here is the formula of decomposition ：

　　 here r Is the rank of the decomposition matrix ,V Is an approximation of the original matrix ,W And H Is the decomposition of two matrices .

　　 Here is W and H The way of seeking , It's an iterative algorithm , Initial W And H It's random ：

　　 About the code , I learned from this blog ：http://fxy1211.blog.163.com/blog/static/68255322007826111015905/, Thank you so much for this blogger .

　　 Here is the code ：

clear all; close all; clc; V=double(imread('lena.jpg')); imshow(mat2gray(V)); [i u]=size(V); % Calculation V Specifications  r=100; % Set the rank of the decomposition matrix  W=rand(i,r); % initialization WH, It's a nonnegative number  H=rand(r,u); maviter=100; % Maximum number of iterations  for iter=1:maviter W=W.*((V./(W*H))*H'); % Note that the three formulas here correspond to those in the text 
    W=W./(ones(i,1)*sum(W)); H=H.*(W'*(V./(W*H)));
end img_V=W*H; figure; imshow(mat2gray(img_V));

Copy

　　 The following is the original image and the reconstructed effect , If the number of rank sum iterations is greater , Then the reconstructed graph is closer to the original graph ：

Original picture

Reconstruction graph

Because this is based on my related direction. I happened to see this algorithm in the quotation of a paper , So I got a little understanding , There must be something wrong , be it so .

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