# Matrix Completion.m

### From Wikimization

(Difference between revisions)

(New page: == Matlab demonstration of the paper by Cai, Candès, & Shen, [http://arxiv.org/abs/0810.3286 A Singular Value Thresholding Algorithm for Matrix Completion, 2008]== <pre> %% Set path and g...) |
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- | == Matlab demonstration of | + | == Matlab demonstration of Cai, Candès, & Shen == |

+ | [http://arxiv.org/abs/0810.3286 A Singular Value Thresholding Algorithm for Matrix Completion, 2008] | ||

<pre> | <pre> | ||

%% Set path and global variables | %% Set path and global variables |

## Revision as of 16:42, 15 February 2009

## Matlab demonstration of Cai, Candès, & Shen

A Singular Value Thresholding Algorithm for Matrix Completion, 2008

%% Set path and global variables global SRB SRB = true; %% Setup a matrix randn('state',2008); rand('state',2008); n = 1000; r = 10; M = randn(n,r)*randn(r,n); df = r*(2*n-r); oversampling = 5; m = 5*df; Omega = randsample(n^2,m); data = M(Omega); %% Set parameters and solve p = m/n^2; delta = 1.2/p; maxiter = 500; tol = 1e-4; %% Approximate minimum nuclear norm solution by SVT algorithm tic [U,S,V,numiter] = SVT(n,Omega,data,delta,maxiter,tol); toc %% Show results X = U*S*V'; disp(sprintf('The relative error on Omega is: %d ', norm(data-X(Omega))/norm(data))) disp(sprintf('The relative recovery error is: %d ', norm(M-X,'fro')/norm(M,'fro'))) disp(sprintf('The relative recovery in the spectral norm is: %d ', norm(M-X)/norm(M)))