多维矩阵的小数值和大数值的梯度下降

Question

I have a matrix R which I want to estimate using gradient descent method. The code is working good for small dimension matrix (eg 100x1) but it gives NaN values as I increase dimension (eg 10x3). Please help!

R =[196,242,3;186,302,3;22,377,1;244,51,2;166,346,1;298,474,4;115,265,2;253,465,5;305,451,3;6,86,3];
N = length(R);
M = size(R,2);
K = 3;

P = rand(N,K);
Q = rand(M,K);
alpha = 0.002;
beta = 0.02;


for iter = 1 : 5000
e = R - P*Q';
P_new = P + 2*alpha*(e*Q-beta*P);
Q_new= Q + 2*alpha*(e'*P-beta*Q);
mse2(iter) = norm(R - P*Q')/norm(R); 

P=P_new;
Q=Q_new;
end

R_est = P*Q';

Answer 1

Your problem lies in the for loop. The largest double matlab can store is 1.7977e+308 , after 7 runs of the loop your values for P and Q are on the order of 10^101 and after 8 runs inf . I'm not sure what you mean by estimate matrix but your nan values are coming from the way P an Q grow so rapidly. One other things of note, the mse2 variable is not to used. What is its purpose?