Fast technique for normalizing a matrix in MATLAB

I want to normalise each column of a matrix in Matlab. I have tried two implementations:

Option A:

mx=max(x);
mn=min(x);
mmd=mx-mn;
for i=1:size(x,1)
    xn(i,:)=((x(i,:)-mn+(mmd==0))./(mmd+(mmd==0)*2))*2-1; 
end

Option B:

mn=mean(x);
sdx=std(x);
for i=1:size(x,1)
    xn(i,:)=(x(i,:)-mn)./(sdx+(sdx==0));
end

However, these options take too much time for my data, e.g. 3-4 seconds on a 5000x53 mat开发者_如何学编程rix. Thus, is there any better solution?

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Use bsxfun instead of the loop. This may be a bit faster; however, it may also use more memory (which may be an issue in your case; if you're paging, everything'll be really slow).

To normalize with mean and std, you'd write

mn = mean(x);
sd = std(x);
sd(sd==0) = 1;

xn = bsxfun(@minus,x,mn);
xn = bsxfun(@rdivide,xn,sd);

---

Remember, in MATLAB, vectorizing = speed.

If A is an M x N matrix,

A = rand(m,n);
minA = repmat(min(A), [size(A, 1), 1]);
normA = max(A) - min(A);               % this is a vector
normA = repmat(normA, [length(normA) 1]);  % this makes it a matrix
                                       % of the same size as A
normalizedA = (A - minA)./normA;  % your normalized matrix

---

Note: I am not providing a freshly new answer, but I am comparing the proposed answers.

Option A: Using bsxfun()

function xn = normalizeBsxfun(x)

    mn = mean(x);
    sd = std(x);
    sd(sd==0) = eps;

    xn = bsxfun(@minus,x,mn);
    xn = bsxfun(@rdivide,xn,sd);

end

Option B: Using a for-loop

function xn = normalizeLoop(x)

    xn = zeros(size(x));

    for ii=1:size(x,2)
        xaux = x(:,ii);
        xn(:,ii) = (xaux - mean(xaux))./mean(xaux);
    end

end

We compare both implementations for different matrix sizes:

expList = 2:0.5:5;
for ii=1:numel(expList)
    expNum = round(10^expList(ii));
    x = rand(expNum,expNum); 
    tic;
    xn = normalizeBsxfun(x);
    ts(ii) = toc; 
    tic;
    xn = normalizeLoop(x);
    tl(ii) = toc; 
end

figure;
hold on;
plot(round(10.^expList),ts,'b');
plot(round(10.^expList),tl,'r');
legend('bsxfun','loop');
set(gca,'YScale','log') 

The results show that for small matrices, the bsxfun is faster. But, the difference is neglect able for higher dimensions, as it was also found in other post.

The x-axis is the squared root number of matrix elements, while the y-axis is the computation time in seconds.

---

Let X be a m x n matrix and you want to normalize column wise.

The following matlab code does it

XMean = repmat(mean(X),m,1);
XStd = repmat(std(X),m,1);
X_norm = (X - XMean)./(XStd);

The element wise ./ operator is explained here: http://www.mathworks.in/help/matlab/ref/arithmeticoperators.html

Note: As op mentioned, this is simply a faster solution and performs the same task as looping through the matrix. The underlying implementation of this inbuilt function makes it work faster

---

Note: This code works in Octave and MATLAB versions R2016b or higher.

function X_norm = normalizeMatrix(X)      
      mu = mean(X); %mean    
      sigma = std(X); %standard deviation   
      X_norm = (X - mu)./sigma;    
end

---

How about using

normc(X)

that would normalize the matrix X columnwise. You need to include the Neural Network Toolbox in your install though.

---

How about this?

A = [7, 2, 6; 3, 8, 4]; % a 2x3 matrix

Asum = sum(A); % sum the columns

Anorm = A./Asum(ones(size(A, 1), 1), :); % normalise the columns