Optimize feature normalization code

Question

Given a matrix X with an arbitrary number of columns and rows (Each row representing a feature of the dataset), I want to normalize each value to be ((value - column mean) / column standard deviation). I came up with the following code, which works. Can this be optimized for less computation or is this optimal?

mu = mean(X);
sigma = std(X);
x_ones = ones(size(X));
zero_mean_X = X - x_ones * diag(mu);
X_norm = zero_mean_X ./ (x_ones * diag(sigma));

score 2 · Accepted Answer · answered Jan 09 '16 at 21:06

2

Here is an optimization using bsxfun from Matlab

M = mean(X);
S = std(X);
Y = bsxfun(@minus,X, M);
Y = bsxfun(@rdivide, Y, S);

It is faster by 4 times

X = rand(1000);

t = zeros(100,2);
for ii = 1:100
    tic;
    M = mean(X);
    S = std(X);
    Y = bsxfun(@minus,X, M);
    Y = bsxfun(@rdivide, Y, S);
    t(ii,1) = toc;
end


for ii = 1:100
    tic;
    mu = mean(X);
    sigma = std(X);
    x_ones = ones(size(X));
    zero_mean_X = X - x_ones * diag(mu);
    X_norm = zero_mean_X ./ (x_ones * diag(sigma));
    t(ii,2) = toc;
end

figure('Color', 'w');
plot(t);
legend({'bsxfun', 'matrix'});
xlabel('NUmber of simulations');
ylabel('Time');

answered Jan 09 '16 at 21:06

marsei

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Perfect. Thank you. The speed testing is a nice bonus. Good tool to have. – Laizer Jan 09 '16 at 21:12
Wait before accepting the answer - some power users might join the party! – marsei Jan 09 '16 at 21:14
1

@marsei there's no better way to do it other than `bsxfun`. In fact the duplicate I've marked uses this as the best way to do it. – rayryeng Jan 09 '16 at 21:29

Optimize feature normalization code

1 Answers1