Compute covariance

compute_covariance.m

clc;
close all;

mm = []
E1 = []
E2 = []

for  m = 10:50:1000

  e1 = 0.0;
  e2 = 0.0;
  
  mm = [mm m];
  
  # averaging the error performance
  for a = 1:10
    n = 20;
    X = 3 * rand(m,n) - 1.5; 
    C1 = cov(X);
    
    # computing covariance feature by feature (column wise inner product)
    C2 = (1/m) * X' * X;

    # estimate covariance by computing covariance on each sample and then average
    C = zeros(n, n);
    for i = 1:m
      C += X(i,:)' * X(i, :);
    end

    C = (1/m) * C;

    e1 += (1/m*n) * sum(sum((C1 - C).^2, 1), 2);
    e2 += (1/m*n) * sum(sum((C2 - C1).^2, 1), 2);
  end
  
  E1 = [E1 e1/10];
  E2 = [E2 e2/10];
end

hold on;
semilogy(mm, E1, '-k');
semilogy(mm, E2, '-xr');
legend("sq err cov = avg cov per sample", "sq err cov = (1/m) * X' * X");
grid on;
hold off;