The empirical covariance is with 1/N, that is a biased estimator of the covariance : E[co-var] = (n-1)/n*co-var.
That is why we often prefert to use a co-variance formula with 1/(N-1), that is an unbiased estimator of the co-variance E[co-var] = co-var.
Both formula can be use. One is empirical, the other as better statistical properties.
pca empirical covariance
hello,
I was wondering why in the empirical formula we don't have 1/N-1 instead of 1/N for covariances in the covariance matrix?
Thank you
1
The empirical covariance is with 1/N, that is a biased estimator of the covariance : E[co-var] = (n-1)/n*co-var.
That is why we often prefert to use a co-variance formula with 1/(N-1), that is an unbiased estimator of the co-variance E[co-var] = co-var.
Both formula can be use. One is empirical, the other as better statistical properties.
(I am not a teacher, it is my understanding)
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