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Assuming a big number of data points, with 3 features each. Let's assume 20,000 data points. I was trying to calculate eigen vectors and values, and I followed this algorithm in 3 steps [1], basically my steps are:

  • calculate the mean vector for the 3 features x,y and z
  • calculate covariance matrix, it will be of size 3 x 3
  • calculate eigen vectors and values. There will be 3 eigen vectors of size 3 and 3 eigen values.
  • other steps for projecting, etc.

Is it right to obtain only a 3 x 3 projection matrix for such a large sample of data, or I should calculate in chunks of 1000 data points for example and obtain more eigen vectors, like 20 sets? The purpose is plotting the eigenvectors to see a variation... At the moment I can't see what is the effect of having only 3 eigenvectors vs. more of them for subsets of data.

[1] http://sebastianraschka.com/Articles/2015_pca_in_3_steps.html

Thanks

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1 Answer 1

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Your original feature space spans three dimensions. PCA rotates that space so the first component has maximum variance, and so on. The resulting space is three dimensional as well in your case, so it's right.

But having abundant data is also good, so you have a good estimate of the covariance/correlation matrix.

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