Can I use the eigenvectors values as columns weight for a machine learning model?

1
votes

The output of PCA are the eigenvectors and eigenvalues of the covariance (or correlation) matrix of the original data. Let's say the are $x_1,...,x_n$ columns, then, there are $z_1,...,z_n$ eigenvalues and $\tilde{z_1},...,\tilde{z_n}$ eigenvectors. My question are:

  • can I use the value $\tilde{z_1}^{(1)},...,\tilde{z_1}^{(n)}$ of the first (or also the other) eigenvector as weight of my model? for example as the weight of the columns $x_1,...,x_n$, a kind of Unsupervised method.
  • I understand the weight $\tilde{z_1}^{(1)},...,\tilde{z_1}^{(n)}$ as the contribution value of every column. Is it correct?
  • Can I use Spearman or Kendall correlation instead of covariance? Is it going to change the results?

I know that is it not a conventional way to use PCA but I would like to know if it makes sense.

1
machine-learningpca
ok, but I cannot really figure out, what this weight means. For example if I use kendall correlation, what the weight $\phi^{(1)}_1,...,\phi^{(n)}_1$ means?if the weight of an element is bigger the respective column is more important? and if I take $\phi^{(1)}_n,...,\phi^{(n)}_n$ the eigenvector of the smallest eigenvalue, what it is represent? - Andrea Madotto

1 Answers

0
votes

First of all, you can do whatever you want my friend. It's your model and you can use it in the way you want.

However, I wouldn't do that. PCA is a way to reduce dimensionality, you lose data to train your model faster. PCA can be seen as if you reduce a sphere of 3 dimensions to a circle of 2 dimensions. In some situations it can be useful.

With the output of PCA you can train your model and see what you get. However, have you tried to train your model without PCA? Maybe you don't need it and you are losing information that would improve your model