2
$\begingroup$

Doing PCA on a matrix using SVD yields a result of three matrices, expressed as:

$$ M = U \Sigma V^T $$

where $M$ is our initial data with zero mean.

If we want to make a plot of the two principle components we project the data onto principal component space.

$$ Z = M * V $$

and then use the two first columns of Z for our plot. Maybe I have already answered my own question, but I am struggling to understand if $Z$ is what would be called the Principle Component matrix, and if not, how do we find that?

Also, I am not sure what the operation $M*V$ does to the data. As I understand it, $V$ is an expression of the general trends of each of the attributes in the data set. By calculating the dot product between our data $M$ and the trends $V$ of the data, we end up with a matrix (PC matrix?) that captures the original data in a structured manner which allows for dimensionality reduction.

Are my assumptions correct, or have I misread the theory?

  • 2
    question is not very clear. What do you wanna learn exactly?2012-09-13
  • 0
    I apologize for the vagueness of my question, which probably reflects my vague understanding of the subject matter. I specifically wish to learn if what I calculate to be matrix Z contains the principal components of my PCA analysis. I.e. would column one of Z be the first principal component of my data matrix M?2012-09-13
  • 1
    You are right. Basically you obtain your principle components by multiplying it with the eigen matrices that you obtained after $SVD$ The most significant components after multiplication are called principle components.2012-09-13

1 Answers 1