Principal Component Analysis

Principal Component Analysis is a statistical procedure of reducing dimensionality of data by orthogonal Transformation. It converts correlated data into set of linearly uncorrelated variables called Principal Components.

Step for finding Principal Components

1. Generate Random data using any distribution.
2. Calculate of that data.
3. Calculate shift in mean of data or Estimate mean(mu hat)
4. Generate Covariance Matrix either with Expectation or using Properties of positive semi-definite.
5. Calculate EigenVectors of Covariance Matrix
6. Compute the bigger eigen value and the vector corresponding to that value is the 1st Principal Component vector.
   1. 2nd Bigger Eigen value corresponds to 2nd EigenVector and they are perpendicular.