Details

Given n feature vectors x₁= (x₁₁,…,x_1p), ..., x_n= (x_n1,…,x_np) of dimension p or a p x p correlation matrix Cor, the problem is to compute the principal components for the data set. The library returns the transformation matrix T, which contains eigenvectors in the row-major order and a vector of corresponding eigenvalues. You can use the results to choose the new dimension d < p and apply the transformation T_d: x_i -> y_i to the original data set according to the rule y_i = T_dx_i^T, where the matrix T_d is the submatrix of T that contains d eigenvectors corresponding to the d largest eigenvalues.

You can provide these types of input data to the PCA algorithms of the library:

• Original, non-normalized data set

• Normalized data set, where each feature has the zero mean and unit variance

• Correlation matrix