Principle Component Analysis (PCA)

Given L data points in R^n (z_l, l=1,2,...,L), the problem is to find an n-m dimensional hyperplane that best represents the data points. Mathematically, the problem is to find an mxn matrix A whose rows are orthonormal to each other and an n vector a that minimizes sum_l || A(z_l - a) ||^2.
The following model is a robust version of the PCA model. That is, it minimizes the sum of the Euclidean distances rather than the sum of their squares.