## 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 *m*x*n* 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.