In section 84 we used perturbation theory to derive the

Question

Principal-Components Analysis: Constrained-Optimization Approach

In Section 8.4, we used perturbation theory to derive the PCA.In this problem we address this same issue from the perspective of a constrained-optimization approach.

Let x denote an m-dimensional zero-mean data vector and w denote an adjustable parameter vector of the same dimension m.

Let σ² denote the variance of the projection of the data vector x onto the parameter vector w.