PCA and convex optimization

Soledad Villar (JHU) and I talked about bi-linear problems today, in the context of instrument calibration and computer vision. We looked at the kinds of optimizations that are involved in these problems. She showed me that, if you think of PCA as delivering a projection operator (that is, not the specific eigenvectors and amplitudes, but just the projection operator you would construct from those eigenvectors), that projection operator can be derived from a convex optimization in which the objective is purely mean squared error. That was news to me!