Estimating common principal components in high dimensions

We consider the problem of minimizing an objective function that depends on an orthonormal matrix. This situation is encountered, for example, when looking for common principal components. The Flury method is a popular approach but is not effective for higher dimensional problems. We obtain several simple majorization-minimization (MM) algorithms that provide solutions to this problem and are effective in higher dimensions. We use mixture model-based clustering applications to illustrate our MM algorithms. We then use simulated data to compare them with other approaches, with comparisons drawn with respect to convergence and computational time.