Natural power method for fast subspace tracking

Elaborates on a natural version of the power method for fast estimation and tracking of principal subspace or/and principal components of a vector sequence. The natural power method has the fastest convergence rate among a class of power-based methods such as the Oja method, the projection approximation subspace tracking (PAST) method, and the novel information criterion (NIC) method. Like the above three methods, the natural power method can also be implemented with only O(np) flops of computation at each iteration but maintain the fastest convergence rate, where n is the dimension of the vector sequence and p is the dimension of the principal subspace. Also like other power-based methods, the natural power method can be easily adopted for principal components tracking, constrained subspace tracking, and detection of the dimension of the principal subspace. In great contrast to non-power-based methods such as MALASE and OPERA, the natural power method is globally convergent.