Randomized PCA Algorithms with Regret Bounds that are Logarithmic in the Dimension

We design an on-line algorithm for Principal Component Analysis. The instances are projected into a probabilistically chosen low dimensional subspace. The total expected quadratic approximation error equals the total quadratic approximation error of the best subspace chosen in hindsight plus some additional term that grows linearly in dimension of the subspace but logarithmically in the dimension of the instances.

Author: Manfred K. Warmuth, Department Of Computer Science, University Of California