The Power-Oja method for decentralized subspace estimation/tracking

This work proposes a decentralized and adaptive subspace estimation method, called the Power-Oja (P-Oja) method. Existing decentralized subspace tracking algorithms have slow convergence rate or are unable to adapt to time varying statistics. To resolve these issues, the P-Oja method is developed by combining the power method with Oja's learning rule. Our key innovation lies on the design of a modified objective function with enhanced spectral gap property. This allows the P-Oja method to track the principal subspace more quickly with a finite number of samples. Interestingly, the resulting method coincides with the conventional Oja's learning rule in some special cases. To enable decentralized signal processing, we further demonstrate that the proposed method can be implemented by using a gossip algorithm. Our simulation results show that the proposed P-Oja outperforms the conventional Oja's method in terms of estimation accuracy, and the power method in terms of tracking performance. The effect of the communication graph on the tracking performance is also studied.