Decentralized Eigendecomposition for Online Learning over Graphs

We address the problem of decentralized eigenvalue decomposition of a general symmetric matrix that is important, e.g., in Principal Component Analysis. The proposed algorithm only uses local interactions among neighboring agents and is based on the representation of the matrix as a recursive update of rank-one components. This makes the algorithm attractive for online eigenvalue and eigenvector tracking applications. We study the performance of the proposed algorithm in two important application examples: First, we consider the online eigendecomposition of a sample covariance matrix over the network. Then, we investigate the online computation of the spectra of the graph Laplacian that is important in, e.g., graph Fourier analysis and graph-dependent filter design. Simulation results reveal that the proposed algorithm outperforms existing decentralized algorithms both in terms of estimation accuracy as well as communication cost.