  Due to the rapid growth of smart agents such as weakly connected
computational nodes and sensors, developing decentralized algorithms that can
perform computations on local agents becomes a major research direction. This
paper considers the problem of decentralized Principal components analysis
(PCA), which is a statistical method widely used for data analysis. We
introduce a technique called subspace tracking to reduce the communication
cost, and apply it to power iterations. This leads to a decentralized PCA
algorithm called \texttt{DeEPCA}, which has a convergence rate similar to that
of the centralized PCA, while achieving the best communication complexity among
existing decentralized PCA algorithms. \texttt{DeEPCA} is the first
decentralized PCA algorithm with the number of communication rounds for each
power iteration independent of target precision. Compared to existing
algorithms, the proposed method is easier to tune in practice, with an improved
overall communication cost. Our experiments validate the advantages of
\texttt{DeEPCA} empirically.
