In-Network Principal Component Analysis with Diffusion Strategies

Principal component analysis (PCA) is a very well-known statistical analysis technique. In its conventional formulation, it requires the eigen-decomposition of the sample covariance matrix. Due to its high-computational complexity and large memory requirements, the estimation of the covariance matrix and its eigen-decomposition do not scale up when dealing with big data, such as in large-scale networks. Numerous studies have been conducted to overcome this issue, often by partitioning the unknown matrix. In this paper, we propose a novel framework for estimating the principal axes, iteratively and in a distributed in-network scheme, without the need to estimate the covariance matrix. To this end, a coupling is operated between criteria for iterative PCA and several strategies for in-network processing. The investigated strategies can be grouped in two classes, noncooperative and cooperative such as information diffusion and consensus strategies. Theoretical results on the performance of these strategies are provided, as well as a convergence analysis. The performance of the proposed approach for in-network PCA is illustrated on diverse applications, such as image processing and time series in wireless sensor networks, with a comparison to state-of-the-art techniques.