Consensus-based distributed principal component analysis in wireless sensor networks

Principal component analysis is a powerful technique for data analysis and compression, with a wide range of potential applications in wireless sensor networks. However, its centralized implementation, with a fusion center collecting all the samples, is inefficient in terms of energy consumption, scalability, and fault tolerance. Previous distributed approaches reduce the communication cost, but not the lack of flexibility, as they require multi-hop communications if the network is not fully connected. We present two fully distributed consensus-based algorithms that are guaranteed to converge to the global results, using only local communications among neighbors, regardless of the data distribution or the sparsity of the network: CB-DPCA is based on finding the eigenvectors of local covariance matrices, while CB-EM-DPCA is a distributed version of the expectation maximization algorithm. Both offer a flexible trade-off between the tightness of the achieved approximation and the associated communication cost.