On-the-Fly Communication-and-Computing for Distributed Tensor Decomposition Over MIMO Channels

Distributed tensor decomposition (DTD) is a fundamental data-analytics technique that extracts latent important properties from high-dimensional multi-attribute datasets distributed over edge devices. Conventionally its wireless implementation follows a one-shot approach that first computes local results at devices using local data and then aggregates them to a server with communication-efficient techniques such as over-the-air computation (AirComp) for global computation. Such implementation is confronted with the issues of limited storage-and-computation capacities and link interruption, which motivates us to propose a framework of on-the-fly communication-and-computing (FlyCom${}^{2}$) in this work. The proposed framework enables streaming computation with low complexity by leveraging a random sketching technique and achieves progressive global aggregation through the integration of progressive uploading and multiple-input-multiple-output (MIMO) AirComp. To develop FlyCom${}^{2}$, an on-the-fly sub-space estimator is designed to take real-time sketches accumulated at the server to generate online estimates for the decomposition. Its performance is evaluated by deriving both deterministic and probabilistic error bounds using the perturbation theory and concentration of measure. Both results reveal that the decomposition error is inversely proportional to the population of sketching observations received by the server. To further rein in the noise effect on the error, we pro...
Source: IEEE Transactions on Signal Processing - Category: Biomedical Engineering Source Type: research