A novel recursive least-squares adaptive method for streaming tensor-train decomposition with incomplete observations

Tensor tracking which is referred to as online (adaptive) decomposition of streaming tensors has recently gained much attention in the signal processing community due to the fact that many modern applications generate a huge number of multidimensional data streams over time. In this paper, we propose an effective tensor tracking method via the tensor-train format for decomposing high-order incomplete streaming tensors. On the arrival of new data, the proposed algorithm minimizes a weighted least-squares objective function accounting for both missing values and time-variation constraints on the underlying tensor-train cores, thanks to the recursive least-squares filtering technique and the block coordinate descent framework. Our algorithm is fully capable of tensor tracking from noisy, incomplete, and high-dimensional observations in both static and time-varying environments. Its tracking ability is validated with several experiments on both synthetic and real data.