Streaming Factor Trajectory Learning for Temporal Tensor Decomposition

TL;DR

This paper introduces Streaming Factor Trajectory Learning (SFTL), a novel method using Gaussian processes and state-space models for capturing the temporal evolution of tensor data in streaming scenarios, enabling efficient online updates.

Contribution

The paper proposes a new streaming tensor decomposition approach that models factor trajectories with Gaussian processes converted into state-space models for efficient online estimation.

Findings

Effective in synthetic and real-world data

Enables parallel computation of factor trajectories

Outperforms existing methods in capturing temporal evolution

Abstract

Practical tensor data is often along with time information. Most existing temporal decomposition approaches estimate a set of fixed factors for the objects in each tensor mode, and hence cannot capture the temporal evolution of the objects' representation. More important, we lack an effective approach to capture such evolution from streaming data, which is common in real-world applications. To address these issues, we propose Streaming Factor Trajectory Learning for temporal tensor decomposition. We use Gaussian processes (GPs) to model the trajectory of factors so as to flexibly estimate their temporal evolution. To address the computational challenges in handling streaming data, we convert the GPs into a state-space prior by constructing an equivalent stochastic differential equation (SDE). We develop an efficient online filtering algorithm to estimate a decoupled running posterior of the involved factor states upon receiving new data. The decoupled estimation enables us to conduct standard Rauch-Tung-Striebel smoothing to compute the full posterior of all the trajectories in parallel, without the need for revisiting any previous data. We have shown the advantage of SFTL in both synthetic tasks and real-world applications. The code is available at {https://github.com/xuangu-fang/Streaming-Factor-Trajectory-Learning}.