# Streaming Factor Trajectory Learning for Temporal Tensor Decomposition Source: [Streaming Factor Trajectory Learning for Temporal Tensor Decomposition]() Collection index: [llms.txt]() Data updated: 2026-01-04T04:38:51.835Z Authors: Shikai Fang, Xin Yu, Shibo Li, Zheng Wang, Robert Kirby, Shandian Zhe Published: 2023-10-25T21:58:52.000Z ## 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}. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Missing Value Prediction on FitRecord](): Missing value prediction; FitRecord; RMSE: 0.418. - [Missing Value Prediction on BeijingAir-2](): Missing value prediction; BeijingAir-2; RMSE: 0.288. - [Missing Value Prediction on BeijingAir 3](): Missing value prediction; BeijingAir 3; RMSE: 0.41. - [Missing Value Prediction on BeijingAir 2 (test)](): Missing value prediction; BeijingAir 2 (test); RMSE: 0.249. - [Missing Value Prediction on FitRecord (test)](): Missing value prediction; FitRecord (test); RMSE: 0.424. - [Missing Value Prediction on ServerRoom (test)](): Missing value prediction; ServerRoom (test); RMSE: 0.166. - [Missing Value Prediction on BeijingAir-3 (test)](): Missing value prediction; BeijingAir-3 (test); RMSE: 0.432. - [Missing Value Prediction on ServerRoom](): Missing value prediction; ServerRoom; RMSE: 0.178. ## Original sources and implementation [Original paper]() [PDF]() [Implementation]()