# Fast online low-rank tensor subspace tracking by CP decomposition using recursive least squares from incomplete observations

arXiv: https://arxiv.org/abs/1709.10276 · HTML: https://mlsanity.com/paper/1709.10276/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2017.

## Built on by (most cited first, 4 of 4)

- [SubTrack++ : Gradient Subspace Tracking for Scalable LLM Training](https://mlsanity.com/paper/2502.01586/) (2025)
- [Geometrically Principled Randomized Optimization for Efficient LLM Training](https://mlsanity.com/paper/2510.01878/) (2025)
- [GOCPT: Generalized Online Canonical Polyadic Tensor Factorization and Completion](https://mlsanity.com/paper/2205.03749/) (2022)
- [A Spatio-Temporal Online Robust Tensor Recovery Approach for Streaming Traffic Data Imputation](https://mlsanity.com/paper/2511.01267/) (2025)

## Abstract (arXiv)

We consider the problem of online subspace tracking of a partially observed high-dimensional data stream corrupted by noise, where we assume that the data lie in a low-dimensional linear subspace. This problem is cast as an online low-rank tensor completion problem. We propose a novel online tensor subspace tracking algorithm based on the CANDECOMP/PARAFAC (CP) decomposition, dubbed OnLine Low-rank Subspace tracking by TEnsor CP Decomposition (OLSTEC). The proposed algorithm especially addresses the case in which the subspace of interest is dynamically time-varying. To this end, we build up our proposed algorithm exploiting the recursive least squares (RLS), which is the second-order gradient algorithm. Numerical evaluations on synthetic datasets and real-world datasets such as communication network traffic, environmental data, and surveillance videos, show that the proposed OLSTEC algorithm outperforms state-of-the-art online algorithms in terms of the convergence rate per iteration.