# A system identification approach to clustering vector autoregressive time series

arXiv: https://arxiv.org/abs/2505.14421 · HTML: https://mlsanity.com/paper/2505.14421/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 50 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 3 of 3)

- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [Deep Temporal Clustering : Fully Unsupervised Learning of Time-Domain Features](https://mlsanity.com/paper/1802.01059/) (2018)
- [Clustering-Based Average State Observer Design for Large-Scale Network Systems](https://mlsanity.com/paper/2205.13633/) (2022)

## Abstract (arXiv)

Clustering of time series based on their underlying dynamics is keeping attracting researchers due to its impacts on assisting complex system modelling. Most current time series clustering methods handle only scalar time series, treat them as white noise, or rely on domain knowledge for high-quality feature construction, where the autocorrelation pattern/feature is mostly ignored. Instead of relying on heuristic feature/metric construction, the system identification approach allows treating vector time series clustering by explicitly considering their underlying autoregressive dynamics. We first derive a clustering algorithm based on a mixture autoregressive model. Unfortunately it turns out to have significant computational problems. We then derive a `small-noise' limiting version of the algorithm, which we call k-LMVAR (Limiting Mixture Vector AutoRegression), that is computationally manageable. We develop an associated BIC criterion for choosing the number of clusters and model order. The algorithm performs very well in comparative simulations and also scales well computationally.