# Mode Clustering for Markov Jump Systems

arXiv: https://arxiv.org/abs/1910.02193 · HTML: https://mlsanity.com/paper/1910.02193/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2019.

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

- [Identification and Adaptive Control of Markov Jump Systems: Sample Complexity and Regret Bounds](https://mlsanity.com/paper/2111.07018/) (2021)
- [Detection and Evaluation of Clusters within Sequential Data](https://mlsanity.com/paper/2210.01679/) (2022)
- [System Identification via Nuclear Norm Regularization](https://mlsanity.com/paper/2203.16673/) (2022)
- [Mode Reduction for Markov Jump Systems](https://mlsanity.com/paper/2205.02697/) (2022)

## Abstract (arXiv)

In this work, we consider the problem of mode clustering in Markov jump models. This model class consists of multiple dynamical modes with a switching sequence that determines how the system switches between them over time. Under different active modes, the observations can have different characteristics. Given the observations only and without knowing the mode sequence, the goal is to cluster the modes based on their transition distributions in the Markov chain to find a reduced-rank Markov matrix that is embedded in the original Markov chain. Our approach involves mode sequence estimation, mode clustering and reduced-rank model estimation, where mode clustering is achieved by applying the singular value decomposition and k-means. We show that, under certain conditions, the clustering error can be bounded, and the reduced-rank Markov chain is a good approximation to the original Markov chain. Through simulations, we show the efficacy of our approach and the application of our approach to real world scenarios.