# Detection and Evaluation of Clusters within Sequential Data

arXiv: https://arxiv.org/abs/2210.01679 · HTML: https://mlsanity.com/paper/2210.01679/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 111 references that are in the map.
- First posted on arXiv 4 Oct 2022.

## Builds on (most cited first, 13 of 13)

- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Sequential Transfer in Multi-armed Bandit with Finite Set of Models](https://mlsanity.com/paper/1307.6887/) (2013)
- [Model Selection Techniques -- An Overview](https://mlsanity.com/paper/1810.09583/) (2018)
- [Achieving Optimal Misclassification Proportion in Stochastic Block Model](https://mlsanity.com/paper/1505.03772/) (2015)
- [Harnessing Structures for Value-Based Planning and Reinforcement Learning](https://mlsanity.com/paper/1909.12255/) (2019)
- [State Aggregation Learning from Markov Transition Data](https://mlsanity.com/paper/1811.02619/) (2018)
- [New Alignment Methods for Discriminative Book Summarization](https://mlsanity.com/paper/1305.1319/) (2013)
- [Spectral State Compression of Markov Processes](https://mlsanity.com/paper/1802.02920/) (2018)
- [Reinforcement Learning in Rich-Observation MDPs using Spectral Methods](https://mlsanity.com/paper/1611.03907/) (2016)
- [Learning Markov models via low-rank optimization](https://mlsanity.com/paper/1907.00113/) (2019)
- [Value function approximation via low-rank models](https://mlsanity.com/paper/1509.00061/) (2015)
- [Clustering time series under the Fr'echet distance](https://mlsanity.com/paper/1512.04349/) (2015)
- [Mode Clustering for Markov Jump Systems](https://mlsanity.com/paper/1910.02193/) (2019)

## Built on by (most cited first, 1 of 1)

- [Estimating the number of clusters of a Block Markov Chain](https://mlsanity.com/paper/2407.18287/) (2024)

## Abstract (arXiv)

Sequential data is ubiquitous -- it is routinely gathered to gain insights into complex processes such as behavioral, biological, or physical processes. Challengingly, such data not only has dependencies within the observed sequences, but the observations are also often high-dimensional, sparse, and noisy. These are all difficulties that obscure the inner workings of the complex process under study. One solution is to calculate a low-dimensional representation that describes (characteristics of) the complex process. This representation can then serve as a proxy to gain insight into the original process. However, uncovering such low-dimensional representation within sequential data is nontrivial due to the dependencies, and an algorithm specifically made for sequences is needed to guarantee estimator consistency. Fortunately, recent theoretical advancements on Block Markov Chains have resulted in new clustering algorithms that can provably do just this in synthetic sequential data. This paper presents a first field study of these new algorithms in real-world sequential data; a wide empirical study of clustering within a range of data sequences. We investigate broadly whether, when given sparse high-dimensional sequential data of real-life complex processes, useful low-dimensional representations can in fact be extracted using these algorithms. Concretely, we examine data sequences containing GPS coordinates describing animal movement, strands of human DNA, texts from English writing, and daily yields in a financial market. The low-dimensional representations we uncover are shown to not only successfully encode the sequential structure of the data, but also to enable gaining new insights into the underlying complex processes.