# Unsupervised Discovery of Temporal Structure in Noisy Data with Dynamical Components Analysis

arXiv: https://arxiv.org/abs/1905.09944 · HTML: https://mlsanity.com/paper/1905.09944/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2019.

## Built on by (most cited first, 6 of 6)

- [Multifactor Sequential Disentanglement via Structured Koopman Autoencoders](https://mlsanity.com/paper/2303.17264/) (2023)
- [TLDR: Twin Learning for Dimensionality Reduction](https://mlsanity.com/paper/2110.09455/) (2021)
- [Recurrences reveal shared causal drivers of complex time series](https://mlsanity.com/paper/2301.13516/) (2023)
- [Compressed Predictive Information Coding](https://mlsanity.com/paper/2203.02051/) (2022)
- [Information Subtraction: Learning Representations for Conditional Entropy](https://mlsanity.com/paper/2501.02012/) (2025)
- [Inference of hidden common driver dynamics by anisotropic self-organizing neural networks](https://mlsanity.com/paper/2504.01811/) (2025)

## Abstract (arXiv)

Linear dimensionality reduction methods are commonly used to extract low-dimensional structure from high-dimensional data. However, popular methods disregard temporal structure, rendering them prone to extracting noise rather than meaningful dynamics when applied to time series data. At the same time, many successful unsupervised learning methods for temporal, sequential and spatial data extract features which are predictive of their surrounding context. Combining these approaches, we introduce Dynamical Components Analysis (DCA), a linear dimensionality reduction method which discovers a subspace of high-dimensional time series data with maximal predictive information, defined as the mutual information between the past and future. We test DCA on synthetic examples and demonstrate its superior ability to extract dynamical structure compared to commonly used linear methods. We also apply DCA to several real-world datasets, showing that the dimensions extracted by DCA are more useful than those extracted by other methods for predicting future states and decoding auxiliary variables. Overall, DCA robustly extracts dynamical structure in noisy, high-dimensional data while retaining the computational efficiency and geometric interpretability of linear dimensionality reduction methods.