Unsupervised Discovery of Temporal Structure in Noisy Data with Dynamical Components Analysis
This addresses the challenge of unsupervised temporal structure discovery in noisy data for researchers and practitioners in fields like time series analysis, offering a linear, interpretable method with computational efficiency.
The authors tackled the problem of extracting meaningful dynamics from noisy, high-dimensional time series data, where existing linear methods often fail, by introducing Dynamical Components Analysis (DCA), which robustly discovers subspaces with maximal predictive information and outperforms other linear methods in extracting dynamical structure.
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.