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

• DOI: 10.48550/arxiv.1905.09944
• Publication Date: 2019-01-01
• Authors: David G. Clark; Jesse A. Livezey; Kristofer E. Bouc...
• Keywords: Interpretability

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