Learning Linear Dynamical Systems from Multivariate Time Series: A Matrix Factorization Based Framework.

Area of Science:

• Machine Learning
• Time Series Analysis
• Dynamical Systems

Background:

• Linear dynamical systems (LDS) are widely used in engineering and finance for time series modeling.
• Traditional LDS learning methods include Expectation-Maximization (EM) and spectral learning.
• Existing methods may lack flexibility in incorporating constraints and ensuring prediction stability.

Purpose of the Study:

• To propose a novel generalized linear dynamical system (gLDS) framework for learning from multivariate time series (MTS) data.
• To introduce a matrix factorization approach for gLDS, distinct from traditional algorithms.
• To develop a temporal smoothing regularization technique for enhanced model stability and prediction accuracy.

Main Methods:

• Developed a gLDS framework utilizing matrix factorization for MTS data.
• Each MTS sequence is factorized into a shared emission matrix and sequence-specific hidden state dynamics.
• Incorporated a novel temporal smoothing regularization for learning LDS models.

Main Results:

• gLDS learned LDS models demonstrated superior time series predictive performance compared to other algorithms.
• The framework effectively integrates constraints, enabling properties like stability and low-rankness.
• Temporal smoothing regularization led to more stable and accurate predictions in real-world MTS data.

Conclusions:

• The gLDS framework offers a flexible and powerful approach for multivariate time series analysis.
• Matrix factorization and temporal smoothing are key innovations for improved LDS modeling.
• The proposed methods show significant potential for applications requiring robust and accurate time series predictions.