Multivariate Time Series Imputation: An Approach Based on Dictionary Learning.

Area of Science:

• Machine Learning
• Time Series Analysis
• Data Science

Background:

• Dictionary learning (DL) represents data via sparse linear combinations.
• Learning both the dictionary and sparse representations from data is key.
• Multivariate time series imputation is a significant challenge.

Purpose of the Study:

• To apply dictionary learning for imputing missing data in multivariate time series.
• To introduce a structured dictionary approach for time series data.
• To develop dimensionality reduction techniques for high-dimensional time series.

Main Methods:

• Utilized a structured dictionary with individual and common blocks.
• Employed information theoretic criteria for selecting dictionary block size and sparsity.
• Optimized learning objective functions to minimize squared or absolute errors.
• Proposed dimensionality reduction for high-dimensional time series.

Main Results:

• Demonstrated DL's efficacy in multivariate time series imputation through extensive experiments.
• Evaluated performance across five real-life datasets with simulated missing data.
• Identified specific scenarios where DL-based methods show superiority over existing approaches.
• Assessed impact of missing data percentage and sequence length on imputation accuracy.

Conclusions:

• Dictionary learning offers a powerful framework for multivariate time series imputation.
• The proposed structured dictionary and dimensionality reduction techniques enhance imputation performance.
• Novel DL-based methods provide a competitive alternative to existing imputation strategies, particularly in challenging data conditions.