An Innovative Method of Singular Spectrum Analysis to Conduct Gap-filling and Denoising on Time Series Data

Area of Science:

• Biomedical Engineering
• Data Science
• Signal Processing

Background:

• Wearable devices generate time series data (e.g., heart rate) valuable for health monitoring.
• Missing data segments in time series, common in wearable data, compromise analysis validity.
• Existing Singular Spectrum Analysis (SSA) methods for gap-filling require pre-specified parameters, limiting their application.

Purpose of the Study:

• To propose an innovative iterative procedure for filling gaps in time series data.
• To overcome limitations of traditional Singular Spectrum Analysis (SSA) by eliminating the need for pre-specifying window length and number of groups.
• To enhance the accuracy and reliability of time series data analysis, particularly for physiological signals.

Main Methods:

• Developed an iterative gap-filling procedure leveraging Singular Spectrum Analysis (SSA).
• The method incorporates an initialization step using a large window length and initial singular values to prevent convergence issues.
• Employs iterative singular value decomposition for imputation, adaptable for gap-filling and denoising.

Main Results:

• The proposed method consistently achieved lower reconstruction and gap-filling errors compared to traditional SSA-based approaches.
• Simulation results indicated that optimal performance is independent of pre-specified parameters like window length and group number.
• Demonstrated that long window lengths, often recommended, may not be suitable for variable-frequency time series like heart rate data.

Conclusions:

• The novel iterative SSA-based method offers a robust solution for handling missing data in time series.
• The approach provides flexibility for researchers, enabling standalone gap-filling or combined gap-filling and denoising.
• This widens the applicability of SSA for analyzing complex time series data, including physiological signals from wearable devices.