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This study introduces a new geometric view of Singular Spectrum Analysis (SSA) for time series noise reduction. The novel sequential approach improves accuracy and adaptability for complex data like heart rate monitoring.

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Area of Science:

  • Time Series Analysis
  • Signal Processing
  • Data Science

Background:

  • Singular Spectrum Analysis (SSA) is widely used but its complex mechanism for time series reconstruction and noise elimination is not well understood.
  • Conventional SSA relies on fixed parameters like window length and group thresholds, limiting its application to certain data types.

Purpose of the Study:

  • To provide a novel geometric perspective for elucidating the underlying mechanism of SSA.
  • To propose a sequential reconstruction approach that overcomes limitations of conventional SSA.
  • To enhance SSA's applicability to time series with varying structures.

Main Methods:

  • Developed a sequential reconstruction approach for SSA, averaging reconstructions from various window lengths.
  • Implemented a stopping rule based on a symmetric test to determine the number of groups.
  • Validated the method through simulations and analysis of real-world 7-day heart rate data.

Main Results:

  • The proposed method requires no prior knowledge of window length or group number.
  • Achieved smaller root mean square error (RMSE) values compared to conventional SSA.
  • Successfully revealed local features and sudden changes in heart rate data, indicating event-related patterns.

Conclusions:

  • The novel geometric perspective clarifies SSA's reconstruction and noise elimination processes.
  • The sequential SSA approach offers improved accuracy and adaptability over conventional methods.
  • This enhanced SSA is particularly suitable for dynamic time series data, such as smartwatch heart rate monitoring, expanding its application scope.