Efficient matrix profile computation with Euclidean distance using Eigen transformation: Performance evaluation based...

Area of Science:

• Computational data science
• Time series analysis
• Biomedical signal processing

Background:

• Matrix profile is key for time series pattern discovery.
• Existing methods use normalized Euclidean distance, unsuitable for some data.
• Beat-to-beat interval (BBI) data from smartwatches requires Euclidean distance for heart rate analysis.

Purpose of the Study:

• To develop an efficient matrix profile computation method using Euclidean distance for long time series.
• To address computational challenges of Euclidean distance in matrix profile algorithms.
• To enable better analysis of physiological data, such as e-cigarette user heart rate patterns.

Main Methods:

• Proposed a novel methodology for Euclidean distance-based matrix profile computation.
• Key steps include eigenspace projection, enhanced Singular Value Decomposition (SVD), an early abandon strategy, and lower bound determination using the first left singular vector.
• Validated through simulation studies using BBI data.

Main Results:

• Achieved significant reductions in computational time, from one-fourth to one-twentieth of conventional methods.
• Demonstrated consistent performance across various time series and query sequence lengths.
• Outperformed conventional methods, which degrade sharply with increased data length.

Conclusions:

• The proposed methodology offers a computationally efficient solution for matrix profile analysis with Euclidean distance.
• This advancement is particularly beneficial for analyzing long time series data, such as physiological signals from wearable devices.
• Enables more effective monitoring and analysis of heart rate variability and other patterns in health applications.