Equivalence partition based morphological similarity clustering for large-scale time series

Area of Science:

• Data Science
• Machine Learning
• Dynamic Systems

Background:

• Unsupervised learning, specifically data clustering, is vital for dynamic systems and big data analysis.
• Clustering sampled time-series data presents significant challenges compared to repeatable sampling data.
• Existing time-series clustering methods often lack theoretical rigor and efficiency for large datasets.

Purpose of the Study:

• To establish a robust mathematical theory for large-scale time-series clustering in dynamic systems.
• To address the limitations of current methods in terms of theoretical foundation and computational efficiency.
• To introduce a novel clustering approach for complex time-series data.

Main Methods:

• Proposed the concept of time-series morphological isomorphism.
• Proved translation and stretching isomorphism as equivalent relations.
• Developed a morphological similarity measure calculation method.
• Established a new clustering method based on equivalent partition and morphological similarity.

Main Results:

• Demonstrated the equivalence of translation and stretching isomorphism.
• Introduced a practical method for calculating morphological similarity.
• Developed an effective time-series clustering algorithm for large datasets.
• Validated the approach through simulations on typical applications.

Conclusions:

• The proposed mathematical theory and clustering method offer a new foundation for large-scale time-series analysis.
• The method provides enhanced validity and practicability for clustering dynamic system time-series data.
• This work advances the field of unsupervised learning for complex, large-scale time-series datasets.