Using Permutations for Hierarchical Clustering of Time Series.

Area of Science:

• Time Series Analysis
• Statistical Modeling
• Machine Learning

Background:

• Traditional time series similarity measures may not fully capture dependency structures.
• Hierarchical clustering is a powerful technique for grouping data, but its application to time series based on dependency requires specialized metrics.

Purpose of the Study:

• To develop and evaluate new permutation-based distance measures for quantifying time series similarity based on dependency strength.
• To integrate these distance measures into hierarchical clustering frameworks for effective time series grouping.
• To assess the performance of the proposed methods on both simulated and real-world data.

Main Methods:

• Utilized two permutation-based distance measures to quantify the similarity between time series, focusing on their dependency.
• Implemented hierarchical clustering by combining these distance measures with various linkage methods.
• Applied the clustering methods to simulated time series with linear and non-linear dependencies, as well as to real-world data series.

Main Results:

• The proposed distance measures and clustering methods yielded good results for simulated time series, accurately reflecting both linear and non-linear dependencies.
• Analysis indicated the influence of embedding dimension and linkage method on clustering outcomes.
• Successfully clustered several real-world data series, demonstrating the practical applicability of the approach.

Conclusions:

• Permutation-based distance measures are effective for clustering time series according to dependency strength.
• The developed hierarchical clustering methods offer a robust approach for analyzing complex time series data.
• The findings support the utility of these novel methods in various scientific domains involving time series analysis.