Ranked differences Pearson correlation dissimilarity with an application to electricity users time series clustering

TL;DR

This work introduces Ranked Differences Pearson correlation dissimilarity (RDPC), a time-series dissimilarity that interpolates between the Pearson dissimilarity and a weighted top-difference term (RankDiff). Integrated with hierarchical clustering, RDPC captures both magnitude-based and pattern-based similarities, showing superior performance on datasets with seasonal patterns, trends, and peaks. The authors derive RDPC's definition and key properties, demonstrate its superiority on synthetic groups with complex structures, and apply it to Thai electricity consumption data to reveal seven distinct user clusters. The study highlights RDPC's flexibility and potential applicability to diverse real-world time-series clustering tasks, with future directions including broader algorithmic integrations and additional parameters.

Abstract

Time series clustering is an unsupervised learning method for classifying time series data into groups with similar behavior. It is used in applications such as healthcare, finance, economics, energy, and climate science. Several time series clustering methods have been introduced and used for over four decades. Most of them focus on measuring either Euclidean distances or association dissimilarities between time series. In this work, we propose a new dissimilarity measure called ranked Pearson correlation dissimilarity (RDPC), which combines a weighted average of a specified fraction of the largest element-wise differences with the well-known Pearson correlation dissimilarity. It is incorporated into hierarchical clustering. The performance is evaluated and compared with existing clustering algorithms. The results show that the RDPC algorithm outperforms others in complicated cases involving different seasonal patterns, trends, and peaks. Finally, we demonstrate our method by clustering a random sample of customers from a Thai electricity consumption time series dataset into seven groups with unique characteristics.

Figures (8)

• Figure 1: Examples of PEA users' behaviors
• Figure 2: Dendrogram
• Figure 3: Elbow point
• Figure 4: DTW Alignment
• Figure 5: Artificial datasets

Theorems & Definitions (14)

• Definition 3.1
• Definition 3.2
• Remark 3.3
• Definition 3.4
• Proposition 3.5
• proof
• Proposition 3.6
• proof
• Proposition 3.7
• proof