$k$-Graph: A Graph Embedding for Interpretable Time Series Clustering

Time series clustering poses a significant challenge with diverse applications across domains. A prominent drawback of existing solutions lies in their limited interpretability, often confined to presenting users with centroids. In addressing this gap, our work presents <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-Graph, an unsupervised method explicitly crafted to augment interpretability in time series clustering. Leveraging a graph representation of time series subsequences, <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-Graph constructs multiple graph representations based on different subsequence lengths. This feature accommodates variable-length time series without requiring users to predetermine subsequence lengths. Our experimental results reveal that <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-Graph outperforms current state-of-the-art time series clustering algorithms in accuracy, while providing users with meaningful explanations and interpretations of the clustering outcomes.