GALACTIC: Global and Local Agnostic Counterfactuals for Time-series Clustering

2026-03-05

AI Summary

Existing time series clustering methods lack interpretability regarding dynamic transitions across cluster boundaries. This work proposes GALACTIC, the first unified framework that integrates counterfactual explanations into unsupervised time series clustering. At the local level, GALACTIC generates minimal-perturbation counterfactuals through cluster-aware optimization; at the global level, it extracts non-redundant, representative explanations based on the Minimum Description Length (MDL) principle to characterize inter-cluster transitions. We formulate a submodular MDL objective and develop an efficient greedy algorithm with theoretical approximation guarantees. Experiments on UCR datasets demonstrate that GALACTIC significantly outperforms baseline methods, producing sparser local counterfactuals and more concise global explanation summaries.

Technology Category

• Machine Learning: Clustering
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Time-series clustering is a fundamental tool for pattern discovery, yet existing explainability methods, primarily based on feature attribution or metadata, fail to identify the transitions that move an instance across cluster boundaries. While Counterfactual Explanations (CEs) identify the minimal temporal perturbations required to alter the prediction of a model, they have been mostly confined to supervised settings. This paper introduces GALACTIC, the first unified framework to bridge local and global counterfactual explainability for unsupervised time-series clustering. At instance level (local), GALACTIC generates perturbations via a cluster-aware optimization objective that respects the target and underlying cluster assignments. At cluster level (global), to mitigate cognitive load and enhance interpretability, we formulate a representative CE selection problem. We propose a Minimum Description Length (MDL) objective to extract a non-redundant summary of global explanations that characterize the transitions between clusters. We prove that our MDL objective is supermodular, which allows the corresponding MDL reduction to be framed as a monotone submodular set function. This enables an efficient greedy selection algorithm with provable $(1-1/e)$ approximation guarantees. Extensive experimental evaluation on the UCR Archive demonstrates that GALACTIC produces significantly sparser local CEs and more concise global summaries than state-of-the-art baselines adapted for our problem, offering the first unified approach for interpreting clustered time-series through counterfactuals.

Problem

• time-series clustering
• counterfactual explanations
• unsupervised learning
• explainability
• cluster transitions

Innovation

• Counterfactual Explanations
• Time-series Clustering
• Minimum Description Length
• Submodular Optimization
• Unsupervised Explainability