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

Christos Fragkathoulas, Eleni Psaroudaki, Themis Palpanas, Evaggelia Pitoura

TL;DR

GALACTIC is introduced, the first unified framework to bridge local and global counterfactual explainability for unsupervised time-series clustering, offering the first unified approach for interpreting clustered time-series through counterfactuals.

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.

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

TL;DR

GALACTIC is introduced, the first unified framework to bridge local and global counterfactual explainability for unsupervised time-series clustering, offering the first unified approach for interpreting clustered time-series through counterfactuals.

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 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.
Paper Structure (48 sections, 2 theorems, 16 equations, 7 figures, 6 tables, 4 algorithms)

This paper contains 48 sections, 2 theorems, 16 equations, 7 figures, 6 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Definition
  4. Preliminaries
  5. Probabilistic Surrogate of Cluster Assignments
  6. Local Counterfactual Explanations
  7. Desired properties for time-series clustering counterfactual explanations
  8. Global Counterfactual Explanations
  9. GALACTIC Framework
  10. Local Approach
  11. Segmentation and Subgrouping
  12. Importance-Guided Perturbation
  13. Gradient-Based Optimization
  14. Global Approach
  15. Candidate Generation
  16. ...and 33 more sections

Key Result

Proposition 1

For a source cluster $C_k$ and the finite set of candidate perturbations $\Delta_k$ for $C_k$, the set function $L(C_k, \mathbb S) = L(\mathbb S) + L(C_k \mid \mathbb S)$ is supermodular on $\Delta_k$. That is, for all $\mathbb A \subseteq \mathbb B \subseteq \Delta_k$ and all $\bm{\delta} \in \Delt

Figures (7)

  • Figure 1: Example of a Perturbation $\bm \delta$
  • Figure 2: Comparison of local explanations for a time-series generated under different importance weighting strategies.
  • Figure 3: Galactic-L Target Selection Analysis. Comparison of second possible and random policies across UCR datasets.
  • Figure 4: Importance Weighting Strategies Comparison. Points denote individual datasets; bars indicate dataset-wide averages and standard deviations for validity and sparsity.
  • Figure 5: Galactic-L Target Selection Analysis. Comparison of the second possible and the all random policies across the UCR datasets.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Proposition 1: Supermodularity of the MDL objective
  • Proposition 2: Submodularity of the MDL reduction