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

Christos Fragkathoulas; Eleni Psaroudaki; Themis Palpanas; Evaggelia Pitoura

cs.LGMar 5, 2026

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

Authors: Christos Fragkathoulas, Eleni Psaroudaki, Themis Palpanas, Evaggelia Pitoura

Organizations: University of Ioannina Ioannina, Greece · Archimedes, Athena Research Center Athens, Greece · Université Paris Cité, LIPADE, F-75006 Paris, France

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.

Figures & tables

Figure 1. Example of a Perturbation

\bm{\delta}

Panel of Figure 2 — Figure 2. Comparison of local explanations for a time-series generated under different importance weighting strategies.

Panel of Figure 3 — Figure 3. Galactic-L Target Selection Analysis. Comparison of second possible and random policies across UCR datasets.

Panel of Figure 4 — Figure 4. Importance Weighting Strategies Comparison. Points denote individual datasets; bars indicate dataset-wide averages and standard deviations for validity and sparsity.

Dataset	KNN					TSEvo					Glacier-L					Glacier-G					Galactic-L
Dataset	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT
ACSF1	100	0.08	24.82	1460	0.15	100	0.09	24.82	1460	405.54	28.33	0.01	21.88	1460	9.69	26.67	0.01	21.94	1459.94	9.95	98.33	0.03	7.75	892.08	22.12
ArrowHead	100	0.1	35.79	251	0.17	100	0.09	35.79	251	385.22	36.51	0	34.22	251	11.06	52.38	0.01	33.73	251	18.27	98.41	0.02	9.47	131.39	11.21
Car	100	0.12	27.61	577	0.07	100	0.17	27.61	577	240.77	69.44	0.01	27.44	577	12.04	88.89	0.01	27.25	576.97	15.22	100	0.03	7.36	318.06	5.13
CBF	100	0.16	26.49	128	1.34	100	0.19	26.49	128	1751.15	0.36	0.02	28	128	0.64	0.36	0.02	28	128	0.63	76.7	0.09	8.55	53.03	158.08
Coffee	100	0.24	14.76	286	0.05	100	0.21	14.76	286	105.57	29.41	0.06	15.6	286	3.14	58.82	0.06	15.3	286	5.99	94.12	0.18	4	119.75	4.82

Table 1. Local Performance Benchmarking. Comparative analysis of Galactic-L against kNN , TSEvo , and Glacier variants across effectiveness, average flipping cost, average segments changed, average timesteps changed, and runtime. The null indicator “-” is assigned throughout the metrics where the corresponding effectiveness is zero. Results for additional datasets can be found in Appendix Table 5 .

Dataset	Optimal					Greedy					Hierarchical					Hierarchical Greedy					GLOBE-CE ∗					Glacier-G ∗
	Galactic-G																				Competitors
	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT
ACSF1	62.8	0.031	3.7	813	4.17	62.8	0.021	3.7	812	0.66	37.6	0.010	3.4	591	1.49	37.6	0.009	3.2	581	0.89	21.2	0.006	4.0	730	60.93	31.2	0.006	5.4	1022	0.01
ArrowHead	75.9	0.021	5.0	102	49.55	75.9	0.019	4.7	102	5.34	72.0	0.021	4.9	97	3.34	72.0	0.019	4.6	102	2.80	54.6	0.088	9.4	251	35.57	20.2	0.006	7.9	167	10.30
Car	70.8	0.024	4.8	350	106.68	70.8	0.023	4.8	361	3.18	55.2	0.015	4.4	282	3.24	58.6	0.015	4.2	280	2.41	74.2	0.056	6.7	433	32.16	33.4	0.008	8.8	577	0.00
CBF	39.4	0.105	3.3	47	36.93	39.4	0.105	3.3	47	10.21	33.7	0.098	3.3	51	1.57	33.7	0.094	3.3	51	1.65	26.0	0.186	7.1	128	50.57	0.0	-	-	-	0.00

Table 2. Global Performance Benchmarking. Comparative analysis of Galactic-G variants against GLOBE-CE ∗ and Glacier-G ∗ across effectiveness, average flipping cost, average segments changed, average timesteps changed, and runtime. The ∗ indicates adaptations for the global timeseries clustering context; the null indicator “-” is assigned throughout the metrics where the corresponding effectiveness is zero. Results for additional datasets can be found in Appendix Table 6 .

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Meaning
$\mathcal{T},T$	Space of series $\mathbb{R}^{T}$ ; Series length
$\bm{x}=[x_{1},\dots,x_{T}]$	A time-series instance of length $T$
$X=\{x^{(i)}\}_{i=1}^{N}$	Dataset containing $N$ series
$f:\mathcal{T}\to\{1,\dots,K\}$	Underlying clustering algorithm
$\mathcal{C}=\{C_{1},\dots,C_{K}\}$	Cluster partition
$g:\mathcal{T}\to[0,1]^{K}$	Probabilistic surrogate classifier

Appendix

Table 3. Notation Table for the Galactic Framework

Panel of Figure 5 — Figure 5. Galactic-L Target Selection Analysis. Comparison of the second possible and the all random policies across the UCR datasets.

Panel of Figure 6 — Figure 6. Galactic-L Target Selection Analysis. Comparison of the random and the all random policies across the UCR datasets.

Panel of Figure 7 — Figure 7. Galactic-G selections with varied $\mu$

Dataset	Instances	Length	Clusters	Type	ResNet Acc.	Dataset	Instances	Length	Clusters	Type	ResNet Acc.
ArrowHead	211	251	3	IMAGE	73.81%	ItalyPowerDemand	1096	24	2	SENSOR	95.45%
Lightning7	143	319	7	SENSOR	75.86%	CBF	930	128	3	SIMUL.	100.00%
Car	120	577	4	SENSOR	91.67%	MiddlePhalanxTW	553	80	6	IMAGE	58.56%
Coffee	56	286	2	SPECTRO	100.00%	Computers	500	720	2	DEVICE	92.00%
CricketZ	780	300	12	HAR	84.62%	PowerCons	360	144	2	DEVICE	82.61%
Earthquakes	461	512	2	SENSOR	75.27%	Rock	70	2844	4	SPECTRO	78.57%

Appendix

Table 4. Metadata of the selected UCR time-series datasets and Surrogate classification accuracies.

Dataset	KNN					TSEvo					Glacier-L					Glacier-G					Galactic-L
Dataset	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT
Computers	100	0.1	29.83	720	0.41	100	0.07	29.83	720	906.87	35.33	0	29.68	640.91	31.52	36	0	29.72	648.85	34.47	87.33	0.01	8.53	399.92	29.42
CricketZ	100	0.09	30.22	300	1.01	100	0.1	30.22	300	2366.73	11.97	0.01	32.11	300	22.94	14.53	0.01	32.97	300	26.57	99.57	0.01	8	190.56	75.75
Earthquakes	100	0.24	39.67	512	0.37	100	0.19	39.67	512	1289.46	31.65	0.01	41.41	509.32	27.06	34.53	0	41.56	509.77	29.7	94.24	0.03	10.97	294.5	65.15
ECG5000	100	0.07	20.15	140	7.12	100	0.14	20.15	140	9583.36	3.27	0.01	26.51	133.78	28.94	5.13	0.01	24.45	128.92	44.97	61.8	0.01	7.43	50.2	282.68
ECGFiveDays	100	0.11	22.79	136	1.47	100	0.09	22.79	136	1737.3	22.93	0.01	22.44	132.8	36.41	52.63	0.02	22.51	129.69	78.49	100	0.03	5.94	36.84	121.5

Appendix

Table 5. Additional Local Performance Benchmarking. Comparative analysis of Galactic-L against kNN , TSEvo , and Glacier variants across effectiveness, average flipping cost, average segments changed, average timesteps changed, and runtime. The null indicator “-” is assigned throughout the metrics where the corresponding effectiveness is zero.

Dataset	Optimal					Greedy					Hierarchical					Hierarchical Greedy					GLOBE-CE ∗					Glacier-G ∗
	Galactic-G																				Competitors
	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT	eff	afc	asc	atc	RT
Computers	36.9	0.006	5.0	580	303.33	36.9	0.006	5.0	580	25.60	34.7	0.007	5.0	577	17.03	34.9	0.006	5.0	579	8.12	42.1	0.012	7.8	720	218.32	8.2	0.003	12.5	720	15.24
CricketZ	29.4	0.014	3.6	178	145.44	29.0	0.012	3.8	175	10.90	15.6	0.009	4.1	167	6.35	15.7	0.009	4.1	168	5.09	85.8	0.032	6.4	275	29.49	4.4	0.006	5.8	250	25.44
Earthquakes	50.1	0.055	3.7	241	303.97	50.1	0.055	3.7	241	30.57	36.1	0.029	4.0	233	20.74	40.3	0.034	3.9	234	15.52	21.3	0.034	7.0	512	139.45	3.1	0.005	7.0	512	20.94
ECG5000	48.3	0.018	4.6	37	778.67	48.1	0.019	4.6	37	41.15	44.7	0.018	4.6	36	47.73	45.2	0.017	4.5	35	31.83	75.7	0.106	8.4	140	175.61	0.2	0.000	3.0	27	0.00

Appendix

Table 6. Additional Global Performance Benchmarking. Comparative analysis of Galactic-G variants against GLOBE-CE ∗ and Glacier-G ∗ across effectiveness, average flipping cost, average segments changed, average timesteps changed, and runtime. The ∗ indicates adaptations for the global timeseries clustering context; the null indicator “-” is assigned throughout the metrics where the corresponding effectiveness is zero.

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What-If Explanations Over Time: Counterfactuals for Time Series Classification

Udo Schlegel, Thomas Seidl

LMU Munich, Germany · Munich Center for Machine Learning (MCML), Germany

Graph Counterfactual Explanations Counterfactual Explanations Counterfactual Evaluation Interpretable Time-Series Classification Time Series Classification

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Counterfactual explanations emerge as a powerful approach in explainable AI, providing what-if scenarios that reveal how minimal changes to an input time series can alter the model's prediction. This work presents a survey of recent algorithms for counterfactual explanations for time series classification. We review state-of-the-art methods, spanning instance-based nearest-neighbor techniques, pattern-driven algorithms, gradient-based optimization, and generative models. For each, we discuss the underlying methodology, the models and classifiers they target, and the datasets on which they are evaluated. We highlight unique challenges in generating counterfactuals for temporal data, such as maintaining temporal coherence, plausibility, and actionable interpretability, which distinguish the temporal from tabular or image domains. We analyze the strengths and limitations of existing approaches and compare their effectiveness along key dimensions (validity, proximity, sparsity, plausibility, etc.). In addition, we implemented an open-source implementation library, Counterfactual Explanations for Time Series (CFTS), as a reference framework that includes many algorithms and evaluation metrics. We discuss this library's contributions in standardizing evaluation and enabling practical adoption of explainable time series techniques. Finally, based on the literature and identified gaps, we propose future research directions, including improved user-centered design, integration of domain knowledge, and counterfactuals for time series forecasting.

Abstract

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