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L2GTX: From Local to Global Time Series Explanations

Conference: CVPR 2026 arXiv: 2603.13065 Code: N/A Area: Explainable AI / Time Series Classification Keywords: time series explanation, local-to-global aggregation, model-agnostic XAI, parameterized event primitives, representative instance selection

TL;DR

L2GTX is proposed as a fully model-agnostic local-to-global explanation method for time series, employing parameterized event primitives (increasing/decreasing trends, local extrema) as explanation units. Through hierarchical clustering merging, greedy budget selection, and attribute statistics aggregation, it produces compact and faithful class-level global explanations across 6 UCR datasets (GF = 0.792 on ECG200 with FCN).

Background & Motivation

Background: Deep learning achieves high accuracy in time series classification (finance, sensors, medical ECG), yet operates as a black box, undermining trust and regulatory compliance.

Limitations of Prior Work: (1) Image/tabular XAI methods such as LIME/SHAP treat each time step as an independent feature, ignoring temporal dependencies; (2) global explanation synthesis for time series remains largely unexplored; (3) the few existing global methods (CAM/LRP-based) are architecture-specific and lack generality.

Key Challenge: The temporal position, duration, and amplitude of time series events vary substantially across instances, so directly aggregating local explanations introduces heavy redundancy and loses temporal structural information.

Goal: Generate class-level global explanations for arbitrary black-box time series classifiers while preserving faithfulness and compactness.

Key Insight: Parameterized event primitives (PEPs) serve as semantic units, enabling structured local-to-global aggregation via hierarchical clustering merging, greedy selection, and attribute statistics.

Core Idea: Replace time-step attributions with event primitives such as "increasing trend / decreasing trend / local extrema," endowing time series explanations with behavioral semantics.

Method

Overall Architecture

A five-step pipeline: input \(n_{inst}\) instances per class → Step 1 LOMATCE generates local explanations (event primitives + importance) → Step 2 hierarchical clustering merges similar event clusters across instances, constructing instance–cluster matrix \(\mathbf{M}\) → Step 3 compute global cluster importance \(I_j = \sqrt{\sum_i |M_{i,j}|}\) → Step 4 greedy selection of \(B\) representative instances to maximize coverage → Step 5 aggregate event attribute statistics (mean ± std) to output class-level global explanations.

Key Designs

  1. LOMATCE Parameterized Event Primitives (Step 1): For each instance, \(S\) perturbed neighborhood samples are constructed and four types of PEPs are extracted—increasing segment \((start\_time, duration, avg\_gradient)\), decreasing segment, local maximum \((time, value)\), and local minimum. K-means clustering (with silhouette-based \(K\) selection) constructs an event matrix \(\mathbf{Z} \in \mathbb{R}^{S \times K}\); a weighted Ridge regression surrogate is trained to obtain cluster importance scores \(\hat{\beta}\), from which the top-\(n\) clusters are retained. Core motivation: using "event behaviors" rather than "time steps" as explanation units preserves temporal structural semantics—conveying not only where is important but also what behavior is important.

  2. Adaptive Hierarchical Clustering Merging (Step 2): Agglomerative hierarchical clustering (Euclidean distance) is applied to the cluster centroids of all instances, grouped by PEP type. A user-specified merging percentile \(p\) determines the cut distance \(\tau = \text{percentile}_p(\{d_r\})\). Larger \(p\) yields fewer, more compact clusters; after merging, \(M_{i,j} = \sum_{C_{i,k} \in G_j} I(C_{i,k})\). Design motivation: similar events across instances exhibit natural redundancy and require a unified representation to support global reasoning.

  3. Greedy Budget Selection (Step 4): Given budget \(B\), the greedy strategy maximizes marginal gain over uncovered high-importance clusters: \(i^* = \arg\max_{i \notin S} \sum_j I_j \cdot \mathbf{1}\{M_{i,j} > 0 \wedge c_j = 0\}\). This adapts the submodular optimization idea of SP-LIME to time series event clusters, ensuring diversity and representativeness among selected instances.

Loss & Training

L2GTX is a post-hoc explanation method that does not modify the classifier. The primary evaluation metric is Global Faithfulness (GF)—the mean local surrogate \(R^2\) across the \(B\) selected representative instances. Black-box classifiers (FCN / LSTM-FCN) are trained independently over 100 random splits; L2GTX results are reported with 3 seeds, macro-averaged with 95% confidence intervals.

Key Experimental Results

Main Results (FCN Model, Global Faithfulness GF)

Dataset p=25 p=50 p=75 p=95
ECG200 0.784±0.015 0.788±0.013 0.780±0.026 0.792±0.014
GunPoint 0.593±0.007 0.599±0.019 0.601±0.007 0.597±0.011
Coffee 0.683±0.010 0.678±0.006 0.678±0.005 0.678±0.015
FordA 0.674±0.021 0.672±0.029 0.673±0.021 0.672±0.028
FordB 0.675±0.008 0.679±0.034 0.673±0.006 0.673±0.029
CBF 0.625±0.018 0.626±0.011 0.633±0.016 0.625±0.008

Ablation Study (LSTM-FCN Model, GF)

Dataset p=25 p=50 p=75 p=95
ECG200 0.828±0.010 0.832±0.013 0.829±0.021 0.831±0.007
GunPoint 0.617±0.074 0.619±0.067 0.588±0.086 0.638±0.011
Coffee 0.617±0.008 0.609±0.004 0.616±0.036 0.608±0.003
FordA 0.618±0.028 0.621±0.015 0.614±0.039 0.627±0.035
FordB 0.661±0.021 0.656±0.039 0.651±0.050 0.655±0.027
CBF 0.519±0.020 0.508±0.025 0.519±0.033 0.502±0.015

Key Findings

  • GF is highly stable with respect to merging granularity: GF varies minimally as \(p\) ranges from 25 to 95 (confidence intervals strongly overlap), indicating that the explanation space can be substantially compressed without sacrificing faithfulness.
  • Global cluster count decreases monotonically with \(p\) without degrading GF: redundant clusters can be safely merged.
  • Cross-architecture consistency: FCN and LSTM-FCN yield highly consistent explanation structures on the same datasets (e.g., similar discriminative regions for Normal vs. Infarction in ECG200).
  • Alignment with domain knowledge: The Infarction class in ECG200 is characterized by local maxima—consistent with the clinical knowledge of prominent deflections in myocardial infarction; the Robusta class in Coffee is characterized by high-intensity spectral peaks.

Highlights & Insights

  • Using parameterized event primitives as explanation units enables a qualitative leap in semantic interpretability—conveying not merely "step 30 is important" but "steps 25–40 exhibit an increasing trend."
  • The local-to-global aggregation pipeline is complete and principled: clustering merging → importance estimation → budget selection → attribute statistics.
  • The method is fully model-agnostic and applicable to arbitrary black-box time series classifiers.
  • The adjustable merging percentile \(p\) provides users with fine-grained control over explanation granularity, from detailed to compact.

Limitations & Future Work

  • Validation limited to univariate time series: extension to multivariate settings (multi-channel sensors / EEG) has not been explored, limiting practical applicability.
  • GF upper bound is modest: approximately 0.6 on GunPoint, reflecting the inherent approximation limitations of the Ridge surrogate model.
  • Computational overhead: LOMATCE event clustering is a bottleneck; cost is high for long sequences or large neighborhoods.
  • Absence of user studies: no expert evaluation of the subjective utility of the generated explanations has been conducted.
  • vs. SP-LIME: borrows the budget selection idea, but SP-LIME targets tabular data, does not perform aggregation, and does not produce class-level summaries.
  • vs. GLocalX: aggregates local rules for tabular data but does not handle temporal structure.
  • vs. LOMATCE: serves as the single-instance explanation foundation; L2GTX extends it to the global level.
  • Inspiration: the local-to-global aggregation paradigm is transferable to explainability in video classification—aggregating frame-level attributions into class-level global video explanations.

Rating

⭐⭐⭐ (3/5)

Rationale: The research problem (global explanation for time series) has clear value; the methodological pipeline is complete and principled; and the event primitive design carries meaningful semantics. However, (1) individual components offer limited novelty in isolation; (2) evaluation is restricted to small UCR datasets; (3) absolute GF values are not high (0.5–0.6 in some cases); and (4) no human evaluation is provided. Recommended primarily for readers specializing in XAI subfields.