Interpretable Time-Series Classification

The ecological insurance theory posits that diverse forests are more resilient and better able to adapt to changing environmental conditions. Increasing drought and heat stress in Central Europe promotes mixed forests for maintaining ecosystem services. However, a diverse species distribution complicates remote sensing-based species mapping, as distinguishing pure from mixed species compositions at the pixel level remains challenging. We evaluated the potential of recurrent neural networks (RNNs) for tree-species classification from Sentinel-2 time series and investigated the spectral-temporal features underlying class discrimination, with particular emphasis on separating pure from mixed Norway spruce pixels. We compared RNN classification models with Random Forest (RF) and Extreme Gradient Boosting (XGBoost) and used Integrated Gradients (IG) to quantify feature attributions across spectral bands and time. The best-performing RNN achieved a Macro-F1 score of 0.851 on the test data, outperforming XGBoost by 0.012 and Random Forest by 0.103. Beyond classification performance, the attribution analysis revealed distinct spectral-temporal patterns associated with the separation of pure and mixed Norway spruce pixels. Attribution values increased particularly after approximately day of year (DOY) 125, while B11 showed the strongest contribution during periods of increasing spectral divergence between the two classes. These findings show that recurrent models can provide competitive classification performance while also revealing the phenological periods and spectral regions that are most relevant for distinguishing closely related forest compositions. Combining time-series classification with explainability therefore provides additional insight into the spectral-temporal mechanisms underlying tree-species discrimination and may support more detailed mapping of mixed forest structures.

Traditional time-series classification methods often operate as black boxes, providing a class prediction without indicating which time point or time interval within the series led to that prediction. To improve temporal interpretability, MILLET (Multiple Instance Learning with Temporal Explanation), which combines an InceptionTime encoder with Conjunctive Pooling, provides both classification and temporal explanations. However, MILLET contains approximately 424 K parameters, making it unsuitable for deployment on resource-constrained micro-controllers, and it achieves an overall time-series accuracy of 0.888 and an explanation score of 0.681 NDCG@n. We therefore propose SEA-Net, a lightweight architecture using small multi-scale depthwise-separable convolutional TSC encoders and improved Multiple Instance Learning (MIL) pooling heads. Our SEA-Net bottleneck encoder with Top-k pooling achieves 0.931 accuracy and 0.765 NDCG@n with only 41 K parameters. Another variant, using a gated encoder with Top-k pooling, achieves 0.955 accuracy and 0.750 NDCG@n with 62 K parameters. These results demonstrate that lightweight architectures can maintain strong classification performance and temporal explanations while substantially reducing model size. The proposed variants address specific limitations of the pooling strategy used by MILLET, providing a practical direction for interpretable time-series classification on resource-constrained edge devices.

Irregular time series, characterized by non-uniform sampling intervals, missing observations, and variable lengths, are ubiquitous in healthcare, mobility, and environmental monitoring, yet effective and interpretable classifiers for this setting are limited. Existing approaches often rely on imputation, which can obscure the temporal structure of the data, or require complex neural architectures that are opaque and difficult to explain. In this work, we extend the Bag-Of-Receptive-Fields (BORF), a fast, deterministic, and interpretable transform for time series, to the irregular setting. Our key contribution is a time-weighted normalization scheme in which each observation is weighted proportionally to its associated time delta, making pattern extraction sensitive to the actual temporal distribution of samples rather than only their index position. This requires deriving an efficient sliding-window recurrence for the time-weighted standard deviation, preserving the linear time complexity of BORF. We benchmark the resulting method against state-of-the-art irregular time series classifiers on datasets from the PYRREGULAR repository, demonstrating competitive classification performance with the added benefit of human-interpretable explanations.

Time-series explainability remains challenging because discriminative information is often encoded in latent frequency or time-frequency features rather than in the raw signal itself. Existing attribution methods typically operate either in the time domain or in a fixed transform domain, limiting their ability to capture salient information across different representations. We propose XACT, a general framework that learns sparse attribution masks over coefficients from arbitrary invertible time-frequency transforms. We evaluate the framework on the STFT, the continuous wavelet transform, and the discrete wavelet transform. In addition, we extend the virtual inspection layer approach from the STFT to both wavelet transforms, enabling LRP to generate explanations in these representations. On a synthetic dataset, XACT produces precise explanations and is less prone to highlighting spurious features than the tested baselines. Across two real-world datasets, XACT produces sparse and structured explanations, although no method performs best across all quantitative evaluation criteria. These results demonstrate that learning explanations directly in time-frequency representations offers a flexible approach to interpreting deep-learning models for time series data.

Time series arise in a wide range of application domains and are analyzed using machine learning in decision-critical settings. Time series classification (TSC) is one of the most widely studied and relevant tasks. In this context, ensuring the transparency and trustworthiness of TSC models has become an important requirement, motivating the use of explainable artificial intelligence (XAI) methods. Despite growing interest, research on XAI for TSC remains fragmented, and a systematic understanding of the available software frameworks for explanation generation, their evaluation practices, and practical limitations is still lacking. Prior work largely focused on individual explanation methods, while cross-framework consistency, time-series-specific evaluation, and reproducibility have received little attention. In this survey, we analyze existing software frameworks for explanation generation and evaluation in TSC. We compare them along multiple dimensions, including supported XAI methods, evaluation metrics, usability, benchmarking support, and reproducibility, providing the first time-series-specific survey of frameworks with implementation comparisons and an analysis of frequency-domain support. We identify six frameworks that explicitly support time series and reveal common limitations: only one method supports frequency-domain explanations despite their relevance; only two evaluation metrics have been developed specifically for time series; and identical XAI methods can yield substantially different explanations across frameworks. Based on these findings, we discuss open challenges and outline directions for future research, highlighting the need for unified, time-series-specific XAI frameworks that enable faithful, reproducible, and time-series-aware explanations.

Faithful explanations of time-series classifiers should identify subsequences that are not only sufficient to preserve a black-box model's prediction, but also necessary for maintaining it. However, existing sufficiency-oriented methods can assign high importance to spurious subsequences that support the prediction without being essential to the model's decision. We introduce TimePNS, a necessity-aware framework for time-series explanation. Inspired by Pearl's counterfactual notion of necessity, TimePNS assesses whether a temporal factor is necessary by intervening on it and measuring whether the original prediction is disrupted. The framework adopts a two-stage design. Stage I learns an identifiable causal generative process together with a sufficiency-oriented explanation mask. Stage II performs counterfactual interventions on temporal factors to derive necessity signals, which supervise a temporal gate that refines the initial explanation by suppressing non-essential components and emphasizing counterfactually necessary ones. Experiments on synthetic and real-world time-series benchmarks show that TimePNS more accurately identifies decision-critical subsequences and consistently improves sufficiency-necessity trade-offs over strong baselines.

Training deep neural networks for clinical time-series analysis is computationally demanding, yet many healthcare settings lack the resources required for repeated model development and deployment. This challenge is particularly evident in electrocardiogram classification, where large datasets and long training schedules make efficiency practically important. Progressive Data Dropout reduces training cost by excluding samples from gradient updates once they are learned, but it relies on model confidence and may retain samples that are difficult due to noise or ambiguity rather than useful signal. In this work, we introduce ERTS, an explainability-based reliability training signal for efficient ECG classification. ERTS uses explanation quality during training to distinguish between informative and unreliable uncertainty. Building on progressive data selection, we compute Grad-CAM attention maps for candidate samples and derive a focus score that measures whether model predictions are supported by coherent and localised patterns. Samples with low focus are filtered out, while those with meaningful attention are prioritised for gradient updates. We evaluate ERTS across three ECG datasets and multiple backbone architectures, showing consistent improvements in macro-F1 alongside reduced effective training cost. These results suggest that explanation quality can serve as a practical signal for improving both efficiency and reliability in clinical time-series learning. Code will be released.

Multivariate time series classification (MTSC) is pivotal in high-stakes domains, such as clinical diagnosis and industrial fault detection, where safe deployment necessitates transparent decision-making. However, isolating the temporal segments that drive model predictions is challenging because discriminative signals in real-world time series are typically sparse, heterogeneous, and heavily obscured by background noise. This paper, therefore, proposes AnchorMoE, an interpretable-by-construction classification framework. Built upon a Mixture-of-Experts (MoE) architecture, AnchorMoE encodes multi-view representations of local patches and routes them to specialized experts, ensuring that the final prediction is formulated as an exact additive decomposition over the input segments, facilitating ante-hoc transparency rather than relying on post-hoc estimations. To maintain the reliability of this decomposition under sparse signal distributions, we introduce a geometric orthogonality constraint that penalizes representational redundancy, compelling distinct experts to specialize in heterogeneous predictive patterns. Furthermore, an uncertainty-aware reliability gate is designed to dynamically calibrate the contribution of each segment, effectively suppressing residual background noise. Extensive experiments on real-world and synthetic benchmarks demonstrate that AnchorMoE achieves highly competitive classification performance while faithfully grounding its decisions in the raw time series.

Time Series Classification (TSC) is a long-standing research problem that has gained increasing attention in recent years with the rapid growth of large-scale temporal data. Despite substantial progress enabled by deep learning, designing TSC models that are both accurate and interpretable remains a challenging task. Many existing approaches adopt a direct feature-to-label classification paradigm, by collapsing high-dimensional temporal embeddings into class logits via a single linear projection (often after global pooling), the paradigm conflates feature extraction and decision logic into an inseparable mapping. To address these limitations, we propose PDFTime, a prototype-guided framework that reformulates time series classification as a multi-stage decision process. Instead of direct feature-to-label mapping, PDFTime leverages learned prototypes to approximate class-conditional feature distributions in the latent space, enabling progressive discrimination through classification sub-tasks of varying granularity. To our knowledge, PDFTime is the first framework to reformulate time series classification as a decoupled, multi-stage similarity-based reasoning process, breaking the long-standing paradigm of direct, black-box feature-to-label mapping. Extensive evaluations demonstrate that PDFTime achieves state-of-the-art (SOTA) performance across UEA and UCR benchmarks. Notably, it secures the top-$1$ accuracy on 80 out of 128 datasets in the UCR archive, significantly outperforming recent strong baselines in both consistency and generalization.

Discovering shapelets -- i.e., discriminative temporal patterns within time series -- has been widely studied to address the inherent complexity of time-series classification (TSC) and to make model decision-making processes more transparent. However, existing methods primarily focus on population-level shapelets optimized across the entire dataset, which leads to two fundamental limitations: (i) population-level patterns often misalign with instance-specific features, resulting in suboptimal performance and potentially misleading interpretations, and (ii) most methods treat shapelets as independent entities, overlooking important temporal dependencies and interactions among multiple patterns. To address these limitations, we propose INSHAPE, an interpretable TSC framework that discovers variable-length, discriminative temporal patterns specific to each time series. INSHAPE identifies these patterns as non-overlapping segments and models their temporal dependencies, thereby providing clear instance-level interpretations while achieving strong predictive performance. Furthermore, INSHAPE bridges local and global interpretability through a bottom-up approach, aggregating instance-level shapelets into prototypical (population-level) shapelets. Extensive experiments on 128 UCR and 30 UEA benchmark datasets show that INSHAPE consistently outperforms state-of-the-art shapelet-based methods while providing more intuitive and interpretable insights.

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.

Due to the prevalence of temporal data and its inherent dependencies in many real-world problems, time series classification is of paramount importance in various domains. However, existing models often struggle with series of variable length or high dimensionality. This paper introduces the MIHT (Multi-instance Hoeffding Tree) algorithm, an efficient model that uses multi-instance learning to classify multivariate and variable-length time series while providing interpretable results. The algorithm uses a novel representation of time series as "bags of subseries," together with an optimization process based on incremental decision trees that distinguish relevant parts of the series from noise. This methodology extracts the underlying concept of series with multiple variables and variable lengths. The generated decision tree is a compact, white-box representation of the series' concept, providing interpretability insights into the most relevant variables and segments of the series. Experimental results demonstrate MIHT's superiority, as it outperforms 11 state-of-the-art time series classification models on 28 public datasets, including high-dimensional ones. MIHT offers enhanced accuracy and interpretability, making it a promising solution for handling complex, dynamic time series data.

Persistent homology (PH) -- the conventional method in topological data analysis -- is computationally expensive, requires further vectorization of its signatures before machine learning (ML) can be applied, and captures information along only the spatial axis. For time series data, we propose Euler Characteristic Surfaces (ECS) as an alternative topological signature based on the Euler characteristic ($χ$) -- a fundamental topological invariant. The ECS provides a computationally efficient, spatiotemporal, and inherently discretized feature representation that can serve as direct input to ML models. We prove a stability theorem guaranteeing that the ECS remains stable under small perturbations of the input time series. We first demonstrate that ECS effectively captures the nontrivial topological differences between the limit cycle and the strange attractor in the Rössler system. We then develop an ECS-based classification framework and apply it to five benchmark biomedical datasets (four ECG, one EEG) from the UCR/UEA archive. On $\textit{ECG5000}$, our single-feature ECS classifier achieves $98\%$ accuracy with $O(n+R\cdot T)$ complexity, compared to $62\%$ reported by a recent PH-based method. An AdaBoost extension raises accuracy to $98.6\%$, matching the best deep learning results while retaining full interpretability. Strong results are also obtained on $\textit{TwoLeadECG}$ ($94.1\%$) and $\textit{Epilepsy2}$ ($92.6\%$).

Deep learning models achieve high accuracy in time series classification, yet understanding their class-level decision behaviour remains challenging. Explanations for time series must respect temporal dependencies and identify patterns that recur across instances. Existing approaches face three limitations: model-agnostic XAI methods developed for images and tabular data do not readily extend to time series, global explanation synthesis for time series remains underexplored, and most existing global approaches are model-specific. We propose L2GTX, a model-agnostic framework that generates class-wise global explanations by aggregating local explanations from a representative set of instances. L2GTX extracts clusters of parameterised temporal event primitives, such as increasing or decreasing trends and local extrema, together with their importance scores from instance-level explanations produced by LOMATCE. These clusters are merged across instances to reduce redundancy, and an instance-cluster importance matrix is used to estimate global relevance. Under a user-defined instance selection budget, L2GTX selects representative instances that maximise coverage of influential clusters. Events from the selected instances are then aggregated into concise class-wise global explanations. Experiments on six benchmark time series datasets show that L2GTX produces compact and interpretable global explanations while maintaining stable global faithfulness measured as mean local surrogate fidelity.

Evaluating time series attribution methods is difficult because real-world datasets rarely provide ground truth for which time points drive a prediction. A common workaround is to generate synthetic data where class-discriminating features are placed at known locations, but each study currently reimplements this from scratch. We introduce xaitimesynth, a Python package that provides reusable infrastructure for this evaluation approach. The package generates synthetic time series following an additive model where each sample is a sum of background signal and a localized, class-discriminating feature, with the feature window automatically tracked as a ground truth mask. A fluent data generation API and YAML configuration format allow flexible and reproducible dataset definitions for both univariate and multivariate time series. The package also provides standard localization metrics, including AUC-PR, AUC-ROC, Relevance Mass Accuracy, and Relevance Rank Accuracy. xaitimesynth is open source and available at https://github.com/gregorbaer/xaitimesynth.

The current trend in the literature on Time Series Classification is to develop increasingly accurate algorithms by combining multiple models in ensemble hybrids, representing time series in complex and expressive feature spaces, and extracting features from different representations of the same time series. As a consequence of this focus on predictive performance, the best time series classifiers are black-box models, which are not understandable from a human standpoint. Even the approaches that are regarded as interpretable, such as shapelet-based ones, rely on randomization to maintain computational efficiency. This poses challenges for interpretability, as the explanation can change from run to run. Given these limitations, we propose the Bag-Of-Receptive-Field (BORF), a fast, interpretable, and deterministic time series transform. Building upon the classical Bag-Of-Patterns, we bridge the gap between convolutional operators and discretization, enhancing the Symbolic Aggregate Approximation (SAX) with dilation and stride, which can more effectively capture temporal patterns at multiple scales. We propose an algorithmic speedup that reduces the time complexity associated with SAX-based classifiers, allowing the extension of the Bag-Of-Patterns to the more flexible Bag-Of-Receptive-Fields, represented as a sparse multivariate tensor. The empirical results from testing our proposal on more than 150 univariate and multivariate classification datasets demonstrate good accuracy and great computational efficiency compared to traditional SAX-based methods and state-of-the-art time series classifiers, while providing easy-to-understand explanations.