In a paper published in Nonlinear Processes in Geophysics, V. Mithlesh Kumar, Anil Yildiz, and Julia Kowalski of RWTH Aachen University introduce a Bayesian data selection workflow that quantifies, in a rigorous information-theoretic sense, how much each candidate dataset actually contributes to calibrating a landslide runout model. Their central finding is striking: more data does not automatically mean better calibration. What matters is whether an observation captures the specific dynamics that a given parameter governs. An observation that seems superficially relevant — say, the total runout distance, when the ultimate goal is predicting impact area — may be nearly useless for constraining certain parameters, while a less obvious choice, such as a time series of velocity, can be dramatically more informative.

The technical backbone of the approach is Bayesian calibration. Rather than producing a single best-fit parameter value, Bayesian methods represent uncertainty about a parameter as a probability distribution, called the prior, and then update it with observational data to yield a narrower posterior distribution. For landslide models, whose parameters are conceptual rather than physically measurable, this framework is especially attractive because it explicitly handles both measurement noise and model inadequacy — the two dominant sources of discrepancy between what a model predicts and what is actually observed. The catch is computational: Bayesian calibration requires enormous numbers of forward model evaluations, which is why the field has increasingly turned to fast surrogate models, such as Gaussian process emulators, to stand in for the expensive simulation.

Kumar and colleagues go a step further by asking a question that earlier studies had only addressed qualitatively: given several possible observational datasets, which one is most informative? Their answer draws on the Kullback-Leibler divergence, a classic measure from information theory that quantifies how much one probability distribution differs from another. In the Bayesian setting, the KL divergence between the posterior and the prior has a direct interpretation as information gain — it measures how much the data reduced uncertainty about the parameters. A dataset that produces a large KL divergence has done more work; one that leaves the posterior barely changed has contributed little, no matter how abundant or precise it appears.

Computing this quantity is far from trivial, because it involves intractable integrals over posterior distributions. The team sidestepped this with a k-nearest-neighbor-based divergence estimator, and they made the whole pipeline feasible by embedding it in a three-phase workflow built on the Python package PSimPy: first a Gaussian process surrogate is trained on model outputs and validated by cross-validation, then Markov Chain Monte Carlo sampling produces posterior distributions for each candidate dataset, and finally the KL divergences are computed and compared. The result is a matrix that, for every combination of parameter and observation type, quantifies the informational value of that pairing — a systematic tool for deciding where scarce measurement resources should be spent.

To demonstrate the method, the researchers used an idealized lumped mass model governed by the Voellmy rheology, which combines a dry Coulomb friction coefficient that resists basal motion with a velocity-dependent turbulent friction term. They generated synthetic observations with known ground-truth parameters, deliberately isolating the effect of data selection from model error. The experiments compared aggregated observations — maximum velocity and runout distance — against time series of velocity and position, and probed how the length and temporal resolution of the time series influenced the outcome.

The results revealed a clean division of labor. Calibrating with maximum velocity strongly constrained the turbulent friction coefficient but left the Coulomb coefficient nearly untouched, while runout distance did the opposite: it pinned down the Coulomb coefficient while leaving the turbulent coefficient badly biased, with its most probable estimate falling far from the true value. The explanation lies in the physics — runout distance varies almost entirely with the Coulomb friction coefficient, whereas peak velocity is governed by the turbulent term. Time series data, whether of velocity or position, outperformed both aggregated datasets, delivering substantial information about both parameters simultaneously, because they capture the evolving acceleration and deceleration phases that the friction parameters actually control.

Perhaps the most practically valuable insight concerns diminishing returns. As the researchers lengthened the velocity time series used for calibration, information gain rose — but the rate of increase fell steeply and plateaued. Remarkably, the optimal observation window corresponded to the time the sliding mass needed to reach its maximum velocity, the point at which the system’s dynamics have evolved and stabilized. Data collected beyond that threshold added progressively less. This echoes findings from hydrology, where longer calibration records and finer temporal resolution improve parameter inference only up to a point, and it suggests that monitoring campaigns could be designed around the dynamics that matter rather than around maximal data volume.

The workflow also proved capable of inferring the noise characteristics of the observations themselves. When the discrepancy parameters of the statistical noise model were calibrated alongside the friction coefficients, the estimates closely matched the known noise levels used to generate the synthetic data — evidence that rich, time-resolved observations can help quantify the very uncertainty they carry, offsetting the effects of imperfect data quality.

The authors are candid about the limitations of their demonstration. The study relies on synthetic data and idealized topography, and it assumes negligible model discrepancy — an assumption that may not hold for real field observations, where structural model errors can cause posteriors to contract toward incorrect parameter regions, inflating KL divergence in misleading ways. They recommend complementing information-theoretic metrics with posterior predictive checks in such cases. Still, the framework is model-agnostic and transferable to complex models and real terrain, and it offers geohazard practitioners something they have lacked: a way to assess, before an expensive field campaign, which measurements will actually sharpen their predictions. For a hazard community working with sparse, costly data, knowing which observations carry the most information may prove as important as the models themselves.

Subject of Research: Bayesian data selection and information-theoretic quantification of observational data value for calibrating landslide runout model parameters

Article Title: Bayesian data selection to quantify the value of data for landslide runout calibration

Article References: Kumar, V. M., Yildiz, A., & Kowalski, J. (2026). Bayesian data selection to quantify the value of data for landslide runout calibration. Nonlinear Processes in Geophysics, 33(3), 425-453. https://doi.org/10.5194/npg-33-425-2026

Image Credits: AI Generated

DOI: 10.5194/npg-33-425-2026

Keywords: landslide runout, Bayesian calibration, Kullback-Leibler divergence, data selection, information gain, Gaussian process emulator, MCMC, Voellmy rheology, friction parameters, natural hazards, uncertainty quantification, surrogate modeling

The answer proposed by the researchers is a framework called SCLS, short for shapelet-based soft contrastive learning for multivariate time series clustering. Published online in the journal Knowledge and Information Systems, the method combines two powerful ideas from machine learning, discriminative subsequences known as shapelets and a gentler form of contrastive learning, into a four-stage pipeline that avoids the noise and uncertainty that plague earlier approaches. In experiments spanning dozens of real-world datasets, the authors report that SCLS achieved the highest performance ranking compared with state-of-the-art clustering methods.

To appreciate why this matters, it helps to understand what shapelets are and why they have become a cornerstone of time series analysis. A shapelet is a short, distinctive subsequence that captures the essence of a pattern, such as the characteristic spike in an electrocardiogram that signals a particular cardiac event or the telltale wobble in a sensor reading that precedes a machine failure. Since shapelets were introduced as a primitive for data mining in 2009, researchers have used them for classification and clustering because they are inherently interpretable: a human can look at a shapelet and see exactly which fragment of the signal drove the decision. That transparency is precious in domains like medicine and industrial monitoring, where a bare accuracy number is not enough.

Contrastive learning, meanwhile, has become one of the dominant paradigms for learning representations without labels. The idea is to teach a neural network to pull similar examples together in an embedding space while pushing dissimilar ones apart. In time series work, this is usually done through data augmentation: the same series is distorted in two different ways, for example by jittering, scaling, or cropping, and the network is trained to recognize that both distorted views came from the same source. The problem, as Wang and Yang point out, is that augmentation introduces noise and uncertainty of its own. A badly chosen distortion can destroy the very pattern that defines a class, and the augmented views may no longer resemble anything in the real data. Worse, in shapelet-based methods that lean on augmentation, the extracted shapelets can drift away from true subsequences of the original signals, eroding both interpretability and clustering quality.

SCLS sidesteps this difficulty by working directly with the original sequences rather than their distorted copies. The framework unfolds in four carefully sequenced stages. In the first, an attention mechanism fuses multiple feature components drawn from the original series. Attention, the same mechanism that powers modern language models, allows the network to weigh different parts of the signal according to their relevance, which reduces uncertainty and helps extract more representative shapelets. Rather than treating every time point and every channel as equally informative, the model learns where the discriminative structure lives.

The second stage mines multi-scale shapelets using a perceptually important points selection method based on information gain. Perceptually important points are the salient peaks, valleys, and inflection points of a curve, the skeleton of a signal that survives even when the details are smoothed away. By selecting these anchor points and measuring how much each candidate subsequence contributes to distinguishing between groups, quantified through information gain, the method can discover shapelets at multiple lengths and granularities. This multi-scale view matters because the discriminative fingerprint of a time series may be a brief transient in one dataset and a long, slow trend in another.

Third, the framework employs a shapelet encoder enhanced with a pseudo-label clustering mechanism. Pseudo-labeling is a well-known strategy in semi-supervised learning in which a model’s own provisional cluster assignments are treated as soft training signals. Here, the encoder embeds the mined shapelets into structure-aware representations, meaning the embedding preserves the relationships among shapelets rather than treating them as isolated vectors. These structure-aware embeddings then serve as the substrate for the final stage of learning.

That final stage is the soft contrastive learning strategy that gives the method its name and its distinctive character. Instead of the hard binary logic of conventional contrastive learning, where two samples are either a positive pair to be attracted or a negative pair to be repelled, soft contrastive learning assigns graded, probabilistic relationships between samples. The hierarchical strategy introduced in SCLS jointly optimizes the shapelet representation space at two levels: the temporal level, where fragments within a series are compared, and the sample level, where whole series are compared with one another. The result is a representation space whose geometry is explicitly shaped for clustering analysis, with coherent groups emerging naturally rather than being forced by rigid pairwise constraints.

The authors evaluated the framework through extensive experiments on dozens of real-world datasets, measuring clustering quality against a battery of state-of-the-art competitors. According to the published results, SCLS attained the highest performance ranking among the methods tested, suggesting that the combination of augmentation-free shapelet extraction and hierarchical soft contrastive optimization translates into a genuine advantage rather than a theoretical curiosity. The study draws on a rich lineage of prior work, from the original shapelet primitive through shapelet transformers presented at the 2024 KDD conference, multiview unsupervised shapelet learning, and recent soft contrastive approaches for time series presented at ICLR, positioning SCLS as a synthesis that resolves the specific weaknesses of each ingredient when used alone.

The practical implications reach well beyond the benchmark suite. Clustering multivariate time series underpins customer segmentation in dynamic markets, electricity consumption analysis, fault diagnosis in industrial equipment, and the discovery of patterns in online popularity dynamics, all areas represented in the study’s bibliography. Because the shapelets at the heart of SCLS remain anchored to true subsequences of the original data, practitioners gain not only clusters but also an explanation of what distinguishes them, a feature that matters whenever algorithmic decisions must be audited or acted upon by domain experts. The code supporting the findings is available from the corresponding author upon reasonable request, and the research was supported by the Guangdong Basic and Applied Basic Research Foundation and the National Natural Science Foundation of China. As sensors multiply and the volume of unlabeled temporal data grows, methods like SCLS point toward a future in which machines can find the hidden rhythms of the world without needing humans to label every beat first.

Subject of Research: Shapelet-based soft contrastive learning for multivariate time series clustering

Article Title: SCLS: Shapelet-based soft contrastive learning for multivariate time series clustering

Article References: SCLS: Shapelet-based soft contrastive learning for multivariate time series clustering. (n.d.). https://doi.org/10.1007/s10115-026-02902-2

Image Credits: AI Generated

DOI: 10.1007/s10115-026-02902-2

Keywords: multivariate time series, clustering, shapelets, contrastive learning, attention mechanism, pseudo-labeling, information gain, representation learning, data mining, unsupervised learning, feature fusion, Knowledge and Information Systems