The paper introduces the Clustering Occupation Kernel (CLOCK) method, a representation-based framework that embeds time series from dynamical systems into a reproducing kernel Hilbert space using a time‑averaged occupation kernel. This embedding allows trajectory comparison via the RKHS norm and, for differential equation systems, approximates the kernel mean embedding of the invariant Sinai‑Ruelle‑Bowen measure, effectively measuring the maximum mean discrepancy between attractors. CLOCK handles unequal‑length and irregularly‑spaced data, incorporates Takens’ embedding for general time series, and demonstrates superior performance over benchmark methods on synthetic data and real intracranial EEG recordings, with ablation studies confirming theoretical convergence and noise robustness.
arXiv:2606. 23472v2 Announce Type: replace-cross Abstract: Time series classification involves learning a mapping from a continuous, temporally ordered sequence of real-valued observations to discrete response variables, like class labels.
SPDAlign is an interpretable framework that aligns domain-specific EEG data by applying linear transformations on the Symmetric Positive Definite manifold, correcting mean differences and global rotations across domains using Wasserstein Procrustes. It leverages a generative model of EEG to recover distribution shifts caused by factors like head geometry, and demonstrates competitive performance on extensive public EEG datasets. The method is globally linear, enabling identification of frequency ranges, spatial patterns, and cross-subject variability without requiring labeled calibration data.
The paper introduces Diffusion-Conditioned Representation Alignment (DCRA), a training framework that uses the forward diffusion process as a structured corruption scheduler for time‑series representation learning. DCRA aligns representations across noise levels with a feature‑level consistency objective, preserving class‑discriminative structure and enabling smooth, semantically coherent trajectories in latent space. Experiments on the CHB‑MIT EEG dataset demonstrate that DCRA improves seizure detection performance under various noise conditions, achieving higher sensitivity at low false‑positive rates and producing more balanced, structured representations than baseline methods.
arXiv:2610.07229v1 Announce Type: new Abstract: Motivated by sequence-to-sequence transport in the context time-series domain adaptation, we study the problem of transportation between trajectories o...
arXiv:2607. 21823v1 Announce Type: new Abstract: We show that, up to isotropic scaling, the Gaussian RBF reproducing kernel Hilbert space (RKHS) is asymptotically isometric to Euclidean space in the large bandwidth limit.
The paper investigates how Markov chains converge within a geometry defined by Hilbertian embeddings of positive definite kernels, also known as Maximum Mean Discrepancy (MMD). By assuming a contraction in this kernel-induced geometry and a standard spectral gap, the authors derive non-asymptotic, high‑probability bounds on the empirical occupation measure’s convergence to the invariant measure. These bounds separate the influence of the spectral gap, which sets the effective sample size, from the kernel contraction, which appears only as a linear correction. The results are applied to one‑step prediction of dynamical systems from a single trajectory, yielding fast learning rates for a nonlinear least‑squares estimator that illustrate the interaction between kernel‑induced mixing and classical source and capacity conditions.
arXiv:2609.00647v1 Announce Type: new Abstract: Multiple kernel $k$-means integrates complementary nonlinear similarities by learning a combination of base kernels. Its pointwise optimization, howeve...
The paper introduces Dynafit, a kernel-based method for classifying trajectories produced by distinct nonlinear dynamical systems. It learns a distance metric by approximating the Koopman operator, enabling classification in a feature space without explicit dimensionality. The authors demonstrate Dynafit on logistic map chaos detection, handwritten dynamical pattern recognition, and visual dynamic texture classification.
The paper investigates why prescribed‑parameter convolutional kernels, such as those used in ROCKET and its variants, perform well on time‑series classification. It analyzes the proportion of positive values (PPV) pooling operator, proving exact invariance to circular translations and quantifying deviations under finite boundaries. Experiments on the UCR collection show that increasing kernel count yields diminishing returns, while longer kernels raise effective dimensionality and distance correlation, with optimal test performance at intermediate lengths.
arXiv:2609. 10767v1 Announce Type: cross Abstract: We develop an exact almost-sure learning theory for smooth parametric models trained by regularly weighted empirical risk minimization on long-range dependent data.
arXiv:2607. 01279v1 Announce Type: new Abstract: Cross-subject EEG stress detection remains challenging because discriminative stress-related patterns are both subject-dependent and frequency-specific.
arXiv:2608.29304v1 Announce Type: new Abstract: Translating electroencephalography (EEG) into functional magnetic resonance imaging (fMRI) is important for medical neuroimaging, clinical brain-state...