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.
By Michael L. Wells, Kamel Lahouel, Victor Rielly, Bruno Jedynak
Cluster labels are often used twice: first to discover groups, and then to test whether the discovered groups differ. This double use of the data makes ordinary two-sample $p$-values anti-conservative...
arXiv:2512. 05926v2 Announce Type: replace Abstract: We consider the fundamental problem of balanced $k$-means clustering.
By Wenyan Luo, Dustin G. Mixon
arXiv:2608. 14215v1 Announce Type: new Abstract: Constrained optimization extends classical optimization by integrating side information, making it widely applicable across scientific and engineering domains.
By Johanna Hillebrand, Jan H\"ockendorff, J\"urgen Kusche, Kelin Luo, Heiko R\"oglin, Melanie Schmidt, Christian Sohler, Bernd Uebbing
arXiv:2509. 22879v2 Announce Type: replace-cross Abstract: Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions.
By Sre\'cko {\DJ}ura\v{s}inovi\'c, Jean-Bernard Lasserre, Victor Magron
arXiv:2610.33177v1 Announce Type: new
Abstract: The Gaussian Mixture Model (abbrv. GMM) is a classic generative model for clustered data, for which spectral clustering based on dimension reduction vi...
By Xiaoyu Dong, Subhro Ghosh, Soumendu Sundar Mukherjee, Himasish Talukdar
arXiv:2607. 08987v1 Announce Type: new Abstract: Spectral embedding methods are widely used for dimensionality reduction and clustering of high-dimensional datasets with intrinsic low-dimensional structures.
By Yeari Vigder, Paulina Hoyos, David Thong, Joakim and\'en, Joe Kileel, Amit Moscovich
arXiv:2606.20811v2 Announce Type: replace-cross
Abstract: We study the problem of system identification in heterogeneous settings, where different systems may follow distinct underlying dynamics. Exi...
By Abdulmoneam Ali, Dipankar Maity, Ahmed Arafa
arXiv:2609.06468v1 Announce Type: new
Abstract: K-Means is one of the most widely used clustering algorithms, but its susceptibility to initial centroid selection remains a primary bottleneck for its...
By Abhiyan Dhakal (Kathmandu University), Pranish Kafle (Kathmandu University), Rajani Chulyadyo (Kathmandu University)
arXiv:2401. 10927v3 Announce Type: replace-cross Abstract: In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of $2$ sub-gaussian distributions in $\mathbb{R}^p$.
By Shuheng Zhou
The paper introduces a control‑theoretic framework for evolutionary clustering using quasi‑stationary Mean Field Games. Each cluster is modeled as a probability density whose dynamics follow a Fokker–Planck equation, while a stationary Hamilton–Jacobi equation determines the velocity field. In a Gaussian specialization, affine dynamics replicate the mean and covariance trajectories of the classical Expectation–Maximization algorithm, and the authors propose causal and non‑causal time‑averaged log‑likelihood objectives to enhance temporal coherence, along with a fully density‑based numerical implementation for non‑Gaussian components. The method is evaluated on synthetic and real time‑dependent datasets, compared to snapshot Expectation–Maximization, temporally smoothed observations, and an evolutionary k‑means baseline.
By Alessio Basti, Fabio Camilli, Adriano Festa
arXiv:2607. 09490v1 Announce Type: cross Abstract: Terminal embeddings have emerged as a powerful tool for dimension reduction.
By Alexander Munteanu, Matteo Russo, David Saulpic, Chris Schwiegelshohn