arXiv Statistics ML

A Mechanistic Interpretation of Prescribed-Parameter Convolutional Kernels

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 Machine Learning
Aug 20

Multi-Class Electrical and Mechanical Fault Classification Using Random Convolutional Kernels

The paper evaluates SelF‑Rocket, a random convolutional kernel-based method, for multi‑class diagnosis of mechanical and electrical faults in rotating machinery. It introduces a multivariate extension of SelF‑Rocket and compares it with leading ROCKET‑based methods on two public benchmarks, MaFaulDa and ITSC‑UDG. Results show SelF‑Rocket achieves the best accuracy‑latency trade‑off, excelling on MaFaulDa and remaining competitive on the more challenging ITSC‑UDG dataset.

By Mouhamadou Mansour Lo, Mouad Talbaoui, Gildas Morvan, Mathieu Rossi, Fabrice Morganti, David Mercier
arXiv Machine Learning
Sep 10

Minimum distance classification for nonlinear dynamical systems

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.

By Dominique Martinez
arXiv Machine Learning
Jun 17

Eigen-Spike Emergence and Quadratic Equivalents for Conjugate Kernels on Nonlinearly Separable Data

arXiv:2605. 29669v2 Announce Type: replace-cross Abstract: Recent work in random matrix theory (RMT) has developed the notion of deterministic equivalents: typically linear surrogate models that approximate the spectral behavior of large nonlinear random matrices, such as nonlinear feature maps in neural networks (NNs).

By Collin Cranston, Zhichao Wang, Todd Kemp, Michael W. Mahoney