A Two-Channel F-Transform Representation for Early Trajectory Characterization in Iterated Correlation Dynamics

This presentation provides a visual overview of the methodology, mathematical properties, computational evaluation, and geometric interpretation developed in the paper “A Two-Channel F-Transform Representation for Early Trajectory Characterization in Iterated Correlation Dynamics.” The proposed representation summarizes a fixed five-point post-transient window of an iterated Pearson correlation trajectory using two logarithmic signals: the Frobenius step size and the contraction ratio. Each signal is projected onto a three-node triangular fuzzy partition using three zero-degree F-transform coefficients and one centered first-degree coefficient. The resulting eight-dimensional descriptor separates local level from local trend and contraction magnitude from contraction evolution. The presentation covers: - the iterated Pearson correlation map and its contraction observables;- the construction of the eight-dimensional two-channel F-transform descriptor;- Lipschitz stability and exact recovery of affine trends by the centered slope coefficient;- comparison with raw trajectory samples, statistical summaries, and PCA-compressed features;- robustness under repeated train–test splits and a shifted observation window;- feature-importance analysis, principal-component concentration, and exploratory k-means clustering;- the scope, limitations, and future development of the framework. The computational study considers 22 matrix dimensions, ranging from 3 to 2000, with 1000 independently generated trajectories per dimension. The full eight-dimensional F-transform descriptor achieves mean R² = 0.6480, compared with 0.6518 for the ten-dimensional raw trajectory and 0.6528 for the fourteen-dimensional statistical summary. It substantially improves upon the four-dimensional step-size-only descriptor, which achieves mean R² = 0.5001. The first two principal components explain 84.26% of the descriptor variance on average. Among the tested cluster counts k ∈ {3,4,5}, the mean silhouette criterion favors k = 3, indicating reproducible but overlapping coarse organization rather than sharply separated dynamical classes. This presentation is a separate research output associated with the following resources: Associated paper:Alhajj Hassan, I. “A Two-Channel F-Transform Representation for Early Trajectory Characterization in Iterated Correlation Dynamics.” arXiv:2606.05462, 2026.DOI: 10.48550/arXiv.2606.05462 Associated software:Alhajj Hassan, I. “Software and Reproducibility Materials for ‘A Two-Channel F-Transform Representation for Early Trajectory Characterization in Iterated Correlation Dynamics.’” Zenodo, 2026.DOI: 10.5281/zenodo.20057783