Hamiltonian cycle clustering with asymmetric correlation

Analysts who explore high-dimensional data usually want three answers at once: Which samples belong together, how close the resulting groups are, and who influences whom accordingly. Classical clustering provides only hard labels, hiding both inter-cluster affinities and correlation flow. We introduce Hamiltonian Cycle Clustering with Asymmetric Correlation HCC-AC, a framework that converts the clustering task into an interpretable map where structure and directionality are visible at a single glance. HCC-AC first learns soft memberships by optimizing a joint global–local loss, preserving manifold structure while turning each label into a probability. These probabilities drive a Hamiltonian-cycle embedding: cluster anchors are ordered by affinity and placed evenly on a circle; samples fall radially towards their most-likely anchor, so clusters, their similarities (arc lengths), and outliers emerge immediately. Directed arrows connect anchors, their lengths showing correlation strength, transforming the map into a legible narrative of influence. Experiments on five benchmark datasets demonstrate that HCC-AC improves the knowledge discovery in clustering, i.e., indexes the clustering results, flags outliers reliably, and uncovers correlation pathways.