Quantum-Inspired Geometric Classification with Correlation Group Structures and VQC Decision Modeling

2026-04-02

AI Summary

This study addresses the challenges of few-shot learning, class imbalance, and rare event classification in heterogeneous tabular data by proposing a geometry-aware, quantum-inspired classification framework. The method constructs nonlinear feature representations through correlation-based grouping, integrating both Euclidean and angular similarities. Geometric relationships between samples and class centroids are estimated via the SWAP test, and decisions are made using a variational quantum circuit. The work introduces a novel non-probabilistic margin-fused scoring mechanism and an operating-point-oriented strategy for rare event detection. Evaluated on datasets including Heart Disease, the approach achieves accuracy ranging from 0.8478 to 0.9556. In credit card fraud detection, it attains an 85% recall for the minority class at a low alert rate of 1.31%, with a ROC-AUC of 0.9249.

Abstract

We propose a geometry-driven quantum-inspired classification framework that integrates Correlation Group Structures (CGR), compact SWAP-test-based overlap estimation, and selective variational quantum decision modelling. Rather than directly approximating class posteriors, the method adopts a geometry-first paradigm in which samples are evaluated relative to class medoids using overlap-derived Euclidean-like and angular similarity channels. CGR organizes features into anchor-centered correlation neighbourhoods, generating nonlinear, correlation-weighted representations that enhance robustness in heterogeneous tabular spaces. These geometric signals are fused through a non-probabilistic margin-based fusion score, serving as a lightweight and data-efficient primary classifier for small-to-moderate datasets. On Heart Disease, Breast Cancer, and Wine Quality datasets, the fusion-score classifier achieves 0.8478, 0.8881, and 0.9556 test accuracy respectively, with macro-F1 scores of 0.8463, 0.8703, and 0.9522, demonstrating competitive and stable performance relative to classical baselines. For large-scale and highly imbalanced regimes, we construct compact Delta-distance contrastive features and train a variational quantum classifier (VQC) as a nonlinear refinement layer. On the Credit Card Fraud dataset (0.17% prevalence), the Delta + VQC pipeline achieves approximately 0.85 minority recall at an alert rate of approximately 1.31%, with ROC-AUC 0.9249 and PR-AUC 0.3251 under full-dataset evaluation. These results highlight the importance of operating-point-aware assessment in rare-event detection and demonstrate that the proposed hybrid geometric-variational framework provides interpretable, scalable, and regime-adaptive classification across heterogeneous data settings.

Problem

• heterogeneous data classification
• imbalanced datasets
• rare-event detection
• quantum-inspired classification
• geometric representation

Innovation

• Correlation Group Structures
• Quantum-Inspired Classification
• Geometric Similarity
• Variational Quantum Classifier
• SWAP-test-based Overlap