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

• URL: http://arxiv.org/abs/2604.01930v2
• Date: Thu, 09 Apr 2026 15:13:06 GMT
• Title: Quantum-Inspired Geometric Classification with Correlation Group Structures and VQC Decision Modeling
• Abstract summary: 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.<n>CGR organizes features into anchor-centered correlation neighbourhoods, generating nonlinear, correlation-weighted representations.<n>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.
• Score: 0.5039813366558307
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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