Feature Space Dimensional Reduction Based on Quantum Spin-Correlation Encoding

This study introduces a quantum-inspired framework for high-dimensional feature compression by encoding data pairs as parameters in a two-site spin-Hamiltonian system. Unlike traditional manifold learning techniques that suffer from “neighborhood tearing” at extreme compression ratios [1,2,5], the proposed method utilizes a ground-state solver to stabilize local topological structures. We evaluate the method’s performance across a gradient of 512 to 1 dimension using information-theoretic and ordinal metrics. Our results demonstrate a fundamental Dual-Phase behavior: (i) a High-Fidelity Spin Phase (m > 128) where global geometric alignment is preserved with near-unit cosine similarity, and (ii) a Cohesive Topological Phase (m < 128) where global reference frames fracture, yet local neighborhoods exhibit “rigid-body translation.” We prove that while absolute ordinal ranks drift during compression, the local variance remains below 4%, confirming that the Hamiltonian alignment mechanism preserves cluster integrity [7]. This approach is uniquely suited for community detection and resilient non-parametric clustering in deeply compressed feature spaces.