A UNIFIED FRAMEWORK FOR GEOMETRIC-ENTROPIC INFERENCE: THE P-CPDME MODEL FOR HIGH-DIMENSIONAL DATA CLASSIFICATION

Abstract

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The classification of high-dimensional datasets is frequently compromised by the curse of dimensionality, a phenomenon where traditional machine learning models achieve deceptively high accuracy rates while masking profound geometric instability and predictive uncertainty. To address this critical deficiency, this research proposes the Principal Component Class Probability Distribution based on Maximum Entropy (P-CPDME) framework. By combining dimensionality conditioning with a suite of seven statistical data depth functions such as Mahalanobis, Projection, Spatial,  , Halfspace, Zonoid, and Simplicial, the P-CPDME framework maps complex spatial distances into standardized, information-theoretic probability distributions. Extensive empirical evaluations were conducted across structured synthetic simulations and real-world high-dimensional datasets, including Gasoline chemometrics and Colon Cancer genomics. The results exposed a persistent       Paradox. Standard Euclidean ( ) depth achieved high nominal accuracy (93.55% in Colon Cancer) but suffered from destructive entropy (0.4619), causing its probability reliability to plummet to a negligible 0.3121. In contrast, combinatorial depth function specifically, Simplicial, Zonoid, and Halfspace demonstrated supreme geometric stability, consistently maintaining     values of 1.000 across all domains.