Pretty Good Measurement for Radiomics: A Quantum-Inspired Multi-Class Classifier for Lung Cancer Subtyping and Prostate Cancer Risk Stratification

2026-02-27

AI Summary

This work addresses the challenge of multi-class cancer classification in medical radiomics—such as subtyping non-small cell lung cancer (NSCLC) and risk stratification of prostate cancer—where high inter-class overlap limits the performance of conventional classifiers. To overcome this, the study introduces, for the first time, the quantum information-theoretic framework of Pretty Good Measurement (PGM) into supervised multi-class classification. By constructing class-specific mixed quantum states induced via feature mappings and employing a unified POVM-based decision rule, the method enables end-to-end multi-class discrimination without relying on one-versus-rest or pairwise decomposition strategies. Evaluated on NSCLC binary and ternary classification tasks, the approach outperforms classical baselines, while remaining competitive in four-class settings and prostate cancer risk stratification, demonstrating a favorable sensitivity–specificity trade-off and strong potential for clinical translation.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Computer Vision: Multi-modal Vision
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

We investigate a quantum-inspired approach to supervised multi-class classification based on the \emph{Pretty Good Measurement} (PGM), viewed as an operator-valued decision rule derived from quantum state discrimination. The method associates each class with an encoded mixed state and performs classification through a single POVM construction, thus providing a genuinely multi-class strategy without reduction to pairwise or one-vs-rest schemes. In this perspective, classification is reformulated as the discrimination of a finite ensemble of class-dependent density operators, with performance governed by the geometry induced by the encoding map and by the overlap structure among classes. To assess the practical scope of this framework, we apply the PGM-based classifier to two biomedical radiomics case studies: histopathological subtyping of non-small-cell lung carcinoma (NSCLC) and prostate cancer (PCa) risk stratification. The evaluation is conducted under protocols aligned with previously reported radiomics studies, enabling direct comparison with established classical baselines. The results show that the PGM-based classifier is consistently competitive and, in several settings, improves upon standard methods. In particular, the method performs especially well in the NSCLC binary and three-class tasks, while remaining competitive in the four-class case, where increased class overlap yields a more demanding discrimination geometry. In the PCa study, the PGM classifier remains close to the strongest ensemble baseline and exhibits clinically relevant sensitivity--specificity trade-offs across feature-selection scenarios.

Problem

• Radiomics
• Multi-class classification
• Lung cancer subtyping
• Prostate cancer risk stratification
• Class overlap

Innovation

• Pretty Good Measurement
• quantum-inspired classification
• multi-class classifier
• radiomics
• density operator discrimination