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

Giuseppe Sergioli, Carlo Cuccu+5 more|arXiv (Cornell University)|Feb 27, 2026

Radiomics and Machine Learning in Medical Imaging0 citations

TL;DR

This paper introduces a quantum-inspired Pretty Good Measurement (PGM) classifier for multi-class radiomics, applied to NSCLC subtyping and prostate cancer risk stratification, showing competitive or improved performance over classical baselines.

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.

Motivation & Objective

• Motivate and formulate a genuinely multi-class quantum-inspired classifier based on Pretty Good Measurement for discriminating among class-dependent density operators.
• Encode input features as quantum states and construct a single multi-outcome POVM to perform classification without one-vs-rest reductions.
• Evaluate the PGM classifier on two radiomics benchmarks (NSCLC histopathology subtyping and PSMA-PET/CT-based PCa risk stratification) under standard baselines.
• Analyze how class geometry and overlap influence discriminative performance and robustness to acquisition heterogeneity.

Proposed method

• Represent each input x by a density operator rho_x via a feature map (encoding map).
• Create class representatives as quantum centroids rho^(i) by averaging encoded training states per class.
• Construct a single l-outcome POVM {F_i} using Pretty Good Measurement with mixture sigma = sum_i p_i rho^(i) and E_i = sigma^{-1/2} p_i rho^(i) sigma^{-1/2}, completed to a proper POVM with F_i = E_i + (1/l) P_ker(sigma).
• Score f_i(x) = tr(F_i rho_x) and predict Cl_PGM(x) = argmax_i f_i(x).
• Optionally extend with tensor copies: encode rho_x^{⊗n} and form class representatives rho^{(n)}_(i) and repeat PGM to obtain F^{(n)}_i and f^{(n)}_i(x).
• Hyperparameters include encoding choice, number of copies, and rescaling factor alpha; grid-search over these on validation data.

Experimental results

Research questions

• RQ1 Can a genuinely multi-class quantum-inspired classifier based on PGM compete with state-of-the-art radiomics baselines on high-dimensional biomedical data?
• RQ2 How does the geometry of class encoding and overlap affect discrimination performance in NSCLC subtyping and PCa risk stratification?
• RQ3 Does the PGM approach handle multicenter acquisition variability as effectively as or better than classical methods under IBSI-standardized radiomics pipelines?
• RQ4 What is the impact of using tensor copies (n>1) and feature encoding choices on classification accuracy and robustness?

Key findings

• The PGM-based classifier is consistently competitive with classical baselines across the NSCLC and PCa datasets.
• In NSCLC, the method especially excels in binary and three-class settings, with competitive performance in the four-class case.
• In PCa, the PGM approach remains close to strong ensemble baselines and shows clinically relevant sensitivity–specificity trade-offs across feature-selection scenarios.
• The experiments align with established radiomics pipelines (IBSI-compliant features, ComBat harmonization) and utilize matched evaluation protocols, enabling direct comparisons with prior work.
• The study supports the relevance of quantum-inspired, multi-class decision rules as a viable extension of quantum state discrimination for high-dimensional biomedical data.