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

TL;DR

A quantum-inspired approach to supervised multi-class classification based on the PGM, viewed as an operator-valued decision rule derived from quantum state discrimination, which 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.

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.

Figures (7)

• Figure 1: In the first row (NSCLC Case Study) there is an example of CT at the three anatomical planes: sagittal (left), coronal (middle), axial (right). In the second row, there is an example of CT (on the left) and PET/CT (on the right) for the Prostate Case Study. PET/CT highlights high metabolic areas, in this case in the liver, kidneys, spleen and a focal spot in the prostate.
• Figure 2: Comparative evaluation of the proposed PGM classifier against conventional baseline models on the NSCLC two-class dataset. (a) Mean test area under the ROC curve (AUC) reported for each class. (b) Macro-averaged accuracy across the two classes.
• Figure 3: Comparative evaluation of the proposed PGM classifier against conventional baseline models on the NSCLC three-class dataset. (a) Mean test area under the ROC curve (AUC) reported for each class. (b) Macro-averaged accuracy across the three classes.
• Figure 4: Comparative evaluation of the proposed PGM classifier against conventional baseline models on the NSCLC four-class dataset. (a) Mean test area under the ROC curve (AUC) reported for each class. (b) Macro-averaged accuracy across the four classes.
• Figure 5: Win–loss heatmap comparing classifiers for each labeling scenario. The three labeling scenarios are: (a) 2‑class labeling – only two disease categories are considered; (b) 3‑class labeling – three distinct categories are distinguished; (c) 4‑class labeling – all four histopathological subtypes are used. For each pair of classifiers, each cell reports the proportion of classes for which the row classifier attains a higher AUC than the column classifier. Values therefore range from 0$\%$ to 100$\%$ and indicate the fraction of class‑wise pairwise wins. Warmer colors denote a larger proportion of class‑level dominance.