Semi-supervised hyperbolic graph deep clustering for estimation of pediatric reference intervals

Jianguo Zheng; Fanxia Zeng; Yongqiang Tang; Xiaoxia Peng; Ruohua Yan; Jun Zhao; Yaguang Peng; Wensheng Zhang; Jianguo Zheng; Fanxia Zeng; Yongqiang Tang; Xiaoxia Peng; Ruohua Yan; Jun Zhao; Yaguang Peng; Wensheng Zhang

doi:10.3934/era.2026275

Electronic Research Archive

2026, Volume 34, Issue 9: 6286-6314. doi: 10.3934/era.2026275

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Semi-supervised hyperbolic graph deep clustering for estimation of pediatric reference intervals

1.
Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
2.
School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 100049, China
3.
School of Artificial Intelligence, Shenzhen Polytechnic University, Shenzhen 518055, China
4.
National Center for Clinical Laboratories, National Center for Children's Health, Beijing Children's Hospital, Capital Medical University, Beijing 100045, China
† The authors contributed equally to this work

Received: 20 November 2025 Revised: 01 July 2026 Accepted: 09 July 2026 Published: 17 July 2026

Pediatric biomarker reference intervals (RIs) are crucial for clinical diagnosis and health assessment, but the establishment of RIs is often limited by issues such as scarce labeled data and the inadaptability of traditional methods to implicit hierarchical data distributions. To overcome these challenges, we proposed a semi-supervised model integrating partial supervised information guidance and hyperbolic space representation for efficient prediction of pediatric biomarker reference intervals. By introducing hyperbolic space exponential mapping, we mapped the preprocessed high-dimensional features from Euclidean space to the hyperbolic space of the Poincaré ball. Leveraging the negative curvature property of hyperbolic space, the model more accurately characterizes the hierarchical distribution patterns of biomarkers. The partially labeled samples guide hyperbolic representation learning through a supervised loss, and the structural information of unlabeled samples guide the reconstruction of unsupervised loss. This enables the collaborative use of a small number of labeled samples and a large number of unlabeled samples, balancing model performance and data collection cost. Analytical and comparative experiments were conducted on pediatric datasets using two biomarkers, validating the proposed method as a proof of concept.
- indirect estimation,
- reference interval,
- deep clustering,
- graph neural network,
- semi-supervised learning
Citation: Jianguo Zheng, Fanxia Zeng, Yongqiang Tang, Xiaoxia Peng, Ruohua Yan, Jun Zhao, Yaguang Peng, Wensheng Zhang. Semi-supervised hyperbolic graph deep clustering for estimation of pediatric reference intervals[J]. Electronic Research Archive, 2026, 34(9): 6286-6314. doi: 10.3934/era.2026275

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Abstract

Pediatric biomarker reference intervals (RIs) are crucial for clinical diagnosis and health assessment, but the establishment of RIs is often limited by issues such as scarce labeled data and the inadaptability of traditional methods to implicit hierarchical data distributions. To overcome these challenges, we proposed a semi-supervised model integrating partial supervised information guidance and hyperbolic space representation for efficient prediction of pediatric biomarker reference intervals. By introducing hyperbolic space exponential mapping, we mapped the preprocessed high-dimensional features from Euclidean space to the hyperbolic space of the Poincaré ball. Leveraging the negative curvature property of hyperbolic space, the model more accurately characterizes the hierarchical distribution patterns of biomarkers. The partially labeled samples guide hyperbolic representation learning through a supervised loss, and the structural information of unlabeled samples guide the reconstruction of unsupervised loss. This enables the collaborative use of a small number of labeled samples and a large number of unlabeled samples, balancing model performance and data collection cost. Analytical and comparative experiments were conducted on pediatric datasets using two biomarkers, validating the proposed method as a proof of concept.

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