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Journal of Interdisciplinary Mathematics cover

Journal of Interdisciplinary Mathematics

(Since 1998)
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502
CiteScore 2025: 1.9 (Q2)

CiteScore 2025: 1.9 (Q2)

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Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
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Journal of Interdisciplinary Mathematics
Open Access Research Article

Manifold learning and differential geometry for disease detection and risk prediction

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pp. 2059–2069Vol. 28Issue 6September 2025DOI: 10.47974/JIM-2347XML
Received:
09 Dec 2024
Published Online:
30 Sep 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2347
Pages:
2059–2069

Abstract

Healthcare datasets pose unique challenges: they are large, varied, and often contain hidden structure that standard analysis methods struggle to reveal. In this work, we propose a practical approach that combines tools from manifold learning (for example, Isomap or t-SNE) with ideas borrowed from differential geometry (such as curvature and geodesics). First, we use manifold techniques to reduce the dimensionality of complex, multi-modal inputs—ranging from wearable sensors and imaging scans to electronic health records while still preserving the data’s underlying shape. Next, by examining the resulting low-dimensional “surface” through a geometric lens, we extract features that shed light on subtle relationships among patients’ measurements, relationships that might otherwise go unnoticed. These geometric insights are then woven into a deep neural network, effectively guiding the model toward more reliable predictions of disease presence and future health risks. In our experiments, this hybrid strategy yields noticeably higher accuracy for early detection compared to conventional methods. Importantly, because we can trace predictions back to geometric properties such as how data points “bend” or “connect” on the inferred manifold clinicians gain a clearer picture of why certain patients are flagged as high risk. Beyond the technical gains, this framework is well suited for real-world healthcare settings, including resource-limited environments common in parts of India. By focusing on interpretable, scalable methods, we aim to deliver a solution that can be adopted without extensive computational resources. Looking ahead, we plan to refine the pipeline for near-real-time use enabling, for instance, community health workers to monitor groups of patients at once and to explore applications in population-level screening and preventative healthcare.

Keywords

Manifold learningDifferential geometryDisease detectionGeometric deep learningHigh-dimensional dataAI in Healthcare

Subject Classifications

62H25

References

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