<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-interdisciplinary-mathematics</journal-id>
      <journal-title-group>
        <journal-title>Journal of Interdisciplinary Mathematics</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-012X</issn>
      <issn publication-format="print">0972-0502</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JIM-2347</article-id>
      <title-group>
        <article-title>Manifold learning and differential geometry for disease detection and risk prediction</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Kumar</surname>
            <given-names>Ashish</given-names>
          </name>
          <aff>Department of Computer Science and Engineering, Manipal University Jaipur, Jaipur, Rajasthan, 303007, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Bhagat</surname>
            <given-names>Komal Mehta</given-names>
          </name>
          <aff>Department of Electronics &amp; Communication Engineering, Bhagwan Parshuram Institute of Technology, Rohini, Delhi, 110089, India</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Dadheech</surname>
            <given-names>Pankaj</given-names>
          </name>
          <aff>Department of Computer Science and Engineering, Swami Keshvanand Institute of Technology, Management &amp; Gramothan, Jaipur, Rajasthan, 302017, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Dogiwal</surname>
            <given-names>Sanwta Ram</given-names>
          </name>
          <aff>Department of Information Technology, Swami Keshvanand Institute of Technology, Management &amp; Gramothan, Jaipur, Rajasthan, 302017, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Sharma</surname>
            <given-names>Rakesh</given-names>
          </name>
          <aff>Department of Computer Science and Engineering, Vivekanand Global University, Jaipur, Rajasthan, 303012, India</aff>
        </contrib>
      </contrib-group>
      <volume>28</volume>
      <issue>6</issue>
      <fpage>2059</fpage>
      <lpage>2069</lpage>
      <pub-date date-type="pub">
        <day>30</day>
        <month>09</month>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>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.</p>
      </abstract>
      <kwd-group>
        <kwd>Manifold learning</kwd>
        <kwd>Differential geometry</kwd>
        <kwd>Disease detection</kwd>
        <kwd>Geometric deep learning</kwd>
        <kwd>High-dimensional data</kwd>
        <kwd>AI in Healthcare</kwd>
      </kwd-group>
      <custom-meta-group>
        <custom-meta>
          <meta-name>access</meta-name>
          <meta-value>open</meta-value>
        </custom-meta>
        <custom-meta>
          <meta-name>retracted</meta-name>
          <meta-value>no</meta-value>
        </custom-meta>
      </custom-meta-group>
    </article-meta>
  </front>
</article>
