<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-discrete-mathematical-sciences-and-cryptography</journal-id>
      <journal-title-group>
        <journal-title>Journal of Discrete Mathematical Sciences and Cryptography</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-0065</issn>
      <issn publication-format="print">0972-0529</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JDMSC-2295</article-id>
      <title-group>
        <article-title>Finite discrete RGCN model for kinship verification</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Sharma</surname>
            <given-names>Vijay Prakash</given-names>
          </name>
          <aff>Department of Information and Technology, Manipal University Jaipur, Jaipur, Rajasthan, India</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Kumar</surname>
            <given-names>Sunil</given-names>
          </name>
          <aff>Department of Computer and Communication Engineering, Manipal University Jaipur, Jaipur, Rajasthan, India</aff>
        </contrib>
      </contrib-group>
      <volume>28</volume>
      <issue>3</issue>
      <fpage>991</fpage>
      <lpage>1005</lpage>
      <pub-date date-type="pub">
        <day>18</day>
        <month>04</month>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>Kinship verification has been a challenging problem for generations, technology has been trying to resolve the same last two decades, without any success. It determines the blood relation between two people with help of their given pair of images. This problem has attracted significant attention in various fields, such as biometrics, forensic research, and social media, but age and gender differences make this problem more complicated, especially when we want to find the relationship between Descendants with skipped levels like grandparents and grandsons/daughters. In this paper, we proposed a novel approach by formulating kinship data as a finite discrete structure (FDS), which provides a mathematical model of kinship relations. We represent the data as a graph, where nodes denote individuals, and edges determine the relationships among them. This structured representation serves as the foundation for learning relational patterns. Using this Finite Discrete Structure framework, we employ Relational Graph Convolutional Networks (RGCN) to extract and analyze the complex relational dependencies in kinship verification. Initially EfficientNet is used to extract facial features, these feature vectors along with relations, form the graph structure.  RGCN processes this graph to derive kin relations and effectively capture complex patterns within the discrete structured space. To improve model’s ability for enhancing Class-wise discriminability we used ArcFace and Center loss functions to enforce feature separability and robust kinship classification.  We evaluate our approach on the FIW dataset, achieving an accuracy of 89.45%, demonstrating that our method effectively addresses the kinship verification problem within the framework of finite discrete structures. This work highlights the potential of graph-based models in analyzing and classifying complex relationships in structured, discrete domains.</p>
      </abstract>
      <kwd-group>
        <kwd>Finite discrete structure</kwd>
        <kwd>Kinship verification</kwd>
        <kwd>RGCN</kwd>
        <kwd>Feature extraction face image</kwd>
        <kwd>ArcFace loss</kwd>
        <kwd>Center loss</kwd>
      </kwd-group>
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        <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>
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  </front>
</article>
