Information Geometry and Manifold Learning: A Novel Framework for Analyzing Alzheimer’s Disease MRI Data
<b>Background</b>: Alzheimer’s disease is a progressive neurological condition marked by a decline in cognitive abilities. Early diagnosis is crucial but challenging due to overlapping symptoms among impairment stages, necessitating non-invasive, reliable diagnostic tools. <b>Metho...
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MDPI AG
2025-01-01
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| author | Ömer Akgüller Mehmet Ali Balcı Gabriela Cioca |
| author_facet | Ömer Akgüller Mehmet Ali Balcı Gabriela Cioca |
| author_sort | Ömer Akgüller |
| collection | DOAJ |
| description | <b>Background</b>: Alzheimer’s disease is a progressive neurological condition marked by a decline in cognitive abilities. Early diagnosis is crucial but challenging due to overlapping symptoms among impairment stages, necessitating non-invasive, reliable diagnostic tools. <b>Methods</b>: We applied information geometry and manifold learning to analyze grayscale MRI scans classified into No Impairment, Very Mild, Mild, and Moderate Impairment. Preprocessed images were reduced via Principal Component Analysis (retaining 95% variance) and converted into statistical manifolds using estimated mean vectors and covariance matrices. Geodesic distances, computed with the Fisher Information metric, quantified class differences. Graph Neural Networks, including Graph Convolutional Networks (GCN), Graph Attention Networks (GAT), and GraphSAGE, were utilized to categorize impairment levels using graph-based representations of the MRI data. <b>Results</b>: Significant differences in covariance structures were observed, with increased variability and stronger feature correlations at higher impairment levels. Geodesic distances between No Impairment and Mild Impairment (58.68, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo><</mo><mn>0.001</mn></mrow></semantics></math></inline-formula>) and between Mild and Moderate Impairment (58.28, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo><</mo><mn>0.001</mn></mrow></semantics></math></inline-formula>) are statistically significant. GCN and GraphSAGE achieve perfect classification accuracy (precision, recall, F1-Score: 1.0), correctly identifying all instances across classes. GAT attains an overall accuracy of 59.61%, with variable performance across classes. <b>Conclusions</b>: Integrating information geometry, manifold learning, and GNNs effectively differentiates AD impairment stages from MRI data. The strong performance of GCN and GraphSAGE indicates their potential to assist clinicians in the early identification and tracking of Alzheimer’s disease progression. |
| format | Article |
| id | doaj-art-945ce307a2a746a3900f263eee0a4404 |
| institution | Kabale University |
| issn | 2075-4418 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
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| series | Diagnostics |
| spelling | doaj-art-945ce307a2a746a3900f263eee0a44042025-01-24T13:28:55ZengMDPI AGDiagnostics2075-44182025-01-0115215310.3390/diagnostics15020153Information Geometry and Manifold Learning: A Novel Framework for Analyzing Alzheimer’s Disease MRI DataÖmer Akgüller0Mehmet Ali Balcı1Gabriela Cioca2Department of Mathematics, Faculty of Science, Mugla Sitki Kocman University, Muğla 48000, TurkeyDepartment of Mathematics, Faculty of Science, Mugla Sitki Kocman University, Muğla 48000, TurkeyPreclinical Department, Faculty of Medicine, Lucian Blaga University of Sibiu, 550024 Sibiu, Romania<b>Background</b>: Alzheimer’s disease is a progressive neurological condition marked by a decline in cognitive abilities. Early diagnosis is crucial but challenging due to overlapping symptoms among impairment stages, necessitating non-invasive, reliable diagnostic tools. <b>Methods</b>: We applied information geometry and manifold learning to analyze grayscale MRI scans classified into No Impairment, Very Mild, Mild, and Moderate Impairment. Preprocessed images were reduced via Principal Component Analysis (retaining 95% variance) and converted into statistical manifolds using estimated mean vectors and covariance matrices. Geodesic distances, computed with the Fisher Information metric, quantified class differences. Graph Neural Networks, including Graph Convolutional Networks (GCN), Graph Attention Networks (GAT), and GraphSAGE, were utilized to categorize impairment levels using graph-based representations of the MRI data. <b>Results</b>: Significant differences in covariance structures were observed, with increased variability and stronger feature correlations at higher impairment levels. Geodesic distances between No Impairment and Mild Impairment (58.68, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo><</mo><mn>0.001</mn></mrow></semantics></math></inline-formula>) and between Mild and Moderate Impairment (58.28, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo><</mo><mn>0.001</mn></mrow></semantics></math></inline-formula>) are statistically significant. GCN and GraphSAGE achieve perfect classification accuracy (precision, recall, F1-Score: 1.0), correctly identifying all instances across classes. GAT attains an overall accuracy of 59.61%, with variable performance across classes. <b>Conclusions</b>: Integrating information geometry, manifold learning, and GNNs effectively differentiates AD impairment stages from MRI data. The strong performance of GCN and GraphSAGE indicates their potential to assist clinicians in the early identification and tracking of Alzheimer’s disease progression.https://www.mdpi.com/2075-4418/15/2/153information geometrystatistical manifoldmanifold learningimpairment classes |
| spellingShingle | Ömer Akgüller Mehmet Ali Balcı Gabriela Cioca Information Geometry and Manifold Learning: A Novel Framework for Analyzing Alzheimer’s Disease MRI Data Diagnostics information geometry statistical manifold manifold learning impairment classes |
| title | Information Geometry and Manifold Learning: A Novel Framework for Analyzing Alzheimer’s Disease MRI Data |
| title_full | Information Geometry and Manifold Learning: A Novel Framework for Analyzing Alzheimer’s Disease MRI Data |
| title_fullStr | Information Geometry and Manifold Learning: A Novel Framework for Analyzing Alzheimer’s Disease MRI Data |
| title_full_unstemmed | Information Geometry and Manifold Learning: A Novel Framework for Analyzing Alzheimer’s Disease MRI Data |
| title_short | Information Geometry and Manifold Learning: A Novel Framework for Analyzing Alzheimer’s Disease MRI Data |
| title_sort | information geometry and manifold learning a novel framework for analyzing alzheimer s disease mri data |
| topic | information geometry statistical manifold manifold learning impairment classes |
| url | https://www.mdpi.com/2075-4418/15/2/153 |
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