Persistent Homology vs. Learning Methods: A Comparative Study in Limited Data Scenarios

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dc.contributor.authorVia, Andrea Dien_US
dc.contributor.authorVia, Roberto Dien_US
dc.contributor.authorFugacci, Uldericoen_US
dc.contributor.editorCaputo, Arielen_US
dc.contributor.editorGarro, Valeriaen_US
dc.contributor.editorGiachetti, Andreaen_US
dc.contributor.editorCastellani, Umbertoen_US
dc.contributor.editorDulecha, Tinsae Gebrechristosen_US
dc.date.accessioned2024-11-11T12:48:10Z
dc.date.available2024-11-11T12:48:10Z
dc.date.issued2024
dc.description.abstractThis exploratory study compares persistent homology methods with traditional machine learning and deep learning techniques for label-efficient classification. We propose pure topological approaches, including persistence thresholding and Bottleneck distance classification, and explore hybrid methods combining persistent homology with machine learning. These are evaluated against conventional machine learning algorithms and deep neural networks on two binary classification tasks: surface crack detection and malaria cell identification. We assess performance across various number of samples per class, ranging from 1 to 500. Our study highlights the efficacy of persistent homology-based methods in low-data scenarios. Using the Bottleneck distance approach, we achieve 95.95% accuracy in crack detection and 93.11% in malaria diagnosis with only one labeled sample per class. These results outperform the best performance from machine learning models, which achieves 69.40% and 39.75% accuracy, respectively, and deep learning models, which attains up to 95.96% in crack detection and 62.72% in malaria diagnosis. This demonstrates the superior performance of topological methods in classification tasks with few labeled data. Hybrid approaches demonstrate enhanced performance as the number of labeled samples increases, effectively leveraging topological features to boost classification accuracy. This study highlights the robustness of topological methods in extracting meaningful features from limited data, offering promising directions for efficient, label-conserving classification strategies. The results underscore the worth of persistent homology, both as a standalone tool and in combination with machine learning, particularly in domains where labeled data scarcity challenges traditional deep learning approaches.en_US
dc.description.sectionheadersAI and Image Processing
dc.description.seriesinformationSmart Tools and Applications in Graphics - Eurographics Italian Chapter Conference
dc.identifier.doi10.2312/stag.20241338
dc.identifier.isbn978-3-03868-265-3
dc.identifier.issn2617-4855
dc.identifier.pages13 pages
dc.identifier.urihttps://doi.org/10.2312/stag.20241338
dc.identifier.urihttps://diglib.eg.org/handle/10.2312/stag20241338
dc.publisherThe Eurographics Associationen_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.titlePersistent Homology vs. Learning Methods: A Comparative Study in Limited Data Scenariosen_US
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Italian Chapter Conference 2024 - Smart Tools and Apps in Graphics