Ponente
Descripción
Recent work at the intersection of Topological Data Analysis (TDA) and machine learning has highlighted the potential of persistent homology to construct feature representations for image classification problems (Hensel, F. et al., Front. Artif. Intell. 4, 681108, 2021; Zia, A. et al., Artif. Intell. Rev. 57, 77, 2024). In medical image analysis, this perspective has motivated the use of mathematically grounded descriptors that can complement learning-based approaches by characterizing topological information in the data (Singh, Y. et al., Insights Imaging 14, 58, 2023). In this work, we investigate the discriminative capacity of descriptors derived from cubical persistent homology in breast ultrasound image classification.
Ultrasound images are modeled through intensity-induced filtrations on cubical complexes, from which persistent homology in dimensions 0 and 1 is computed. These homological dimensions correspond, respectively, to connected components and one-dimensional cycles. The resulting persistence information is vectorized using Betti functions and Persistence Images, yielding fixed-length topological representations suitable for classical machine learning models.
Experiments on the BUSI dataset (Al-Dhabyani, W. et al., Data Brief 28, 104863, 2020) show that these descriptors provide promising performance in the binary classification of benign and malignant lesions. In particular, the best results were obtained using Persistence Image representations combined with an SVM-RBF classifier, achieving a ROC-AUC of 0.886, Accuracy of 0.818, Recall of 0.844, and Precision of 0.750. Betti-function representations also achieved ROC-AUC values above 0.80 when combined with classical machine learning models such as Support Vector Machines, Random Forest, and XGBoost. These findings support the use of cubical persistent homology as a source of meaningful descriptors for breast ultrasound image classification. This work will be extended to additional medical imaging datasets and to hybrid approaches integrating persistent homology with deep learning architectures, including convolutional neural networks and differentiable topological layers (Carrière, M. et al., in: Proc. 23rd Int. Conf. Artificial Intelligence and Statistics, 2020; Hofer, C. et al., in: Proc. 31st Int. Conf. Neural Information Processing Systems, pp. 1633–1643, 2017).