🍩 Database of Original & Non-Theoretical Uses of Topology
(found 3 matches in 0.001947s)
Euler Characteristic Surfaces (2021)Gabriele Beltramo, Rayna Andreeva, Ylenia Giarratano, Miguel O. Bernabeu, Rik Sarkar, Primoz Skraba
AbstractWe study the use of the Euler characteristic for multiparameter topological data analysis. Euler characteristic is a classical, well-understood topological invariant that has appeared in numerous applications, including in the context of random fields. The goal of this paper is to present the extension of using the Euler characteristic in higher-dimensional parameter spaces. While topological data analysis of higher-dimensional parameter spaces using stronger invariants such as homology continues to be the subject of intense research, Euler characteristic is more manageable theoretically and computationally, and this analysis can be seen as an important intermediary step in multi-parameter topological data analysis. We show the usefulness of the techniques using artificially generated examples, and a real-world application of detecting diabetic retinopathy in retinal images.
Topological Detection of Alzheimer’s Disease Using Betti Curves (2021)Ameer Saadat-Yazdi, Rayna Andreeva, Rik Sarkar
AbstractAlzheimer’s disease is a debilitating disease in the elderly, and is an increasing burden to the society due to an aging population. In this paper, we apply topological data analysis to structural MRI scans of the brain, and show that topological invariants make accurate predictors for Alzheimer’s. Using the construct of Betti Curves, we first show that topology is a good predictor of Age. Then we develop an approach to factor out the topological signature of age from Betti curves, and thus obtain accurate detection of Alzheimer’s disease. Experimental results show that topological features used with standard classifiers perform comparably to recently developed convolutional neural networks. These results imply that topology is a major aspect of structural changes due to aging and Alzheimer’s. We expect this relation will generate further insights for both early detection and better understanding of the disease.