🍩 Database of Original & Non-Theoretical Uses of Topology

(found 3 matches in 0.00129s)

  1. Euler Characteristic Surfaces (2021)

    Gabriele Beltramo, Rayna Andreeva, Ylenia Giarratano, Miguel O. Bernabeu, Rik Sarkar, Primoz Skraba
    Abstract We 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.

  2. Topological Detection of Alzheimer’s Disease Using Betti Curves (2021)

    Ameer Saadat-Yazdi, Rayna Andreeva, Rik Sarkar
    Abstract Alzheimer’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.

  3. Machine Learning and Topological Data Analysis Identify Unique Features of Human Papillae in 3D Scans (2023)

    Rayna Andreeva, Anwesha Sarkar, Rik Sarkar
    Abstract The tongue surface houses a range of papillae that are integral to the mechanics and chemistry of taste and textural sensation. Although gustatory function of papillae is well investigated, the uniqueness of papillae within and across individuals remains elusive. Here, we present the first machine learning framework on 3D microscopic scans of human papillae (n = 2092), uncovering the uniqueness of geometric and topological features of papillae. The finer differences in shapes of papillae are investigated computationally based on a number of features derived from discrete differential geometry and computational topology. Interpretable machine learning techniques show that persistent homology features of the papillae shape are the most effective in predicting the biological variables. Models trained on these features with small volumes of data samples predict the type of papillae with an accuracy of 85%. The papillae type classification models can map the spatial arrangement of filiform and fungiform papillae on a surface. Remarkably, the papillae are found to be distinctive across individuals and an individual can be identified with an accuracy of 48% among the 15 participants from a single papillae. Collectively, this is the first unprecedented evidence demonstrating that tongue papillae can serve as a unique identifier inspiring new research direction for food preferences and oral diagnostics.