🍩 Database of Original & Non-Theoretical Uses of Topology

(found 4 matches in 0.00144s)

  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. Constructing Shape Spaces From a Topological Perspective (2017)

    Christoph Hofer, Roland Kwitt, Marc Niethammer, Yvonne Höller, Eugen Trinka, Andreas Uhl
    Abstract We consider the task of constructing (metric) shape space(s) from a topological perspective. In particular, we present a generic construction scheme and demonstrate how to apply this scheme when shape is interpreted as the differences that remain after factoring out translation, scaling and rotation. This is achieved by leveraging a recently proposed injective functional transform of 2D/3D (binary) objects, based on persistent homology. The resulting shape space is then equipped with a similarity measure that is (1) by design robust to noise and (2) fulfills all metric axioms. From a practical point of view, analyses of object shape can then be carried out directly on segmented objects obtained from some imaging modality without any preprocessing, such as alignment, smoothing, or landmark selection. We demonstrate the utility of the approach on the problem of distinguishing segmented hippocampi from normal controls vs. patients with Alzheimer’s disease in a challenging setup where volume changes are no longer discriminative.

  4. Alzheimer Disease Detection From Raman Spectroscopy of the Cerebrospinal Fluid via Topological Machine Learning (2023)

    Francesco Conti, Martina Banchelli, Valentina Bessi, Cristina Cecchi, Fabrizio Chiti, Sara Colantonio, Cristiano D’Andrea, Marella de Angelis, Davide Moroni, Benedetta Nacmias, Maria Antonietta Pascali, Sandro Sorbi, Paolo Matteini
    Abstract The cerebrospinal fluid (CSF) of 19 subjects who received a clinical diagnosis of Alzheimer’s disease (AD) as well as of 5 pathological controls was collected and analyzed by Raman spectroscopy (RS). We investigated whether the raw and preprocessed Raman spectra could be used to distinguish AD from controls. First, we applied standard Machine Learning (ML) methods obtaining unsatisfactory results. Then, we applied ML to a set of topological descriptors extracted from raw spectra, achieving a very good classification accuracy (\textgreater87%). Although our results are preliminary, they indicate that RS and topological analysis may provide an effective combination to confirm or disprove a clinical diagnosis of AD. The next steps include enlarging the dataset of CSF samples to validate the proposed method better and, possibly, to investigate whether topological data analysis could support the characterization of AD subtypes.