🍩 Database of Original & Non-Theoretical Uses of Topology

(found 4 matches in 0.001227s)

  1. Topological Analysis of Low Dimensional Phase Space Trajectories of High Dimensional EEG Signals for Classification of Interictal Epileptiform Discharges (2023)

    A. Stiehl, M. Flammer, F. Anselstetter, N. Ille, H. Bornfleth, S. Geißelsöder, C. Uhl
    Abstract A new topology based feature extraction method for classification of interictal epileptiform discharges (IEDs) in EEG recordings from patients with epilepsy is proposed. After dimension reduction of the recorded EEG signal, using dynamical component analysis (DyCA) or principal component analysis (PCA), a persistent homology analysis of the resulting phase space trajectories is performed. Features are extracted from the persistent homology analysis and used to train and evaluate a support vector machine (SVM). Classification results based on these persistent features are compared with statistical features of the dimension-reduced signals and combinations of all of these features. Combining the persistent and statistical features improves the results (accuracy 94.7 %) compared to using only statistical feature extraction, whereas applying only persistent features does not achieve sufficient performance. For this classification example the choice of the dimension reduction technique does not significantly influence the classification performance of the algorithm.

  2. Topological Biomarkers for Real-Time Detection of Epileptic Seizures (2022)

    Ximena Fernández, Diego Mateos
    Abstract Automated seizure detection is a fundamental problem in computational neuroscience towards diagnosis and treatment's improvement of epileptic disease. We propose a real-time computational method for automated tracking and detection of epileptic seizures from raw neurophysiological recordings. Our mechanism is based on the topological analysis of the sliding-window embedding of the time series derived from simultaneously recorded channels. We extract topological biomarkers from the signals via the computation of the persistent homology of time-evolving topological spaces. Remarkably, the proposed biomarkers robustly captures the change in the brain dynamics during the ictal state. We apply our methods in different types of signals including scalp and intracranial EEG and MEG, in patients during interictal and ictal states, showing high accuracy in a range of clinical situations.

  3. 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.

  4. Topology-Based Kernels With Application to Inference Problems in Alzheimer’s Disease (2011)

    Deepti Pachauri, Chris Hinrichs, Moo K. Chung, Sterling C. Johnson, Vikas Singh
    Abstract Alzheimer’s disease (AD) research has recently witnessed a great deal of activity focused on developing new statistical learning tools for automated inference using imaging data. The workhorse for many of these techniques is the Support Vector Machine (SVM) framework (or more generally kernel based methods). Most of these require, as a first step, specification of a kernel matrix between input examples (i.e., images). The inner product between images Ii and Ij in a feature space can generally be written in closed form, and so it is convenient to treat as “given”. However, in certain neuroimaging applications such an assumption becomes problematic. As an example, it is rather challenging to provide a scalar measure of similarity between two instances of highly attributed data such as cortical thickness measures on cortical surfaces. Note that cortical thickness is known to be discriminative for neurological disorders, so leveraging such information in an inference framework, especially within a multi-modal method, is potentially advantageous. But despite being clinically meaningful, relatively few works have successfully exploited this measure for classification or regression. Motivated by these applications, our paper presents novel techniques to compute similarity matrices for such topologically-based attributed data. Our ideas leverage recent developments to characterize signals (e.g., cortical thickness) motivated by the persistence of their topological features, leading to a scheme for simple constructions of kernel matrices. As a proof of principle, on a dataset of 356 subjects from the ADNI study, we report good performance on several statistical inference tasks without any feature selection, dimensionality reduction, or parameter tuning.