🍩 Database of Original & Non-Theoretical Uses of Topology
(found 5 matches in 0.001225s)
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Stochastic Multiresolution Persistent Homology Kernel. (2016)
Xiaojin Zhu, Ara Vartanian, Manish Bansal, Duy Nguyen, Luke Brandl -
Persistence Weighted Gaussian Kernel for Topological Data Analysis (2016)
Genki Kusano, Yasuaki Hiraoka, Kenji FukumizuAbstract
Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and... -
Abnormal Hole Detection in Brain Connectivity by Kernel Density of Persistence Diagram and Hodge Laplacian (2018)
Hyekyoung Lee, Moo K. Chung, Hyejin Kang, Hongyoon Choi, Yu Kyeong Kim, Dong Soo Lee -
Topology-Based Kernels With Application to Inference Problems in Alzheimer’s Disease (2011)
Deepti Pachauri, Chris Hinrichs, Moo K. Chung, Sterling C. Johnson, Vikas SinghAbstract
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.