🍩 Database of Original & Non-Theoretical Uses of Topology
(found 4 matches in 0.00165s)
PI-Net: A Deep Learning Approach to Extract Topological Persistence Images (2020)Anirudh Som, Hongjun Choi, Karthikeyan Natesan Ramamurthy, Matthew Buman, Pavan Turaga
AbstractTopological features such as persistence diagrams and their functional approximations like persistence images (PIs) have been showing substantial promise for machine learning and computer vision applications. This is greatly attributed to the robustness topological representations provide against different types of physical nuisance variables seen in real-world data, such as view-point, illumination, and more. However, key bottlenecks to their large scale adoption are computational expenditure and difﬁculty incorporating them in a differentiable architecture. We take an important step in this paper to mitigate these bottlenecks by proposing a novel one-step approach to generate PIs directly from the input data. We design two separate convolutional neural network architectures, one designed to take in multi-variate time series signals as input and another that accepts multi-channel images as input. We call these networks Signal PI-Net and Image PINet respectively. To the best of our knowledge, we are the ﬁrst to propose the use of deep learning for computing topological features directly from data. We explore the use of the proposed PI-Net architectures on two applications: human activity recognition using tri-axial accelerometer sensor data and image classiﬁcation. We demonstrate the ease of fusion of PIs in supervised deep learning architectures and speed up of several orders of magnitude for extracting PIs from data. Our code is available at https://github.com/anirudhsom/PI-Net.
Atom-Specific Persistent Homology and Its Application to Protein Flexibility Analysis (2020)David Bramer, Guo-Wei Wei
AbstractRecently, persistent homology has had tremendous success in biomolecular data analysis. It works by examining the topological relationship or connectivity of a group of atoms in a molecule at a variety of scales, then rendering a family of topological representations of the molecule. However, persistent homology is rarely employed for the analysis of atomic properties, such as biomolecular flexibility analysis or B-factor prediction. This work introduces atom-specific persistent homology to provide a local atomic level representation of a molecule via a global topological tool. This is achieved through the construction of a pair of conjugated sets of atoms and corresponding conjugated simplicial complexes, as well as conjugated topological spaces. The difference between the topological invariants of the pair of conjugated sets is measured by Bottleneck and Wasserstein metrics and leads to an atom-specific topological representation of individual atomic properties in a molecule. Atom-specific topological features are integrated with various machine learning algorithms, including gradient boosting trees and convolutional neural network for protein thermal fluctuation analysis and B-factor prediction. Extensive numerical results indicate the proposed method provides a powerful topological tool for analyzing and predicting localized information in complex macromolecules.
TopoResNet: A Hybrid Deep Learning Architecture and Its Application to Skin Lesion Classification (2019)Yu-Min Chung, Chuan-Shen Hu, Austin Lawson, Clifford Smyth