Results 31 to 40 of about 1,143,028 (268)
Photonic band structure design using persistent homology
APL Photonics, 2021 The machine learning technique of persistent homology classifies complex systems or datasets by computing their topological features over a range of characteristic scales. There is growing interest in applying persistent homology to characterize physical
Daniel Leykam, Dimitris G. Angelakis
doaj +1 more source
Relational Persistent Homology for Multispecies Data with Application to the Tumor Microenvironment [PDF]
Bulletin of Mathematical Biology, 2023 Topological data analysis (TDA) is an active field of mathematics for quantifying shape in complex data. Standard methods in TDA such as persistent homology (PH) are typically focused on the analysis of data consisting of a single entity (e.g., cells or ...
Bernadette J. Stolz +5 more
semanticscholar +1 more source
A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositions [PDF]
Neural Information Processing Systems, 2023 Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds.
David Loiseaux +2 more
semanticscholar +1 more source
Stability and machine learning applications of persistent homology using the Delaunay-Rips complex [PDF]
Frontiers in Applied Mathematics and Statistics, 2023 Persistent homology (PH) is a robust method to compute multi-dimensional geometric and topological features of a dataset. Because these features are often stable under certain perturbations of the underlying data, are often discriminating, and can be ...
Amisha Mishra, Francis C. Motta
semanticscholar +1 more source
Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening. [PDF]
PLoS Computational Biology, 2018 This work introduces a number of algebraic topology approaches, including multi-component persistent homology, multi-level persistent homology, and electrostatic persistence for the representation, characterization, and description of small molecules and
Zixuan Cang, Lin Mu, Guo-Wei Wei
doaj +1 more source
Promises and pitfalls of topological data analysis for brain connectivity analysis
NeuroImage, 2021 Developing sensitive and reliable methods to distinguish normal and abnormal brain states is a key neuroscientific challenge. Topological Data Analysis, despite its relative novelty, already generated many promising applications, including in ...
Luigi Caputi +2 more
doaj +1 more source
Persistent Homology Meets Object Unity: Object Recognition in Clutter [PDF]
IEEE Transactions on robotics, 2023 Recognition of occluded objects in unseen and unstructured indoor environments is a challenging problem for mobile robots. To address this challenge, we propose a new descriptor, Topological features Of Point cloud Slices (TOPS), for point clouds ...
Ekta U. Samani, A. Banerjee
semanticscholar +1 more source
Object-oriented persistent homology [PDF]
Journal of Computational Physics, 2016 Persistent homology provides a new approach for the topological simplification of big data via measuring the life time of intrinsic topological features in a filtration process and has found its success in scientific and engineering applications. However, such a success is essentially limited to qualitative data classification and analysis.
Wang, Bao, Wei, Guo-Wei
openaire +3 more sources
Leveraging Persistent Homology Features for Accurate Defect Formation Energy Predictions via Graph Neural Networks [PDF]
Chemistry of MaterialsIn machine-learning-assisted high-throughput defect studies, a defect-aware latent representation of the supercell structure is crucial for the accurate prediction of defect properties.
Zhenyao Fang, Qimin Yan
semanticscholar +1 more source
Modeling of persistent homology [PDF]
Communications in Statistics - Theory and Methods, 2019 Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence diagrams.
Agami, Sarit, Adler, Robert J.
openaire +2 more sources