THE PROPOSITIONAL SATISFIABILITY problem (SAT) was the first to be shown NP-complete by Cook and Levin. SAT remained the embodiment of theoretical worst-case hardness. However, in stark contrast to its theoretical hardness, SAT has emerged as a central target problem for efficiently solving a wide variety of computational problems. SAT solving technology has continuously advanced since a breakthrough around the millennium, which catapulted practical SAT solving ahead by orders of magnitudes. Today, the many flavors of SAT technology can be found in all areas of technological innovation.
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Algorithms for manifold learning
The technical report presents popular methods for mapping data into a low-dimensional manifold (nonlinear dimensionality reduction). Specifically, it presents Isomap, Locally Linear Embedding, Laplacian Eigenmaps, Semidefinite Embedding and variants of those.
Geometric data analysis based on manifold learning with applications for image understanding
The conference paper gives in the first section a brief and easy understandable introduction into the basics of Riemannian geometry. Furthermore, it gives a review of classical methods for mapping data into a low-dimensional manifold / nonlinear dimensionality reduction like Local Linear Embedding (LLE), Isometric Feature Mapping (ISOMAP) and Local Riemannian Manifold Learning (LRML).
Terse notes on Riemannian geometry
The technical report gives a compact introduction into the basic definitions and theorems of Riemannian geometry, Lie groups & Lie algebras and symmetric spaces. Key concepts like smooth manifolds, tangent spaces, geodesics as well as the exponential map and logarithm map are presented.
Learning on manifolds
The conference paper provides a brief introduction into manifolds from a computer vision perspective. Important manifolds for this research field, like symmetric positive definite matrices and affine transformation matrices, are presented. Furthermore, deep learning methods for important applications like motion estimation, affine motion tracking and pose invariant object detection are outlined.
A comprehensive survey of geometric deep learning
The survey provides a comprehensive overview of deep learning methods for geometric data (point clouds, voxels, network graphs etc.). The relevant knowledge and theoretical background of geometric deep learning is presented first. In the following section, different network models for graph and manifold data are reviewed. Finally, applications of these methods in various fields and… Continue reading A comprehensive survey of geometric deep learning