Learning Lie groups for invariant visual perception
Proceedings of the 1998 conference on Advances in neural information processing systems II
Group Actions, Homeomorphisms, and Matching: A General Framework
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: Part II
Non-Linear Dimensionality Reduction
Advances in Neural Information Processing Systems 5, [NIPS Conference]
Transformation Invariance in Pattern Recognition-Tangent Distance and Tangent Propagation
Neural Networks: Tricks of the Trade, this book is an outgrowth of a 1996 NIPS workshop
Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
Unsupervised Learning of Image Manifolds by Semidefinite Programming
International Journal of Computer Vision
A duality view of spectral methods for dimensionality reduction
ICML '06 Proceedings of the 23rd international conference on Machine learning
ISICA '08 Proceedings of the 3rd International Symposium on Advances in Computation and Intelligence
Manifold-based learning and synthesis
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Learning 3-D object orientation from images
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Distance approximating dimension reduction of Riemannian manifolds
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Dimensionality Estimation, Manifold Learning and Function Approximation using Tensor Voting
The Journal of Machine Learning Research
Manifold topological multi-resolution analysis method
Pattern Recognition
Learning gradients with gaussian processes
PAKDD'10 Proceedings of the 14th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining - Volume Part II
Orthogonal projection analysis
IScIDE'11 Proceedings of the Second Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
Motion planning and reactive control on learnt skill manifolds
International Journal of Robotics Research
Manifold learning by preserving distance orders
Pattern Recognition Letters
Parallel vector field embedding
The Journal of Machine Learning Research
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In this work we take a novel view of nonlinear manifold learning. Usually, manifold learning is formulated in terms of finding an embedding or 'unrolling' of a manifold into a lower dimensional space. Instead, we treat it as the problem of learning a representation of a nonlinear, possibly non-isometric manifold that allows for the manipulation of novel points. Central to this view of manifold learning is the concept of generalization beyond the training data. Drawing on concepts from supervised learning, we establish a framework for studying the problems of model assessment, model complexity, and model selection for manifold learning. We present an extension of a recent algorithm, Locally Smooth Manifold Learning (LSML), and show it has good generalization properties. LSML learns a representation of a manifold or family of related manifolds and can be used for computing geodesic distances, finding the projection of a point onto a manifold, recovering a manifold from points corrupted by noise, generating novel points on a manifold, and more.