Learning Lie groups for invariant visual perception
Proceedings of the 1998 conference on Advances in neural information processing systems II
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
Semi-Supervised Learning on Riemannian Manifolds
Machine Learning
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
SIAM Journal on Scientific Computing
Label Propagation through Linear Neighborhoods
IEEE Transactions on Knowledge and Data Engineering
Unsupervised learning of image manifolds by semidefinite programming
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
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In this paper, instead of the ordinary manifold assumption, we introduced the bundle manifold assumption that imagines data points lie on a bundle manifold Under this assumption, we proposed an unsupervised algorithm, named as Bundle Manifold Embedding (BME), to embed the bundle manifold into low dimensional space In BME, we construct two neighborhood graphs that one is used to model the global metric structure in local neighborhood and the other is used to provide the information of subtle structure, and then apply the spectral graph method to obtain the low-dimensional embedding Incorporating some prior information, it is possible to find the subtle structures on bundle manifold in an unsupervised manner Experiments conducted on benchmark datasets demonstrated the feasibility of the proposed BME algorithm, and the difference compared with ISOMAP, LLE and Laplacian Eigenmaps.