Intrinsic Dimensionality Estimation With Optimally Topology Preserving Maps
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
N-Dimensional Tensor Voting and Application to Epipolar Geometry Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computational Framework for Segmentation and Grouping
Computational Framework for Segmentation and Grouping
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
Unsupervised learning of image manifolds by semidefinite programming
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Geodesic entropic graphs for dimension and entropy estimation in manifold learning
IEEE Transactions on Signal Processing
Translated Poisson Mixture Model for Stratification Learning
International Journal of Computer Vision
Multiple Manifolds Learning Framework Based on Hierarchical Mixture Density Model
ECML PKDD '08 Proceedings of the European conference on Machine Learning and Knowledge Discovery in Databases - Part II
Proximal support vector machine using local information
Neurocomputing
Dimensionality Estimation, Manifold Learning and Function Approximation using Tensor Voting
The Journal of Machine Learning Research
Nonlinear Dimensionality Reduction by Topologically Constrained Isometric Embedding
International Journal of Computer Vision
Use of dimensionality reduction for intrusion detection
ICISS'07 Proceedings of the 3rd international conference on Information systems security
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We address dimensionality estimation and nonlinear manifold inference starting from point inputs in high dimensional spaces using tensor voting. The proposed method operates locally in neighborhoods and does not involve any global computations. It is based on information propagation among neighboring points implemented as a voting process. Unlike other local approaches for manifold learning, the quantity propagated from one point to another is not a scalar, but is in the form of a tensor that provides considerably richer information. The accumulation of votes at each point provides a reliable estimate of local dimensionality, as well as of the orientation of a potential manifold going through the point. Reliable dimensionality estimation at the point level is a major advantage over competing methods. Moreover, the absence of global operations allows us to process significantly larger datasets. We demonstrate the effectiveness of our method on a variety of challenging datasets.