Dimension reduction by local principal component analysis
Neural Computation
Independent component analysis: theory and applications
Independent component analysis: theory and applications
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
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
SIAM Journal on Scientific Computing
Face Recognition Using Laplacianfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graph Embedding: A General Framework for Dimensionality Reduction
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Incremental Nonlinear Dimensionality Reduction by Manifold Learning
IEEE Transactions on Pattern Analysis and Machine Intelligence
Edge-Preserving Image Denoising and Estimation of Discontinuous Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust locally linear embedding
Pattern Recognition
Local smoothing for manifold learning
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Locally linear embedding: a survey
Artificial Intelligence Review
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Manifold learning is an important dimensionality reduction tool that discovers the structure of high dimensional data and provides understanding of multidimensional patterns in data mining, pattern recognition, and machine learning. Several manifold learning algorithms are applied to extract the intrinsic features of different prototypes in high dimensional space by preserving the local geometric characteristics. However, due to the locality geometry preservation, these manifold learning methods, including locally linear embedding (LLE), are sensitive to noise. To solve the noisy manifold learning problem, this paper proposes a Neighbor Smoothing Embedding (NSE) for noisy points sampled from a nonlinear manifold. Based on LLE and local linear surface estimator, the NSE smoothes the neighbors of each manifold data and then computes the reconstruction matrix of the projections on the principal surface. Experiments on synthetic data as well as real world patterns demonstrate that the suggested algorithm can efficiently maintain an accurate low-dimensional representation of the noisy manifold data with less distortion, and give higher average classification rates compared to others.