Local linear transformation embedding

Authors:
Chenping Hou;Jing Wang;Yi Wu;Dongyun Yi
Affiliations:
Department of Mathematics and System Science, National University of Defense Technology, Changsha 410073, China;School of Information Science and Technology, Huaqiao University, Quanzhou 362021, China;Department of Mathematics and System Science, National University of Defense Technology, Changsha 410073, China;Department of Mathematics and System Science, National University of Defense Technology, Changsha 410073, China
Venue:
Neurocomputing
Year:
2009

Citing 13
Cited 3

Think globally, fit locally: unsupervised learning of low dimensional manifolds

The Journal of Machine Learning Research
A kernel view of the dimensionality reduction of manifolds

ICML '04 Proceedings of the twenty-first international conference on Machine learning
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment

SIAM Journal on Scientific Computing
Neighborhood Preserving Embedding

ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Graph Embedding and Extensions: A General Framework for Dimensionality Reduction

IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust locally linear embedding

Pattern Recognition
Denoising using local projective subspace methods

Neurocomputing
Kernel extrapolation

Neurocomputing
Letters: A new nonlinear feature extraction method for face recognition

Neurocomputing
Discriminant Locally Linear Embedding With High-Order Tensor Data

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Enhancing Human Face Detection by Resampling Examples Through Manifolds

IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Marginal Fisher Analysis and Its Variants for Human Gait Recognition and Content- Based Image Retrieval

IEEE Transactions on Image Processing
Human Gait Recognition With Matrix Representation

IEEE Transactions on Circuits and Systems for Video Technology

Supervised learning of local projection kernels

Neurocomputing
Locally linear embedding: a survey

Artificial Intelligence Review
Robust linearly optimized discriminant analysis

Neurocomputing

Quantified Score

Hi-index	0.01

Visualization

Abstract

Dimensionality reduction is vital in many fields and locally linear embedding (LLE) is one of the most important approaches. However, LLE is unavoidable to derive the nonuniform wraps and folds when the data are of low sample density or unevenly sampled. LLE would also fail when the data are contaminated by even small noises. We have analyzed the performance of LLE and pointed out the reason why LLE fails. An improved algorithm, local linear transformation embedding (LLTE), is then proposed. Local linear transformation is performed on nearby points. The 'Three-stage LLTE' is also provided when the data has outliers. Comparing with LLE and Local tangent space alignment (LTSA), LLTE could derive more practical embedding than LLE and has wider application prospect than LTSA. Meanwhile, it exploits the tight relations between LLE/LLTE and LTSA. Several experiments and numerical results demonstrate the potential of our algorithm.