Robust locally linear embedding

Authors:
Hong Chang;Dit-Yan Yeung
Affiliations:
Department of Computer Science, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;Department of Computer Science, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Venue:
Pattern Recognition
Year:
2006

Citing 7
Cited 30

Matrix analysis

Matrix analysis
Using Generative Models for Handwritten Digit Recognition

IEEE Transactions on Pattern Analysis and Machine Intelligence
A Framework for Robust Subspace Learning

International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
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
Continuous nonlinear dimensionality reduction by kernel eigenmaps

IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Efficient locally linear embeddings of imperfect manifolds

MLDM'03 Proceedings of the 3rd international conference on Machine learning and data mining in pattern recognition

Face recognition using spectral features

Pattern Recognition
Robust self-tuning semi-supervised learning

Neurocomputing
Noisy manifold learning using neighborhood smoothing embedding

Pattern Recognition Letters
Feature extraction using constrained maximum variance mapping

Pattern Recognition
LDR-LLE: LLE with Low-Dimensional Neighborhood Representation

ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
Local linear transformation embedding

Neurocomputing
Stable local dimensionality reduction approaches

Pattern Recognition
Robust feature extraction via information theoretic learning

ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Robust Principal Components for Hyperspectral Data Analysis

ICIAR '09 Proceedings of the 6th International Conference on Image Analysis and Recognition
Enhanced supervised locally linear embedding

Pattern Recognition Letters
Nonlinear dimensionality reduction by locally linear inlaying

IEEE Transactions on Neural Networks
Outlier-resisting graph embedding

Neurocomputing
Finger vein recognition with manifold learning

Journal of Network and Computer Applications
A nonparametric learning approach to range sensing from omnidirectional vision

Robotics and Autonomous Systems
Weighted locally linear embedding for plant leaf visualization

ICIC'10 Proceedings of the Advanced intelligent computing theories and applications, and 6th international conference on Intelligent computing
Robust local tangent space alignment via iterative weighted PCA

Neurocomputing
Locally linear embedding: a survey

Artificial Intelligence Review
High dimensional correspondences from low dimensional manifolds: an empirical comparison of graph-based dimensionality reduction algorithms

ACCV'10 Proceedings of the 2010 international conference on Computer vision - Volume part II
Letters: Extended local tangent space alignment for classification

Neurocomputing
Weighted principal component extraction with genetic algorithms

Applied Soft Computing
Geometrically local embedding in manifolds for dimension reduction

Pattern Recognition
Evolutionary kernel density regression

Expert Systems with Applications: An International Journal
Neighborhood selection and eigenvalues for embedding data complex in low dimension

ACIIDS'12 Proceedings of the 4th Asian conference on Intelligent Information and Database Systems - Volume Part I
Fisher Difference Discriminant Analysis: Determining the Effective Discriminant Subspace Dimensions for Face Recognition

Neural Processing Letters
About eigenvalues from embedding data complex in low dimension

ICSI'12 Proceedings of the Third international conference on Advances in Swarm Intelligence - Volume Part II
Maximal Similarity Embedding

Neurocomputing
Improved locally linear embedding by cognitive geometry

LSMS'07 Proceedings of the 2007 international conference on Life System Modeling and Simulation
A semi-supervised feature selection method using a non-parametric technique with pairwise instance constraints

Journal of Information Science
Statistical shape model for manifold regularization: Gleason grading of prostate histology

Computer Vision and Image Understanding
Regularized discriminant entropy analysis

Pattern Recognition

Quantified Score

Hi-index	0.01

Visualization

Abstract

In the past few years, some nonlinear dimensionality reduction (NLDR) or nonlinear manifold learning methods have aroused a great deal of interest in the machine learning community. These methods are promising in that they can automatically discover the low-dimensional nonlinear manifold in a high-dimensional data space and then embed the data points into a low-dimensional embedding space, using tractable linear algebraic techniques that are easy to implement and are not prone to local minima. Despite their appealing properties, these NLDR methods are not robust against outliers in the data, yet so far very little has been done to address the robustness problem. In this paper, we address this problem in the context of an NLDR method called locally linear embedding (LLE). Based on robust estimation techniques, we propose an approach to make LLE more robust. We refer to this approach as robust locally linear embedding (RLLE). We also present several specific methods for realizing this general RLLE approach. Experimental results on both synthetic and real-world data show that RLLE is very robust against outliers.