Signal detection theory: valuable tools for evaluating inductive learning
Proceedings of the sixth international workshop on Machine learning
Using Discriminant Eigenfeatures for Image Retrieval
IEEE Transactions on Pattern Analysis and Machine Intelligence
Performance Evaluation of the Nearest Feature Line Method in Image Classification and Retrieval
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Database for Handwritten Text Recognition Research
IEEE Transactions on Pattern Analysis and Machine Intelligence
Non-linear dimensionality reduction techniques for classification and visualization
Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
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
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
Weighted locally linear embedding for dimension reduction
Pattern Recognition
On the relevance of linear discriminative features
Information Sciences: an International Journal
Locally linear embedding: a survey
Artificial Intelligence Review
| Hi-index | 0.01 |
Locally linear embedding (LLE) is one of the effective and efficient algorithms for nonlinear dimensionality reduction. This paper discusses the stability of LLE, focusing on the optimal weights for extracting local linearity behind the considered manifold. It is proven that there are multiple sets of weights that are approximately optimal and can be used to improve the stability of LLE. A new algorithm using multiple weights is then proposed, together with techniques for constructing multiple weights. This algorithm is called as nonlinear embedding preserving multiple local-linearities (NEML). NEML improves the preservation of local linearity and is more stable than LLE. A short analysis for NEML is also given for isometric manifolds. NEML is compared with the local tangent space alignment (LTSA) in methodology since both of them adopt multiple local constraints. Numerical examples are given to show the improvement and efficiency of NEML.