An Algorithm for Finding Best Matches in Logarithmic Expected Time
ACM Transactions on Mathematical Software (TOMS)
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
Two-Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
SIAM Journal on Scientific Computing
Incremental Nonlinear Dimensionality Reduction by Manifold Learning
IEEE Transactions on Pattern Analysis and Machine Intelligence
Learning Nonlinear Image Manifolds by Global Alignment of Local Linear Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Classification of gene-expression data: The manifold-based metric learning way
Pattern Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Improving geodesic distance estimation based on locally linear assumption
Pattern Recognition Letters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Incremental Isometric Embedding of High-Dimensional Data Using Connected Neighborhood Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Rapid and brief communication: Incremental locally linear embedding
Pattern Recognition
Unsupervised learning of image manifolds by semidefinite programming
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Incremental locally linear embedding algorithm
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Nonlinear Dimensionality Reduction of Data Lying on the Multicluster Manifold
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Hi-index | 0.00 |
A new manifold learning method, called incremental alignment method (IAM), is proposed for nonlinear dimensionality reduction of high dimensional data with intrinsic low dimensionality. The main idea is to incrementally align low-dimensional coordinates of input data patch-by-patch to iteratively generate the representation of the entire dataset. The method consists of two major steps, the incremental step and the alignment step. The incremental step incrementally searches neighborhood patch to be aligned in the next step, and the alignment step iteratively aligns the low-dimensional coordinates of the neighborhood patch searched to generate the embeddings of the entire dataset. Compared with the existing manifold learning methods, the proposed method dominates in several aspects: high efficiency, easy out-of-sample extension, well metric-preserving, and averting of the local minima issue. All these properties are supported by a series of experiments performed on the synthetic and real-life datasets. In addition, the computational complexity of the proposed method is analyzed, and its efficiency is theoretically argued and experimentally demonstrated.