MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
Local Metric Learning on Manifolds with Application to Query---Based Operations
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
ISICA '08 Proceedings of the 3rd International Symposium on Advances in Computation and Intelligence
Finding representative landmarks of data on manifolds
Pattern Recognition
Incremental Laplacian eigenmaps by preserving adjacent information between data points
Pattern Recognition Letters
A template-based isomap algorithm for real-time removal of ocular artifacts from EEG signals
Proceedings of the 2nd International Conference on Interaction Sciences: Information Technology, Culture and Human
Manifold-based learning and synthesis
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Adaptive Neighborhood Select Based on Local Linearity for Nonlinear Dimensionality Reduction
ISICA '09 Proceedings of the 4th International Symposium on Advances in Computation and Intelligence
Dynamic Neighborhood Selection for Nonlinear Dimensionality Reduction
MDAI '09 Proceedings of the 6th International Conference on Modeling Decisions for Artificial Intelligence
Recognition of multiple configurations of objects with limited data
Pattern Recognition
Distance approximating dimension reduction of Riemannian manifolds
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
A novel local sensitive frontier analysis for feature extraction
ICIC'09 Proceedings of the Intelligent computing 5th international conference on Emerging intelligent computing technology and applications
Linear discriminant projection embedding based on patches alignment
Image and Vision Computing
Fast ISOMAP based on minimum set coverage
ICIC'10 Proceedings of the Advanced intelligent computing theories and applications, and 6th international conference on Intelligent computing
Orthogonal local spline discriminant projection with application to face recognition
Pattern Recognition Letters
Robust Positive semidefinite L-Isomap Ensemble
Pattern Recognition Letters
Neurocomputing
Curvature analysis of frequency modulated manifolds in dimensionality reduction
Calcolo: a quarterly on numerical analysis and theory of computation
Incremental manifold learning by spectral embedding methods
Pattern Recognition Letters
Incremental alignment manifold learning
Journal of Computer Science and Technology - Special issue on natural language processing
Discriminant sparse neighborhood preserving embedding for face recognition
Pattern Recognition
Face recognition using Elasticfaces
Pattern Recognition
Orthogonal projection analysis
IScIDE'11 Proceedings of the Second Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
Geodesic Polar Coordinates on Polygonal Meshes
Computer Graphics Forum
Error-correcting output codes based ensemble feature extraction
Pattern Recognition
Increasing reliability of protein interactome by fast manifold embedding
Pattern Recognition Letters
Human action segmentation and classification based on the Isomap algorithm
Multimedia Tools and Applications
Dimensionality reduction by low-rank embedding
IScIDE'12 Proceedings of the third Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
Parallel vector field embedding
The Journal of Machine Learning Research
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Recently, manifold learning has been widely exploited in pattern recognition, data analysis, and machine learning. This paper presents a novel framework, called Riemannian manifold learning (RML), based on the assumption that the input high-dimensional data lie on an intrinsically low-dimensional Riemannian manifold. The main idea is to formulate the dimensionality reduction problem as a classical problem in Riemannian geometry, i.e., how to construct coordinate charts for a given Riemannian manifold? We implement the Riemannian normal coordinate chart, which has been the most widely used in Riemannian geometry, for a set of unorganized data points. First, two input parameters (the neighborhood size k and the intrinsic dimension d) are estimated based on an efficient simplicial reconstruction of the underlying manifold. Then, the normal coordinates are computed to map the input high-dimensional data into a low-dimensional space. Experiments on synthetic data as well as real world images demonstrate that our algorithm can learn intrinsic geometric structures of the data, preserve radial geodesic distances, and yield regular embeddings.