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
Problems of learning on manifolds
Problems of learning on manifolds
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
SIAM Journal on Scientific Computing
Building k-Connected Neighborhood Graphs for Isometric Data Embedding
IEEE Transactions on Pattern Analysis and Machine Intelligence
Unsupervised Learning of Image Manifolds by Semidefinite Programming
International Journal of Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Local multidimensional scaling
Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
Non-isometric manifold learning: analysis and an algorithm
Proceedings of the 24th international conference on Machine learning
Journal of Cognitive Neuroscience
Gait analysis for human identification through manifold learning and HMM
Pattern Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
MLDM '07 Proceedings of the 5th international conference on Machine Learning and Data Mining in Pattern Recognition
Finding representative landmarks of data on manifolds
Pattern Recognition
Automatic Choice of the Number of Nearest Neighbors in Locally Linear Embedding
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
Regularization parameter choice in locally linear embedding
Neurocomputing
Learning an intrinsic-variable preserving manifold for dynamic visual tracking
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on game theory
Scale-independent quality criteria for dimensionality reduction
Pattern Recognition Letters
An improved local tangent space alignment method for manifold learning
Pattern Recognition Letters
Enhancing Human Face Detection by Resampling Examples Through Manifolds
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Learning and Matching of Dynamic Shape Manifolds for Human Action Recognition
IEEE Transactions on Image Processing
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Manifold learning is a hot research topic in the field of computer science. A crucial issue with current manifold learning methods is that they lack a natural quantitative measure to assess the quality of learned embeddings, which greatly limits their applications to real-world problems. In this paper, a new embedding quality assessment method for manifold learning, named as normalization independent embedding quality assessment (NIEQA) is proposed. Compared with current assessment methods which are limited to isometric embeddings, the NIEQA method has a much larger application range due to two features. First, it is based on a new measure which can effectively evaluate how well local neighborhood geometry is preserved under normalization, hence it can be applied to both isometric and normalized embeddings. Second, it can provide both local and global evaluations to output an overall assessment. Therefore, NIEQA can serve as a natural tool in model selection and evaluation tasks for manifold learning. Experimental results on benchmark data sets validate the effectiveness of the proposed method.