Conjugate Gradient Methods for Toeplitz Systems
SIAM Review
Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
SIAM Journal on Scientific Computing
Learning Appearance Manifolds from Video
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Regression on manifolds using kernel dimension reduction
Proceedings of the 24th international conference on Machine learning
Semi-supervised dimensionality reduction in image feature space
Proceedings of the 2008 ACM symposium on Applied computing
A unified framework for semi-supervised dimensionality reduction
Pattern Recognition
Anomaly detection using manifold embedding and its applications in transportation corridors
Intelligent Data Analysis - Knowledge Discovery from Data Streams
Latent Dirichlet Allocation with topic-in-set knowledge
SemiSupLearn '09 Proceedings of the NAACL HLT 2009 Workshop on Semi-Supervised Learning for Natural Language Processing
Multiple view semi-supervised dimensionality reduction
Pattern Recognition
Embedding new data points for manifold learning via coordinate propagation
PAKDD'07 Proceedings of the 11th Pacific-Asia conference on Advances in knowledge discovery and data mining
A two-step framework for highly nonlinear data unfolding
Neurocomputing
Artificial Intelligence Review
Discriminative semi-supervised feature selection via manifold regularization
IEEE Transactions on Neural Networks
Flexible manifold embedding: a framework for semi-supervised and unsupervised dimension reduction
IEEE Transactions on Image Processing
Similarity preserving principal curve: an optimal 1-D feature extractor for data representation
IEEE Transactions on Neural Networks
GEMS '10 Proceedings of the 2010 Workshop on GEometrical Models of Natural Language Semantics
PRIB'10 Proceedings of the 5th IAPR international conference on Pattern recognition in bioinformatics
Semi-supervised classification by local coordination
ICONIP'10 Proceedings of the 17th international conference on Neural information processing: models and applications - Volume Part II
Local block representation for face recognition
ICSI'11 Proceedings of the Second international conference on Advances in swarm intelligence - Volume Part II
Semi-supervised dimensionality reduction via harmonic functions
MDAI'11 Proceedings of the 8th international conference on Modeling decisions for artificial intelligence
Dimensionality reduction via compressive sensing
Pattern Recognition Letters
Credit scoring for SME using a manifold supervised learning algorithm
IDEAL'12 Proceedings of the 13th international conference on Intelligent Data Engineering and Automated Learning
Biased representation learning for domain adaptation
EMNLP-CoNLL '12 Proceedings of the 2012 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning
Information Sciences: an International Journal
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The problem of nonlinear dimensionality reduction is considered. We focus on problems where prior information is available, namely, semi-supervised dimensionality reduction. It is shown that basic nonlinear dimensionality reduction algorithms, such as Locally Linear Embedding (LLE), Isometric feature mapping (ISOMAP), and Local Tangent Space Alignment (LTSA), can be modified by taking into account prior information on exact mapping of certain data points. The sensitivity analysis of our algorithms shows that prior information will improve stability of the solution. We also give some insight on what kind of prior information best improves the solution. We demonstrate the usefulness of our algorithm by synthetic and real life examples.