SIAM Review
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Geometry and invariance in kernel based methods
Advances in kernel methods
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
A Database for Handwritten Text Recognition Research
IEEE Transactions on Pattern Analysis and Machine Intelligence
Kernel Matrix Completion by Semidefinite Programming
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
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
Learning the Kernel Matrix with Semidefinite Programming
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
Unsupervised learning of image manifolds by semidefinite programming
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
ICML '05 Proceedings of the 22nd international conference on Machine learning
ICML '05 Proceedings of the 22nd international conference on Machine learning
Unsupervised Learning of Image Manifolds by Semidefinite Programming
International Journal of Computer Vision
Learning low-rank kernel matrices
ICML '06 Proceedings of the 23rd international conference on Machine learning
Local distance preservation in the GP-LVM through back constraints
ICML '06 Proceedings of the 23rd international conference on Machine learning
On the Nyström Method for Approximating a Gram Matrix for Improved Kernel-Based Learning
The Journal of Machine Learning Research
Robust non-linear dimensionality reduction using successive 1-dimensional Laplacian Eigenmaps
Proceedings of the 24th international conference on Machine learning
Transductive regression piloted by inter-manifold relations
Proceedings of the 24th international conference on Machine learning
Rank minimization via online learning
Proceedings of the 25th international conference on Machine learning
Topologically-constrained latent variable models
Proceedings of the 25th international conference on Machine learning
Semi-definite Manifold Alignment
ECML '07 Proceedings of the 18th European conference on Machine Learning
Learning a Kernel Matrix for Time Series Data from DTW Distances
Neural Information Processing
Ambiguity Modeling in Latent Spaces
MLMI '08 Proceedings of the 5th international workshop on Machine Learning for Multimodal Interaction
Gaussian kernel optimization for pattern classification
Pattern Recognition
Local Dimensionality Reduction for Non-Parametric Regression
Neural Processing Letters
Nonlinear process monitoring based on maximum variance unfolding projections
Expert Systems with Applications: An International Journal
Learning linear dynamical systems without sequence information
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Geometry-aware metric learning
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Partial order embedding with multiple kernels
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Toward a perceptual space for gloss
ACM Transactions on Graphics (TOG)
An introduction to nonlinear dimensionality reduction by maximum variance unfolding
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Variational Graph Embedding for Globally and Locally Consistent Feature Extraction
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part II
Transfer learning via dimensionality reduction
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 2
Feature selection and kernel design via linear programming
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Constrained many-objective optimization: a way forward
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Features and Metric from a Classifier Improve Visualizations with Dimension Reduction
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part II
Neurocomputing
Dimensionality Estimation, Manifold Learning and Function Approximation using Tensor Voting
The Journal of Machine Learning Research
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
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
Approximately harmonic projection: Theoretical analysis and an algorithm
Pattern Recognition
Scale-independent quality criteria for dimensionality reduction
Pattern Recognition Letters
Exploiting tag and word correlations for improved webpage clustering
SMUC '10 Proceedings of the 2nd international workshop on Search and mining user-generated contents
Manifold learning for object tracking with multiple motion dynamics
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
Robust Positive semidefinite L-Isomap Ensemble
Pattern Recognition Letters
Regression on Fixed-Rank Positive Semidefinite Matrices: A Riemannian Approach
The Journal of Machine Learning Research
A new scheme to learn a kernel in regularization networks
Neurocomputing
Nonlinear dimensionality reduction using a temporal coherence principle
Information Sciences: an International Journal
A Family of Simple Non-Parametric Kernel Learning Algorithms
The Journal of Machine Learning Research
Supervised semi-definite embedding for email data cleaning and visualization
APWeb'05 Proceedings of the 7th Asia-Pacific web conference on Web Technologies Research and Development
Generalized foley-sammon transform with kernels
ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
Nonrigid embeddings for dimensionality reduction
ECML'05 Proceedings of the 16th European conference on Machine Learning
Approximating a gram matrix for improved kernel-based learning
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Metric Learning for Estimating Psychological Similarities
ACM Transactions on Intelligent Systems and Technology (TIST)
Dimensionality reduction by Mixed Kernel Canonical Correlation Analysis
Pattern Recognition
Distance metric learning with eigenvalue optimization
The Journal of Machine Learning Research
Leveraging Social Bookmarks from Partially Tagged Corpus for Improved Web Page Clustering
ACM Transactions on Intelligent Systems and Technology (TIST)
A unifying probabilistic perspective for spectral dimensionality reduction: insights and new models
The Journal of Machine Learning Research
Orthogonal projection analysis
IScIDE'11 Proceedings of the Second Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
Modeling and monitoring of multimodes process
ISNN'12 Proceedings of the 9th international conference on Advances in Neural Networks - Volume Part I
Self-taught dimensionality reduction on the high-dimensional small-sized data
Pattern Recognition
From sBoW to dCoT marginalized encoders for text representation
Proceedings of the 21st ACM international conference on Information and knowledge management
A kernel-based framework for image collection exploration
Journal of Visual Languages and Computing
Image Dimensionality Reduction Based on the Intrinsic Dimension and Parallel Genetic Algorithm
International Journal of Cognitive Informatics and Natural Intelligence
Multiple kernel local Fisher discriminant analysis for face recognition
Signal Processing
Inductive manifold learning using structured support vector machine
Pattern Recognition
Learning social network embeddings for predicting information diffusion
Proceedings of the 7th ACM international conference on Web search and data mining
Isometric sliced inverse regression for nonlinear manifold learning
Statistics and Computing
On the convergence of maximum variance unfolding
The Journal of Machine Learning Research
Parallel vector field embedding
The Journal of Machine Learning Research
Supervised Distance Preserving Projections
Neural Processing Letters
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We investigate how to learn a kernel matrix for high dimensional data that lies on or near a low dimensional manifold. Noting that the kernel matrix implicitly maps the data into a nonlinear feature space, we show how to discover a mapping that "unfolds" the underlying manifold from which the data was sampled. The kernel matrix is constructed by maximizing the variance in feature space subject to local constraints that preserve the angles and distances between nearest neighbors. The main optimization involves an instance of semidefinite programming---a fundamentally different computation than previous algorithms for manifold learning, such as Isomap and locally linear embedding. The optimized kernels perform better than polynomial and Gaussian kernels for problems in manifold learning, but worse for problems in large margin classification. We explain these results in terms of the geometric properties of different kernels and comment on various interpretations of other manifold learning algorithms as kernel methods.