SIAM Review
GTM: the generative topographic mapping
Neural Computation
Self-Organizing Maps
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Rademacher and gaussian complexities: risk bounds and structural results
The Journal of Machine Learning Research
An introduction to variable and feature selection
The Journal of Machine Learning Research
Neighborhood Preserving Embedding
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Improved learning of Riemannian metrics for exploratory analysis
Neural Networks - 2004 Special issue: New developments in self-organizing systems
Generalized Discriminant Analysis Using a Kernel Approach
Neural Computation
Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
Kernel clustering-based discriminant analysis
Pattern Recognition
Parametric Embedding for Class Visualization
Neural Computation
A Nonlinear Mapping for Data Structure Analysis
IEEE Transactions on Computers
Visual Analytics: Scope and Challenges
Visual Data Mining
Nonlinear Dimensionality Reduction
Nonlinear Dimensionality Reduction
An introduction to nonlinear dimensionality reduction by maximum variance unfolding
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Adaptive relevance matrices in learning vector quantization
Neural Computation
Information Retrieval Perspective to Nonlinear Dimensionality Reduction for Data Visualization
The Journal of Machine Learning Research
Dimension reduction and visualization of large high-dimensional data via interpolation
Proceedings of the 19th ACM International Symposium on High Performance Distributed Computing
Supervised nonlinear dimensionality reduction for visualization and classification
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Bankruptcy analysis with self-organizing maps in learning metrics
IEEE Transactions on Neural Networks
Data Visualization and Dimensionality Reduction Using Kernel Maps With a Reference Point
IEEE Transactions on Neural Networks
Discriminative dimensionality reduction mappings
IDA'12 Proceedings of the 11th international conference on Advances in Intelligent Data Analysis
Visualizing the quality of dimensionality reduction
Neurocomputing
Using nonlinear dimensionality reduction to visualize classifiers
IWANN'13 Proceedings of the 12th international conference on Artificial Neural Networks: advances in computational intelligence - Volume Part I
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In recent years, a wealth of dimension-reduction techniques for data visualization and preprocessing has been established. Nonparametric methods require additional effort for out-of-sample extensions, because they provide only a mapping of a given finite set of points. In this letter, we propose a general view on nonparametric dimension reduction based on the concept of cost functions and properties of the data. Based on this general principle, we transfer nonparametric dimension reduction to explicit mappings of the data manifold such that direct out-of-sample extensions become possible. Furthermore, this concept offers the possibility of investigating the generalization ability of data visualization to new data points. We demonstrate the approach based on a simple global linear mapping, as well as prototype-based local linear mappings. In addition, we can bias the functional form according to given auxiliary information. This leads to explicit supervised visualization mappings with discriminative properties comparable to state-of-the-art approaches.