Self-organizing maps
GTM: the generative topographic mapping
Neural Computation
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Mapping a manifold of perceptual observations
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Nonlinear Projection with the Isotop Method
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
Visualization of high-dimensional data with relational perspective map
Information Visualization
Convex Optimization
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
SIAM Journal on Scientific Computing
Local multidimensional scaling
Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
Spherical self-organizing map using efficient indexed geodesic data structure
Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
Online data visualization using the neural gas network
Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
A Nonlinear Mapping for Data Structure Analysis
IEEE Transactions on Computers
Comparison of visualization methods for an atlas of gene expression data sets
Information Visualization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear Dimensionality Reduction
Nonlinear Dimensionality Reduction
Optimization Algorithms on Matrix Manifolds
Optimization Algorithms on Matrix Manifolds
Fast manifold learning based on riemannian normal coordinates
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Outlier-resisting graph embedding
Neurocomputing
Supervised learning of local projection kernels
Neurocomputing
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This paper presents a framework for nonlinear dimensionality reduction methods aimed at projecting data on a non-Euclidean manifold, when their structure is too complex to be embedded in an Euclidean space. The methodology proposes an optimization procedure on manifolds to minimize a pairwise distance criterion that implements a control of the trade-off between trustworthiness and continuity, two criteria that, respectively, represent the risks of flattening and tearing the projection. The methodology is presented as general as possible and is illustrated in the specific case of the sphere.