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
Graph Drawing: Algorithms for the Visualization of Graphs
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Neighborhood Preservation in Nonlinear Projection Methods: An Experimental Study
ICANN '01 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 a kernel matrix for nonlinear dimensionality reduction
ICML '04 Proceedings of the twenty-first international conference on Machine learning
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International Journal of Computer Vision
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Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
A Nonlinear Mapping for Data Structure Analysis
IEEE Transactions on Computers
Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets
IEEE Transactions on Neural Networks
Topology preservation in self-organizing feature maps: exact definition and measurement
IEEE Transactions on Neural Networks
Quantifying the neighborhood preservation of self-organizing feature maps
IEEE Transactions on Neural Networks
Artificial neural networks for feature extraction and multivariate data projection
IEEE Transactions on Neural Networks
Incorporating visualisation quality measures to curvilinear component analysis
Information Sciences: an International Journal
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ANNPR'12 Proceedings of the 5th INNS IAPR TC 3 GIRPR conference on Artificial Neural Networks in Pattern Recognition
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
Visual analysis of a cold rolling process using a dimensionality reduction approach
Engineering Applications of Artificial Intelligence
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Dimensionality reduction aims at representing high-dimensional data in low-dimensional spaces, in order to facilitate their visual interpretation. Many techniques exist, ranging from simple linear projections to more complex nonlinear transformations. The large variety of methods emphasizes the need of quality criteria that allow for fair comparisons between them. This paper extends previous work about rank-based quality criteria and proposes to circumvent their scale dependency. Most dimensionality reduction techniques indeed rely on a scale parameter that distinguish between local and global data properties. Such a scale dependency can be similarly found in usual quality criteria: they assess the embedding quality on a certain scale. Experiments with various dimensionality reduction techniques eventually show the strengths and weaknesses of the proposed scale-independent criteria.