Self-organization and associative memory: 3rd edition
Self-organization and associative memory: 3rd edition
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Topology representing networks
Neural Networks
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Glyphs for Visualizing Uncertainty in Vector Fields
IEEE Transactions on Visualization and Computer Graphics
IWANN '01 Proceedings of the 6th International Work-Conference on Artificial and Natural Neural Networks: Bio-inspired Applications of Connectionism-Part II
Cluster Stability and the Use of Noise in Interpretation of Clustering
INFOVIS '01 Proceedings of the IEEE Symposium on Information Visualization 2001 (INFOVIS'01)
Coordinating Views for Data Visualisation and Algorithmic Profiling
CMV '04 Proceedings of the Second International Conference on Coordinated & Multiple Views in Exploratory Visualization
Low-Level Components of Analytic Activity in Information Visualization
INFOVIS '05 Proceedings of the Proceedings of the 2005 IEEE Symposium on Information Visualization
A Nonlinear Mapping for Data Structure Analysis
IEEE Transactions on Computers
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets
IEEE Transactions on Neural Networks
Topological estimation using witness complexes
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Multidimensional data visualization applied for user's questionnaire data quality assessment
KES-AMSTA'10 Proceedings of the 4th KES international conference on Agent and multi-agent systems: technologies and applications, Part I
Cartogram visualization for nonlinear manifold learning models
Data Mining and Knowledge Discovery
Visualizing the quality of dimensionality reduction
Neurocomputing
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The visualization of continuous multi-dimensional data based on their projection to a 2-dimensional space is a way to detect visually interesting patterns, as far as the projection provides a faithful image of the original data. In order to evaluate this faithfulness, we propose to visualize any measure associated to a projected datum or to a pair of projected data, by coloring the corresponding Voronoi cell in the projection space. We also define specific measures and show how they allow estimating visually whether some part of the projection is or is not a reliable image of the original manifolds. It also helps to figure out what the original topology of the data is, telling where the high-dimensional manifolds have been torn or glued during the projection. We experiment these techniques with the principal component analysis and the curvilinear component analysis applied to artificial and real databases.