Self-Organizing Maps
Sammon's Nonlinear Mapping Using Geodesic Distances
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 2 - Volume 02
Clustering with Bregman Divergences
The Journal of Machine Learning Research
A Triangulation Method for the Sequential Mapping of Points from N-Space to Two-Space
IEEE Transactions on Computers
A Nonlinear Mapping for Data Structure Analysis
IEEE Transactions on Computers
Nonlinear Dimensionality Reduction
Nonlinear Dimensionality Reduction
Extending metric multidimensional scaling with bregman divergences
IEA/AIE'10 Proceedings of the 23rd international conference on Industrial engineering and other applications of applied intelligent systems - Volume Part II
Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets
IEEE Transactions on Neural Networks
Artificial neural networks for feature extraction and multivariate data projection
IEEE Transactions on Neural Networks
Extending Sammon mapping with Bregman divergences
Information Sciences: an International Journal
Neurocomputing
Incorporating visualisation quality measures to curvilinear component analysis
Information Sciences: an International Journal
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Sum of weighted square distance errors has been a popular way of defining stress function for metric multidimensional scaling (MMDS) like the Sammon mapping. In this paper we generalise this popular MMDS with Bregman divergences, as an example we show that the Sammon mapping can be thought of as a truncated Bregman MMDS (BMMDS) and we show that the full BMMDS improves upon the Sammon mapping on some standard data sets and investigate the reasons underlying this improvement. We then extend a well known family of MMDS, that deploy a strategy of focusing on small distances, with BMMDS and investigate limitations of the strategy empirically. Then an opposite strategy is introduced to create another family of BMMDS that gives increasing mapping quality. A data preprocessing method and a distance matrix preprocessing are introduced.