GTM: the generative topographic mapping
Neural Computation
Neighborhood Preservation in Nonlinear Projection Methods: An Experimental Study
ICANN '01 Proceedings of the International Conference on Artificial Neural Networks
Nonlinear Dimensionality Reduction
Nonlinear Dimensionality Reduction
Robust analysis of MRS brain tumour data using t-GTM
Neurocomputing
Manifold constrained finite gaussian mixtures
IWANN'05 Proceedings of the 8th international conference on Artificial Neural Networks: computational Intelligence and Bioinspired Systems
Comparative Evaluation of Semi-supervised Geodesic GTM
HAIS '09 Proceedings of the 4th International Conference on Hybrid Artificial Intelligence Systems
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Nonlinear dimensionality reduction (NLDR) methods aim to provide a faithful low-dimensional representation of multivariate data. The manifold learning family of NLDR methods, in particular, do this by defining low-dimensional manifolds embedded in the observed data space. Generative Topographic Mapping (GTM) is one such manifold learning method for multivariate data clustering and visualization. The non-linearity of the mapping it generates makes it prone to trustworthinessand continuityerrors that would reduce the faithfulness of the data representation, especially for datasets of convoluted geometry. In this study, the GTM is modified to prioritize neighbourhood relationships along the generated manifold. This is accomplished through penalizing divergences between the Euclidean distances from the data points to the model prototypes and the corresponding geodesic distances along the manifold. The resulting Geodesic GTM model is shown to improve not only the continuityand trustworthinessof the representation generated by the model, but also its resilience in the presence of noise.