Visualizing regression data by supervised Generative Topographic Mapping

Generative Topographic Mapping (GTM) is a nonlinear latent variable model introduced by Bishop et al. as a data visualization technique. In this paper, we propose a supervised GTM model and a semi-supervised GTM model. Conventional supervised GTM models use discrete class labels in classification problems, and therefore cannot directly handle continuous output labels in regression problems. To overcome the problem, we propose a supervised GTM model which can naturally handle continuous output labels in regression problems. In order to handle missing labels, we also propose a semi-supervised GTM model that uses both labeled and unlabeled data.

[1]  Alfredo Vellido,et al.  On the improvement of brain tumour data clustering using class information , 2006, STAIRS.

[2]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

[3]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[4]  Nobuhiko Yamaguchi.  Visualizing states in autoregressive hidden Markov models using generative topographic mapping , 2012, 2012 8th International Conference on Natural Computation.

[5]  Alfredo Vellido,et al.  Missing data imputation through GTM as a mixture of t-distributions , 2006, Neural Networks.

[6]  M. V. Velzen,et al.  Self-organizing maps , 2007 .

[7]  Alfredo Vellido,et al.  Advances in clustering and visualization of time series using GTM through time , 2008, Neural Networks.

[8]  Christopher J. Merz,et al.  UCI Repository of Machine Learning Databases , 1996 .

[9]  Christopher M. Bishop,et al.  Developments of the generative topographic mapping , 1998, Neurocomputing.

[10]  Yi Sun,et al.  GTM-based data visualisation with incomplete data , 2001 .

[11]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[12]  Mahesan Niranjan,et al.  Uncertainty in geometric computations , 2002 .

[13]  Yi Sun,et al.  Visualisation of Incomplete Data Using Class Information Constraints , 2002 .

[14]  Christopher M. Bishop,et al.  GTM: The Generative Topographic Mapping , 1998, Neural Computation.