GTM: The Generative Topographic Mapping. Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis which is based on a linear transformations between the latent space and the data space. In this paper we introduce a form of non-linear latent variable model called the Generative Topographic Mapping for which the parameters of the model can be determined using the EM algorithm. GTM provides a principled alternative to the widely used Self-Organizing Map (SOM) of Kohonen (1982), and overcomes most of the significant limitations of the SOM. We demonstrate the performance of the GTM algorithm on a toy problem and on simulated data from flow diagnostics for a multi-phase oil pipeline.

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  1. Biernacki, Christophe; Marbac, Matthieu; Vandewalle, Vincent: Gaussian-based visualization of Gaussian and non-Gaussian-based clustering (2021)
  2. Fong, Youyi; Xu, Jun: Forward stepwise deep autoencoder-based monotone nonlinear dimensionality reduction methods (2021)
  3. Le Bouteiller, Pauline; Charléty, Jean: Semi-supervised multi-facies object retrieval in seismic data (2020)
  4. Bohn, Bastian; Garcke, Jochen; Griebel, Michael: A sparse grid based method for generative dimensionality reduction of high-dimensional data (2016)
  5. Hua, Hao: Image and geometry processing with oriented and scalable map (2016)
  6. Iwasaki, Tohru; Furukawa, Tetsuo: Tensor SOM and tensor GTM: nonlinear tensor analysis by topographic mappings (2016)
  7. Liu, Binghui; Shen, Xiaotong; Pan, Wei: Nonlinear joint latent variable models and integrative tumor subtype discovery (2016)
  8. Chandrapala, Thusitha N.; Shi, Bertram E.: Learning slowness in a sparse model of invariant feature detection (2015)
  9. Deleforge, Antoine; Forbes, Florence; Horaud, Radu: High-dimensional regression with Gaussian mixtures and partially-latent response variables (2015)
  10. Astudillo, César A.; Oommen, B. John: Topology-oriented self-organizing maps: a survey (2014) ioport
  11. Feng, Wenyue; Yang, Zhouwang; Deng, Jiansong: Moving multiple curves/surfaces approximation of mixed point clouds (2014)
  12. Gracia, Antonio; González, Santiago; Robles, Victor; Menasalvas, Ernestina: A methodology to compare dimensionality reduction algorithms in terms of loss of quality (2014) ioport
  13. Pulkkinen, Seppo; Mäkelä, Marko M.; Karmitsa, Napsu: A generative model and a generalized trust region Newton method for noise reduction (2014)
  14. Pulkkinen, Seppo; Mäkelä, Marko Mikael; Karmitsa, Napsu: A continuation approach to mode-finding of multivariate Gaussian mixtures and kernel density estimates (2013)
  15. Vellido, Alfredo; García, David L.; Nebot, Àngela: Cartogram visualization for nonlinear manifold learning models (2013) ioport
  16. Romero, Enrique; Mu, Tingting; Lisboa, Paulo J. G.: Cohort-based kernel visualisation with scatter matrices (2012)
  17. Tan, Huan; Du, Qian; Wu, Na: Robots learn writing (2012) ioport
  18. Taşdemir, Kadim: Vector quantization based approximate spectral clustering of large datasets (2012) ioport
  19. Wang, Kaijun; Yan, Xuanhui; Chen, Lifei: Geometric double-entity model for recognizing far-near relations of clusters (2011) ioport
  20. Zhang, Xiaofeng; Cheung, William K.; Li, C. H.: Learning latent variable models from distributed and abstracted data (2011) ioport

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