This paper introduces the Generative Topographic Mapping (GTM), a non-linear latent variable model that can be trained using the EM algorithm. GTM provides a principled alternative to the Self-Organizing Map (SOM) and overcomes many of its limitations. Unlike the SOM, which lacks a well-defined objective function and theoretical basis for learning rate and neighborhood parameters, GTM defines a probability density model and guarantees convergence to a local maximum using the EM algorithm. GTM is defined in terms of a mapping from the latent space into the data space, and for data visualization, the mapping is inverted using Bayes' theorem to obtain a posterior distribution in latent space. The GTM algorithm is based on a constrained mixture of Gaussians, where the parameters are determined by maximizing the log-likelihood. The model uses a set of latent variables and a set of basis functions to define the mapping from the latent space to the data space. The algorithm alternates between the E-step, which computes the posterior probabilities (responsibilities) of each Gaussian component for each data point, and the M-step, which re-estimates the parameters using linear equations. GTM is particularly useful for data visualization, where it can provide a posterior responsibility map for individual data points in the latent space. The algorithm can also be extended to include regularization terms, allowing for more control over the mapping function. The GTM algorithm has been tested on a toy problem and on simulated data from flow diagnostics for a multi-phase oil pipeline, demonstrating its effectiveness in capturing the structure of the data. Compared to the SOM, GTM has several advantages, including a well-defined objective function, guaranteed convergence, and the ability to incorporate prior knowledge about the data distribution. The GTM algorithm is also more flexible, as it can be extended to include multiple Gaussian components and can be used for a variety of applications beyond data visualization. The paper also discusses the relationship between GTM and other algorithms, such as the elastic net and principal curves, and highlights the computational efficiency of the GTM algorithm. Finally, the paper provides a web site for GTM, which includes software implementations and example data sets.This paper introduces the Generative Topographic Mapping (GTM), a non-linear latent variable model that can be trained using the EM algorithm. GTM provides a principled alternative to the Self-Organizing Map (SOM) and overcomes many of its limitations. Unlike the SOM, which lacks a well-defined objective function and theoretical basis for learning rate and neighborhood parameters, GTM defines a probability density model and guarantees convergence to a local maximum using the EM algorithm. GTM is defined in terms of a mapping from the latent space into the data space, and for data visualization, the mapping is inverted using Bayes' theorem to obtain a posterior distribution in latent space. The GTM algorithm is based on a constrained mixture of Gaussians, where the parameters are determined by maximizing the log-likelihood. The model uses a set of latent variables and a set of basis functions to define the mapping from the latent space to the data space. The algorithm alternates between the E-step, which computes the posterior probabilities (responsibilities) of each Gaussian component for each data point, and the M-step, which re-estimates the parameters using linear equations. GTM is particularly useful for data visualization, where it can provide a posterior responsibility map for individual data points in the latent space. The algorithm can also be extended to include regularization terms, allowing for more control over the mapping function. The GTM algorithm has been tested on a toy problem and on simulated data from flow diagnostics for a multi-phase oil pipeline, demonstrating its effectiveness in capturing the structure of the data. Compared to the SOM, GTM has several advantages, including a well-defined objective function, guaranteed convergence, and the ability to incorporate prior knowledge about the data distribution. The GTM algorithm is also more flexible, as it can be extended to include multiple Gaussian components and can be used for a variety of applications beyond data visualization. The paper also discusses the relationship between GTM and other algorithms, such as the elastic net and principal curves, and highlights the computational efficiency of the GTM algorithm. Finally, the paper provides a web site for GTM, which includes software implementations and example data sets.