The Self-Organizing Map (SOM) algorithm has been extensively studied and has been applied with considerable success to a wide variety of problems. However, the algorithm is derived from heuristic ideas and this leads to a number of significant limitations. In this paper, we consider the problem of modelling the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. We introduce a novel form of latent variable model, which we call the GTM algorithm (for Generative Topographic Mapping), which allows general nonlinear transformations from latent space to data space, and which is trained using the EM (expectation-maximization) algorithm. Our approach overcomes the limitations of the SOM, while introducing no significant disadvantages. We demonstrate the performance of the GTM algorithm on simulated data from flow diagnostics for a multiphase oil pipeline.

The Self-Organizing Map (SOM) algorithm has been extensively studied and has been applied with considerable success to a wide variety of problems. However, the algorithm is derived from heuristic ideas and this leads to a number of significant limitations. In this paper, we consider the problem of modelling the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. We introduce a novel form of latent variable model, which we call the GTM algorithm (for Generative Topographic Mapping), which allows general nonlinear transformations from latent space to data space, and which is trained using the EM (expectation-maximization) algorithm. Our approach overcomes the limitations of the SOM, while introducing no significant disadvantages. We demonstrate the performance of the GTM algorithm on simulated data from flow diagnostics for a multiphase oil pipeline.

The Self-Organizing Map (SOM) algorithm has been extensively studied and has been applied with considerable success to a wide variety of problems. However, the algorithm is derived from heuristic ideasand this leads to a number of significant limitations. In this paper, we consider the problem of modelling the probability densityof data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. We introduce a novel form of latent variable model, which we call the GTM algorithm (forGenerative Topographic Mapping), which allows general nonlinear transformations from latent space to data space, and which is trained using the EM (expectation-maximization) algorithm. Ourapproach overcomes the limitations of the SOM, while introducing no significant disadvantages. We demonstrate the performance ofthe GTM algorithm on simulated data from flow diagnostics for a multiphase oil pipeline.

There is currently considerable interest in developing general nonlinear density models based on latent, or hidden, variables. Such models have the ability to discover the presence of a relatively small number of underlying'causes' which, acting in combination, give rise to the apparent complexity of the observed data set. Unfortunately, to train such models generally requires large computational effort. In this paper we introduce a novel latent variable algorithm which retains the general nonlinear capabilities of previous models but which uses a training procedure based on the EM algorithm. We demonstrate the performance of the model on a toy problem and on data from flow diagnostics for a multiphase oil pipeline.

There is currently considerable interest in developing general nonlinear densitymodels based on latent, or hidden, variables. Such models have the ability to discover the presence of a relatively small number of underlying'causes' which, acting in combination, give rise to the apparent complexity of the observed data set. Unfortunately, totrain such models generally requires large computational effort. In this paper we introduce a novel latent variable algorithm which retains the general nonlinear capabilities of previous models but which uses a training procedure based on the EM algorithm. We demonstrate the performance of the model on a toy problem and on data from flow diagnostics for a multiphase oil pipeline.