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32
GTM: The generative topographic mapping
 Neural Computation
, 1998
"... 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 ..."
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Cited by 275 (5 self)
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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 nonlinear 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 SelfOrganizing 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 multiphase oil pipeline. Copyright c○MIT Press (1998). 1
Probabilistic nonlinear principal component analysis with Gaussian process latent variable models
 Journal of Machine Learning Research
, 2005
"... Summarising a high dimensional data set with a low dimensional embedding is a standard approach for exploring its structure. In this paper we provide an overview of some existing techniques for discovering such embeddings. We then introduce a novel probabilistic interpretation of principal component ..."
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Cited by 134 (14 self)
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Summarising a high dimensional data set with a low dimensional embedding is a standard approach for exploring its structure. In this paper we provide an overview of some existing techniques for discovering such embeddings. We then introduce a novel probabilistic interpretation of principal component analysis (PCA) that we term dual probabilistic PCA (DPPCA). The DPPCA model has the additional advantage that the linear mappings from the embedded space can easily be nonlinearised through Gaussian processes. We refer to this model as a Gaussian process latent variable model (GPLVM). Through analysis of the GPLVM objective function, we relate the model to popular spectral techniques such as kernel PCA and multidimensional scaling. We then review a practical algorithm for GPLVMs in the context of large data sets and develop it to also handle discrete valued data and missing attributes. We demonstrate the model on a range of realworld and artificially generated data sets.
A hierarchical dirichlet language model
 Natural Language Engineering
, 1994
"... We discuss a hierarchical probabilistic model whose predictions are similar to those of the popular language modelling procedure known as 'smoothing'. A number of interesting differences from smoothing emerge. The insights gained from a probabilistic view of this problem point towards new directions ..."
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Cited by 79 (3 self)
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We discuss a hierarchical probabilistic model whose predictions are similar to those of the popular language modelling procedure known as 'smoothing'. A number of interesting differences from smoothing emerge. The insights gained from a probabilistic view of this problem point towards new directions for language modelling. The ideas of this paper are also applicable to other problems such as the modelling of triphomes in speech, and DNA and protein sequences in molecular biology. The new algorithm is compared with smoothing on a two million word corpus. The methods prove to be about equally accurate, with the hierarchical model using fewer computational resources. 1
A comparison of algorithms for inference and learning in probabilistic graphical models
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2005
"... Computer vision is currently one of the most exciting areas of artificial intelligence research, largely because it has recently become possible to record, store and process large amounts of visual data. While impressive achievements have been made in pattern classification problems such as handwr ..."
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Cited by 49 (4 self)
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Computer vision is currently one of the most exciting areas of artificial intelligence research, largely because it has recently become possible to record, store and process large amounts of visual data. While impressive achievements have been made in pattern classification problems such as handwritten character recognition and face detection, it is even more exciting that researchers may be on the verge of introducing computer vision systems that perform scene analysis, decomposing image input into its constituent objects, lighting conditions, motion patterns, and so on. Two of the main challenges in computer vision are finding efficient models of the physics of visual scenes and finding efficient algorithms for inference and learning in these models. In this paper, we advocate the use of graphbased probability models and their associated inference and learning algorithms for computer vision and scene analysis. We review exact techniques and various approximate, computationally efficient techniques, including iterative conditional modes, the expectation maximization (EM) algorithm, the mean field method, variational techniques, structured variational techniques, Gibbs sampling, the sumproduct algorithm and “loopy ” belief propagation. We describe how each technique can be applied in a model of multiple, occluding objects, and contrast the behaviors and performances of the techniques using a unifying cost function, free energy.
GTM: A Principled Alternative to the SelfOrganizing Map
 In Advances in Neural Information Processing Systems
, 1997
"... The SelfOrganizing 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 m ..."
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Cited by 46 (1 self)
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The SelfOrganizing 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 Map), which allows general nonlinear transformations from latent space to data space, and which is trained using the EM (expectationmaximization) 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. GTM: A Principled Alternative to the SelfOrganizing Map 2 1 Introduc...
Local distance preservation in the gplvm through back constraints
 In ICML
, 2006
"... The Gaussian process latent variable model (GPLVM) is a generative approach to nonlinear low dimensional embedding, that provides a smooth probabilistic mapping from latent to data space. It is also a nonlinear generalization of probabilistic PCA (PPCA) (Tipping & Bishop, 1999). While most approac ..."
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Cited by 43 (5 self)
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The Gaussian process latent variable model (GPLVM) is a generative approach to nonlinear low dimensional embedding, that provides a smooth probabilistic mapping from latent to data space. It is also a nonlinear generalization of probabilistic PCA (PPCA) (Tipping & Bishop, 1999). While most approaches to nonlinear dimensionality methods focus on preserving local distances in data space, the GPLVM focusses on exactly the opposite. Being a smooth mapping from latent to data space, it focusses on keeping things apart in latent space that are far apart in data space. In this paper we first provide an overview of dimensionality reduction techniques, placing the emphasis on the kind of distance relation preserved. We then show how the GPLVM can be generalized, through back constraints, to additionally preserve local distances. We give illustrative experiments on common data sets. 1.
A review of dimension reduction techniques
, 1997
"... The problem of dimension reduction is introduced as a way to overcome the curse of the dimensionality when dealing with vector data in highdimensional spaces and as a modelling tool for such data. It is defined as the search for a lowdimensional manifold that embeds the highdimensional data. A cl ..."
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Cited by 30 (4 self)
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The problem of dimension reduction is introduced as a way to overcome the curse of the dimensionality when dealing with vector data in highdimensional spaces and as a modelling tool for such data. It is defined as the search for a lowdimensional manifold that embeds the highdimensional data. A classification of dimension reduction problems is proposed. A survey of several techniques for dimension reduction is given, including principal component analysis, projection pursuit and projection pursuit regression, principal curves and methods based on topologically continuous maps, such as Kohonen’s maps or the generalised topographic mapping. Neural network implementations for several of these techniques are also reviewed, such as the projection pursuit learning network and the BCM neuron with an objective function. Several appendices complement the mathematical treatment of the main text.
Probabilistic Visualisation of Highdimensional Binary Data
, 1999
"... We present a probabilistic latentvariable framework for data visualisation, a key feature of which is its applicability to binary and categorical data types for which few established methods exist. A variational approximation to the likelihood is exploited to derive a fast algorithm for determining ..."
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Cited by 21 (0 self)
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We present a probabilistic latentvariable framework for data visualisation, a key feature of which is its applicability to binary and categorical data types for which few established methods exist. A variational approximation to the likelihood is exploited to derive a fast algorithm for determining the model parameters. Illustrations of application to real and synthetic binary data sets are given.
Hierarchical Gaussian process latent variable models
 In International Conference in Machine Learning
, 2007
"... The Gaussian process latent variable model (GPLVM) is a powerful approach for probabilistic modelling of high dimensional data through dimensional reduction. In this paper we extend the GPLVM through hierarchies. A hierarchical model (such as a tree) allows us to express conditional independencies ..."
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Cited by 21 (4 self)
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The Gaussian process latent variable model (GPLVM) is a powerful approach for probabilistic modelling of high dimensional data through dimensional reduction. In this paper we extend the GPLVM through hierarchies. A hierarchical model (such as a tree) allows us to express conditional independencies in the data as well as the manifold structure. We first introduce Gaussian process hierarchies through a simple dynamical model, we then extend the approach to a more complex hierarchy which is applied to the visualisation of human motion data sets. 1.
EM Optimization of LatentVariable Density Models
 Advances in Neural Information Processing Systems 8
, 1996
"... 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 ..."
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Cited by 17 (0 self)
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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. 1 INTRODUCTION Many conventional approaches to density estimation, such as mixture models, rely on linear superpositions of basis functions to represent the data density. Such approaches are unable to discover structure within the data whereby a relatively small number ...