Results 1  10
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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
Natural Language Processing with Modular PDP Networks and Distributed Lexicon
 Cognitive Science
, 1991
"... An approach to connectionist natural language processing is proposed, which is based on hierarchically organized modular Parallel Distributed Processing (PDP) networks and a central lexicon of distributed input/output representations. The modules communicate using these representations, which are gl ..."
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Cited by 83 (13 self)
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An approach to connectionist natural language processing is proposed, which is based on hierarchically organized modular Parallel Distributed Processing (PDP) networks and a central lexicon of distributed input/output representations. The modules communicate using these representations, which are global and publicly available in the system. The representations are developed automatically by all networks while they are learning their processing tasks. The resulting representations reflect the regularities in the subtasks, which facilitates robust processing in the face of noise and damage, supports improved generalization, and provides expectations about possible contexts. The lexicon can be extended by cloning new instances of the items, that is, by generating a number of items with known processing properties and distinct identities. This technique combinatorially increases the processing power of the system. The recurrent FGREP module, together with a central lexicon, is used as a ba...
Growing a Hypercubical Output Space in a SelfOrganizing Feature Map
 IEEE Transactions on Neural Networks
, 1995
"... Neural maps project data given in a (possibly highdimensional) input space onto a neuron position in a (usually lowdimensional) output space grid. An important property of this projection is the preservation of neighborhoods; neighboring neurons in output space respond to neighboring data points i ..."
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Cited by 50 (11 self)
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Neural maps project data given in a (possibly highdimensional) input space onto a neuron position in a (usually lowdimensional) output space grid. An important property of this projection is the preservation of neighborhoods; neighboring neurons in output space respond to neighboring data points in input space. To achieve this preservation in an optimal way during learning, the topology of the output space has to roughly match the effective structure of the data in the input space. We here present a growth algorithm, called the GSOM, which enhances a widespread map selforganization process, Kohonen's SelfOrganizing Feature Map (SOFM), by an adaptation of the output space grid during learning. During the procedure the output space structure is restricted to a general hypercubical shape, with the overall dimensionality of the grid and its extensions along the different directions being subject of the adaptation. This constraint distinguishes the present algorithm from other, less or ...
Rapid Learning with Parametrized SelfOrganizing Maps
 Neurocomputing
, 1995
"... The construction of computer vision and robot control algorithms from training data is a challenging application for artificial neural networks. However, many practical applications require an approach that is workable with a small number of data examples. In this contribution, we describe results o ..."
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Cited by 31 (17 self)
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The construction of computer vision and robot control algorithms from training data is a challenging application for artificial neural networks. However, many practical applications require an approach that is workable with a small number of data examples. In this contribution, we describe results on the use of "Parametrized Selforganizing Maps" ("PSOMs") with this goal in mind. We report results that demonstrate that a small number of labeled training images is sufficient to construct PSOMs to identify the position of finger tips in images of 3Dhand shapes to within an accuracy of only a few pixel locations. Further we present a framework of hierarchical PSOMs that allows rapid "oneshot learning" after acquiring a number of "basis mappings" during a previous "investment learning stage". We demonstrate the potential of this approach with the task of constructing the positiondependent mapping from camera coordinates to the work space coordinates of a Puma robot. 1 Introduction Lear...
Neural Maps and Topographic Vector Quantization
, 1999
"... Neural maps combine the representation of data by codebook vectors, like a vector quantizer, with the property of topography, like a continuous function. While the quantization error is simple to compute and to compare between different maps, topography of a map is difficult to define and to quantif ..."
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Cited by 19 (4 self)
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Neural maps combine the representation of data by codebook vectors, like a vector quantizer, with the property of topography, like a continuous function. While the quantization error is simple to compute and to compare between different maps, topography of a map is difficult to define and to quantify. Yet, topography of a neural map is an advantageous property, e.g. in the presence of noise in a transmission channel, in data visualization, and in numerous other applications. In this paper we review some conceptual aspects of definitions of topography, and some recently proposed measures to quantify topography. We apply the measures first to neural maps trained on synthetic data sets, and check the measures for properties like reproducability, scalability, systematic dependence of the value of the measure on the topology of the map etc. We then test the measures on maps generated for four realworld data sets, a chaotic time series, speech data, and two sets of image data. The measures ...
Computational Models for Neuromuscular Function
 IEEE Reviews in Biomedical Engineering (2) October
, 2009
"... Abstract—Computational models of the neuromuscular system hold the potential to allow us to reach a deeper understanding of neuromuscular function and clinical rehabilitation by complementing experimentation. By serving as a means to distill and explore specific hypotheses, computational models emer ..."
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Cited by 18 (13 self)
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Abstract—Computational models of the neuromuscular system hold the potential to allow us to reach a deeper understanding of neuromuscular function and clinical rehabilitation by complementing experimentation. By serving as a means to distill and explore specific hypotheses, computational models emerge from prior experimental data and motivate future experimental work. Here we review computational tools used to understand neuromuscular function including musculoskeletal modeling, machine learning, control theory, and statistical model analysis. We conclude that these tools, when used in combination, have the potential to further our understanding of neuromuscular function by serving as a rigorous means to test scientific hypotheses in ways that complement and leverage experimental data. Index Terms—Modeling, biomechanics, neuromuscular control, computational methods.
Neural Maps in Remote Sensing Image Analysis
 Neural Networks
, 2003
"... We study the application of SelfOrganizing Maps for the analyses of remote sensing spectral images. Advanced airborne and satellitebased imaging spectrometers produce very highdimensional spectral signatures that provide key information to many scientific inves tigations about the surface and at ..."
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Cited by 15 (12 self)
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We study the application of SelfOrganizing Maps for the analyses of remote sensing spectral images. Advanced airborne and satellitebased imaging spectrometers produce very highdimensional spectral signatures that provide key information to many scientific inves tigations about the surface and atmosphere of Earth and other planets. These new, so phisticated data demand new and advanced approaches to cluster detection, visualization, and supervised classification. In this article we concentrate on the issue of faithful topo logical mapping in order to avoid false interpretations of cluster maps created by an SaM. We describe several new extensions of the standard SaM, developed in the past few years: the Growing SelfOrganizing Map, magnification control, and Generalized Relevance Learn ing Vector Quantization, and demonstrate their effect on both lowdimensional traditional multispectral imagery and 200dimensional hyperspectral imagery.
Learning nonlinear image manifolds by global alignment of local linear models
 IEEE Trans. Pattern Analysis and Machine Intell
"... Abstract—Appearancebased methods, based on statistical models of the pixel values in an image (region) rather than geometrical object models, are increasingly popular in computer vision. In many applications, the number of degrees of freedom (DOF) in the image generating process is much lower than ..."
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Cited by 12 (0 self)
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Abstract—Appearancebased methods, based on statistical models of the pixel values in an image (region) rather than geometrical object models, are increasingly popular in computer vision. In many applications, the number of degrees of freedom (DOF) in the image generating process is much lower than the number of pixels in the image. If there is a smooth function that maps the DOF to the pixel values, then the images are confined to a lowdimensional manifold embedded in the image space. We propose a method based on probabilistic mixtures of factor analyzers to 1) model the density of images sampled from such manifolds and 2) recover global parameterizations of the manifold. A globally nonlinear probabilistic twoway mapping between coordinates on the manifold and images is obtained by combining several, locally valid, linear mappings. We propose a parameter estimation scheme that improves upon an existing scheme and experimentally compare the presented approach to selforganizing maps, generative topographic mapping, and mixtures of factor analyzers. In addition, we show that the approach also applies to finding mappings between different embeddings of the same manifold. Index Terms—Feature extraction or construction, machine learning, statistical image representation. 1
RealTime Pose Estimation of 3D Objects from Camera Images Using Neural Networks
, 1997
"... This paper deals with the problem of obtaining a rough estimate of three dimensional object position and orientation from a single two dimensional camera image. Such an estimate is required by most 3D to 2D registration and tracking methods that can efficiently refine an initial value by numerical ..."
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Cited by 11 (2 self)
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This paper deals with the problem of obtaining a rough estimate of three dimensional object position and orientation from a single two dimensional camera image. Such an estimate is required by most 3D to 2D registration and tracking methods that can efficiently refine an initial value by numerical optimization to precisely recover 3D pose. However, the analytic computation of an initial pose guess requires the solution of an extremely complex correspondence problem that is due to the large number of topologically distinct aspects that arise when a three dimensional opaque object is imaged by a camera. Hence general analytic methods fail to achieve realtime performance and most tracking and registration systems are initialized interactively or by ad hoc heuristics. To overcome these limitations we present a novel method for approximate object pose estimation that is based on a neural net and that can easily be implemented in realtime. A modification of Kohonen's selforganizing fe...
Local PSOMs and Chebyshev PSOMs Improving the Parametrised SelfOrganizing Maps
 IN PROC. INT. CONF. ON ARTIFICIAL NEURAL NETWORKS (ICANN95), PARIS
, 1995
"... We report on two new improvements for the "Parameterised SelfOrganizing Map" (PSOM). Both achieve a significant increase in mapping accuracy and computational efficiency. For a growing number of training points the use of higher order polynomials to construct the PSOM "mapping manifold" in [7] can ..."
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Cited by 11 (8 self)
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We report on two new improvements for the "Parameterised SelfOrganizing Map" (PSOM). Both achieve a significant increase in mapping accuracy and computational efficiency. For a growing number of training points the use of higher order polynomials to construct the PSOM "mapping manifold" in [7] can suffer from the increasing tendency to oscillate between the support points. We propose here to confine the algorithm to a subset of the training knots, resulting in what we call the "localPSOM" algorithm. This allows to avoid the use of highdegree polynomials without sacrificing accuracy. At the same time, the new approach offers a significant saving in required computations. A second way to improve the mapping preciseness makes use of the superior approximation properties of Chebyshev polynomials for the PSOM mapping manifold. The benefits of the two new approaches are demonstrated with two benchmark problems: (i) approximating a Gaussian bell function and (ii) learning of the (forward a...