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827
Forward models: Supervised learning with a distal teacher
 Cognitive Science
, 1992
"... Internal models of the environment have an important role to play in adaptive systems in general and are of particular importance for the supervised learning paradigm. In this paper we demonstrate that certain classical problems associated with the notion of the \teacher " in supervised learnin ..."
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Cited by 295 (7 self)
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Internal models of the environment have an important role to play in adaptive systems in general and are of particular importance for the supervised learning paradigm. In this paper we demonstrate that certain classical problems associated with the notion of the \teacher " in supervised learning can be solved by judicious use of learned internal models as components of the adaptive system. In particular, we show how supervised learning algorithms can be utilized in cases in which an unknown dynamical system intervenes between actions and desired outcomes. Our approach applies to any supervised learning algorithm that is capable of learning in multilayer networks.
A Growing Neural Gas Network Learns Topologies
 Advances in Neural Information Processing Systems 7
, 1995
"... An incremental network model is introduced which is able to learn the important topological relations in a given set of input vectors by means of a simple Hebblike learning rule. In contrast to previous approaches like the "neural gas" method of Martinetz and Schulten (1991, 1994), this model has n ..."
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Cited by 285 (5 self)
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An incremental network model is introduced which is able to learn the important topological relations in a given set of input vectors by means of a simple Hebblike learning rule. In contrast to previous approaches like the "neural gas" method of Martinetz and Schulten (1991, 1994), this model has no parameters which change over time and is able to continue learning, adding units and connections, until a performance criterion has been met. Applications of the model include vector quantization, clustering, and interpolation. 1 INTRODUCTION In unsupervised learning settings only input data is available but no information on the desired output. What can the goal of learning be in this situation? One possible objective is dimensionality reduction: finding a lowdimensional subspace of the input vector space containing most or all of the input data. Linear subspaces with this property can be computed directly by principal component analysis or iteratively with a number of network models (S...
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
A Unifying Review of Linear Gaussian Models
, 1999
"... Factor analysis, principal component analysis, mixtures of gaussian clusters, vector quantization, Kalman filter models, and hidden Markov models can all be unified as variations of unsupervised learning under a single basic generative model. This is achieved by collecting together disparate observa ..."
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Cited by 260 (17 self)
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Factor analysis, principal component analysis, mixtures of gaussian clusters, vector quantization, Kalman filter models, and hidden Markov models can all be unified as variations of unsupervised learning under a single basic generative model. This is achieved by collecting together disparate observations and derivations made by many previous authors and introducing a new way of linking discrete and continuous state models using a simple nonlinearity. Through the use of other nonlinearities, we show how independent component analysis is also a variation of the same basic generative model. We show that factor analysis and mixtures of gaussians can be implemented in autoencoder neural networks and learned using squared error plus the same regularization term. We introduce a new model for static data, known as sensible principal component analysis, as well as a novel concept of spatially adaptive observation noise. We also review some of the literature involving global and local mixtures of the basic models and provide pseudocode for inference and learning for all the basic models.
Growing Cell Structures  A Selforganizing Network for Unsupervised and Supervised Learning
 Neural Networks
, 1993
"... We present a new selforganizing neural network model having two variants. The first variant performs unsupervised learning and can be used for data visualization, clustering, and vector quantization. The main advantage over existing approaches, e.g., the Kohonen feature map, is the ability of the m ..."
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Cited by 250 (11 self)
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We present a new selforganizing neural network model having two variants. The first variant performs unsupervised learning and can be used for data visualization, clustering, and vector quantization. The main advantage over existing approaches, e.g., the Kohonen feature map, is the ability of the model to automatically find a suitable network structure and size. This is achieved through a controlled growth process which also includes occasional removal of units. The second variant of the model is a supervised learning method which results from the combination of the abovementioned selforganizing network with the radial basis function (RBF) approach. In this model it is possible  in contrast to earlier approaches  to perform the positioning of the RBF units and the supervised training of the weights in parallel. Therefore, the current classification error can be used to determine where to insert new RBF units. This leads to small networks which generalize very well. Results on the t...
Self Organization of a Massive Document Collection
 IEEE Transactions on Neural Networks
"... This article describes the implementation of a system that is able to organize vast document collections according to textual similarities. It is based on the SelfOrganizing Map (SOM) algorithm. As the feature vectors for the documents we use statistical representations of their vocabularies. The m ..."
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Cited by 204 (14 self)
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This article describes the implementation of a system that is able to organize vast document collections according to textual similarities. It is based on the SelfOrganizing Map (SOM) algorithm. As the feature vectors for the documents we use statistical representations of their vocabularies. The main goal in our work has been to scale up the SOM algorithm to be able to deal with large amounts of highdimensional data. In a practical experiment we mapped 6,840,568 patent abstracts onto a 1,002,240node SOM. As the feature vectors we used 500dimensional vectors of stochastic figures obtained as random projections of weighted word histograms. Keywords Data mining, exploratory data analysis, knowledge discovery, large databases, parallel implementation, random projection, SelfOrganizing Map (SOM), textual documents. I. Introduction A. From simple searches to browsing of selforganized data collections Locating documents on the basis of keywords and simple search expressions is a c...
The Helmholtz Machine
, 1995
"... Discovering the structure inherent in a set of patterns is a fundamental aim of statistical inference or learning. One fruitful approach is to build a parameterized stochastic generative model, independent draws from which are likely to produce the patterns. For all but the simplest generative model ..."
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Cited by 194 (22 self)
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Discovering the structure inherent in a set of patterns is a fundamental aim of statistical inference or learning. One fruitful approach is to build a parameterized stochastic generative model, independent draws from which are likely to produce the patterns. For all but the simplest generative models, each pattern can be generated in exponentially many ways. It is thus intractable to adjust the parameters to maximize the probability of the observed patterns. We describe a way of finessing this combinatorial explosion by maximizing an easily computed lower bound on the probability of the observations. Our method can be viewed as a form of hierarchical selfsupervised learning that may relate to the function of bottomup and topdown cortical processing pathways.
Task Decomposition Through Competition in a Modular Connectionist Architecture
 COGNITIVE SCIENCE
, 1990
"... A novel modular connectionist architecture is presented in which the networks composing the architecture compete to learn the training patterns. As a result of the competition, different networks learn different training patterns and, thus, learn to compute different functions. The architecture pe ..."
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Cited by 181 (5 self)
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A novel modular connectionist architecture is presented in which the networks composing the architecture compete to learn the training patterns. As a result of the competition, different networks learn different training patterns and, thus, learn to compute different functions. The architecture performs task decomposition in the sense that it learns to partition a task into two or more functionally independent vii tasks and allocates distinct networks to learn each task. In addition, the architecture tends to allocate to each task the network whose topology is most appropriate to that task, and tends to allocate the same network to similar tasks and distinct networks to dissimilar tasks. Furthermore, it can be easily modified so as to...
Generative models for discovering sparse distributed representations
 Philosophical Transactions of the Royal Society B
, 1997
"... We describe a hierarchical, generative model that can be viewed as a nonlinear generalization of factor analysis and can be implemented in a neural network. The model uses bottomup, topdown and lateral connections to perform Bayesian perceptual inference correctly. Once perceptual inference has b ..."
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Cited by 120 (5 self)
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We describe a hierarchical, generative model that can be viewed as a nonlinear generalization of factor analysis and can be implemented in a neural network. The model uses bottomup, topdown and lateral connections to perform Bayesian perceptual inference correctly. Once perceptual inference has been performed the connection strengths can be updated using a very simple learning rule that only requires locally available information. We demonstrate that the network learns to extract sparse, distributed, hierarchical representations.
SelfOrganizing Maps: Ordering, Convergence Properties and Energy Functions
 Biological Cybernetics
, 1992
"... We investigate the convergence properties of the selforganizing feature map algorithm for a simple, but very instructive case: the formation of a topographic representation of the unit interval [0; 1] by a linear chain of neurons. We extend the proofs of convergence of Kohonen and of Cottrell and F ..."
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Cited by 100 (2 self)
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We investigate the convergence properties of the selforganizing feature map algorithm for a simple, but very instructive case: the formation of a topographic representation of the unit interval [0; 1] by a linear chain of neurons. We extend the proofs of convergence of Kohonen and of Cottrell and Fort to hold in any case where the neighborhood function, which is used to scale the change in the weight values at each neuron, is a monotonically decreasing function of distance from the winner neuron. We prove that the learning dynamics cannot be described by a gradient descent on a single energy function, but may be described using a set of potential functions, one for each neuron, which are independently minimized following a stochastic gradient descent. We derive the correct potential functions for the one and multidimensional case, and show that the energy functions given by Tolat (1990) are an approximation which is no longer valid in the case of highly disordered maps or steep neig...