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	Generative Topographic Map -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-09)
		An alternative to the (additional info and facts about self-organizing map) self-organizing map (SOM), called the generative topographic map (GTM), was presented in 1996 in a paper by Bishop, Svensen, and Williams.
		The GTM is a probabilistic counterpart to SOM, which is provably convergent and does not require a shrinking neighborhood or a decreasing step size.
		The GTM is a (additional info and facts about generative model) generative model of data: the training data is assumed to arise by first probabilistically picking a point in a low-dimensional space, mapping the point to the observed high-dimensional input space (via a smooth function), then adding noise in the high-dimensional input space.
	www.absoluteastronomy.com /encyclopedia/G/Ge/Generative_Topographic_Map.htm (154 words)

	Generative Topographic Map - Wikipedia, the free encyclopedia
		An alternative to the self-organizing map (SOM), called the generative topographic map (GTM), was presented in 1996 in a paper by Bishop, Svensen, and Williams.
		The GTM is a generative model of data: the training data is assumed to arise by first probabilistically picking a point in a low-dimensional space, mapping the point to the observed high-dimensional input space (via a smooth function), then adding noise in the high-dimensional input space.
		The parameters of the low-dimensional probability distribution, the smooth map, and the noise in the high-dimensional input space are all learned from the training set by the Expectation-Maximization (EM) algorithm.
	www.wikipedia.org /wiki/Generative_topographic_map (159 words)

	Encyclopedia: Generative Topographic Mapping (Site not responding. Last check: 2007-10-09)
		In mathematics, a linear transformation (also called linear operator or linear map) is a function between two vector spaces that respects the arithmetical operations addition and scalar multiplication defined on vector spaces, or, in other words, it preserves linear combinations.
		In data analysis, GTMs are like a nonlinear version of PCA, which allow high dimensional data to be modelled as resulting from Gaussian noise added to sources in lower-dimensional latent space.
		In generative deformational modelling, the latent and data spaces have the same dimensions, for example, 2D images or 1 audio sound waves.
	www.nationmaster.com /encyclopedia/Generative-Topographic-Mapping (688 words)

	Neural network - Open Encyclopedia (Site not responding. Last check: 2007-10-09)
		In general the problem of reaching a network that performs well, even on examples that were not used as training examples, is a quite subtle issue that requires additional techniques.
		The Self-organizing map (SOM), sometimes referred to as "Kohonen map" due to its invention by Professor Teuvo Kohonen, is an unsupervised learning technique that reduces the dimensionality of data through the use of a self-organizing neural network.
		A probabilistic version of SOM is the Generative Topographic Map (GTM) of Bishop, Svensen and Williams.
	open-encyclopedia.com /ANN (2361 words)

	Self-organizing map - Wikipedia, the free encyclopedia
		The self-organising map (SOM) is a method for unsupervised learning, based on a grid of artificial neurons whose weights are adapted to match input vectors in a training set.
		Output maps can also be made in different dimensions: 1-dimensional, 2-dimensional, etc., but most popular are 2D and 3D maps, for SOMs are mainly used for dimensionality reduction rather than expansion.
		During the mapping process a new input vector may quickly be given a location on the map, it is automatically classified or categorised.
	www.wikipedia.org /wiki/Self-organizing_map (668 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		IFA generalizes and unifies ordinary factor analysis (FA), principal component analysis (PCA), and independent component analysis (ICA), and can handle not only square noiseless mixing but also the general case where the number of mixtures differs from the number of sources and the data are noisy.
		Based on standard probability density models a generic nonlinearity is developed which allows both 1) identification and visualization of dichotomised clusters inherenet in the observed data nad 2) seperation of sources with arbitrary distributions from mixtures, whose dimensionality may be greater than that of number of sources.
		Since the GTM is non-linear, the relationship between data and its visual representation may be far from trivial, but a better understanding of this relationship can be gained by computing the so-called magnification factor.
	www.lans.ece.utexas.edu /~lans/bib/nn.bib (1208 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		The generative topographic mapping (GTM) was developed and introduced as a principled alternative to the self-organising map for, principally, visualising high-dimensional continuous data.
		The GTM is one method by which a topographically organised low-dimensional data representation may be realised.
		The non-negative factorisation of a positive matrix which ensures a topographic ordering of the constituent factors is also presented as a principled yet non-probabilistic alternative to the GTM model.
	ilab.usc.edu /jtrack/12/Girolami02.bib (268 words)

	Self-organizing map : Self organizing map (Site not responding. Last check: 2007-10-09)
		A newer version of the self-organizing map is called the Generative Topographic Map[?] (GTM).
		The GTM was first presented in 1996 in a paper by Bishop, Svensen, and Williams.
		The GTM is a probabilistic version of SOM, which is provably convergent and doesn't require a shrinking neighborhood or a decreasing step size.
	www.termsdefined.net /se/self-organizing-map.html (599 words)

	Citations: GTM: the generative topographic mapping - Bishop, Svens'en, Williams (ResearchIndex) (Site not responding. Last check: 2007-10-09)
		In GTM mixture components are parameterized by a linear combination of nonlinear basis functions of the locations of the components in the latent space.
		Since GTM is a generative probabilistic model, we were able to formulate training of the visualization hierarchy in a unified and principled framework of maximum likelihood parameter estimation using the expectationmaximization algorithm [8] In this study, we present a further development in....
		Basically, GTM is a probabilistic re formulation of the Kohonen self organizing map (SOM) but unlike SOM, GTM defines an explicit probability density model of the data.
	citeseer.lcs.mit.edu /context/69536/59244 (3042 words)

	Self-Organising Map (Site not responding. Last check: 2007-10-09)
		The map units are organised into a typically two-dimensional grid, where the model vectors of neighbours in the grid are neighbours in the data space.
		It is a decreasing function of the distance between the the ith and cth model on the map grid.
		When the dimensionality gets larger, however, the number of map units grows exponentially and therefore the model is not well suited for tasks with high intrinsic dimensionality.
	www.cis.hut.fi /praiko/dippa/node17.html (155 words)

	Self-organizing map -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-09)
		The self-organising map (SOM) is a method for (additional info and facts about unsupervised learning) unsupervised learning, based on a grid of (additional info and facts about artificial neuron) artificial neurons whose weights are adapted to match input vectors in a training set.
		It was first described by the (The official language of Finland; belongs to the Baltic Finnic family of languages) Finnish professor (additional info and facts about Teuvo Kohonen) Teuvo Kohonen and is thus sometimes referred to as a Kohonen map.
		Output maps can also be made in different dimensions: 1-dimensional, 2-dimensional, etc., but most popular are 2D and 3D maps, for SOMs are mainly used for (additional info and facts about dimensionality reduction) dimensionality reduction rather than expansion.
	www.absoluteastronomy.com /encyclopedia/s/se/self-organizing_map.htm (684 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		In general the problem of reaching a network that performs well, even on examples that were not used as training examples, isa quite subtle issue that requires additional techniques.
		The Self-organizing map (SOM), sometimes referred to as"Kohonen map" due to its invention by Professor Teuvo Kohonen, is an unsupervisedlearning technique that reduces the dimensionality of data through the use of a self-organizing neural network.
		Aprobabilistic version of SOM is the Generative Topographic Map (GTM) of Bishop, Svensen and Williams.
	immune-system-help.com /network/networks/neural_nets.html (1992 words)

	Colloquium Papers - Artificial Intelligence @ RightNow Technologies (Site not responding. Last check: 2007-10-09)
		The general EM is a description of a meta-algorithm, which is used to design a particular algorithm.
		EXACT maps each English user request to an SQL query, which is transformed to create a PDDL goal, and uses the Blackbox planner [13] to map the planning problem to a sequence of appliance commands that satisfy the original request.
		Trees are generated using the well-known C4.5 algorithm, and the classifier consists of multiple trees constructed in pseudo-randomly selected subspaces of the given feature space.
	ai.rightnow.com /colloquium/papers.php (14087 words)

	Neural Computing Research Group: The GTM Homepage (Site not responding. Last check: 2007-10-09)
		GTM, which stands for generative topographic mapping, is a model for density modeling and data visualisation, developed at the Neural Computing Research Group.
		GTM: The Generative Topographic Mapping, PhD thesis by Markus Svensén, 1998.
		GTM: A Principled Alternative to the Self-Organizing Map, presented at NIPS*96.
	www.ncrg.aston.ac.uk /GTM (216 words)

	Neural network - ArtPolitic Encyclopedia of Politics : Information Portal
		The universal approximation theorem for neural networks states that every continuous function that maps intervals of real numbers to some output interval of real numbers can be approximted arbitrary closely by a multi-layer perceptron with just one hidden layer.
		In general the problem of reaching a network that performs well, even on examples that where not used as training examples, is quite a subtle issue that requires additional techniques.
		Other typical problems of the back-propagation algorithm are the speed of convergence, the possibility to end up in a local minimum of the error function, and the issue of overfitting (i.e.
	www.artpolitic.org /infopedia/an/ANN.html (1818 words)

	Developments of the Generative Topographic Mapping - Bishop, Svens'en, Williams (ResearchIndex) (Site not responding. Last check: 2007-10-09)
		Abstract: The Generative Topographic Mapping (GTM) model was introduced by Bishop et al.
		(1998) as a probabilistic re-formulation of the self-organizing map (SOM).
		In this paper we report on several extensions of the GTM, including an incremental version of the EM algorithm for estimating the model parameters, the use of local subspace models, extensions to mixed discrete and...
	citeseer.lcs.mit.edu /bishop98developments.html (765 words)

	Topographic Map Of Mt Ruiz (Site not responding. Last check: 2007-10-09)
		This map was developed from a mosaic of 16 Landsat...
		least 1280 locations from which the topographic map is generated...
		resulting global topographic map is the most accurate of...
	www.mnsps.com /topographic-map-of-mt--ruiz.php (540 words)

	Software for the data mining course (Site not responding. Last check: 2007-10-09)
		General Description: Bow is a library of C code for statistical text analysis, language modeling and information retrieval.
		In general a thorough background knowledge of the algorithms is needed to use them.
		General Description: SVMTorch is an implementation of Vapnik's Support Vector Machine that works both for classification and regression problems, and that has been specifically tailored for large-scale problems (such as more than 20000 examples, even for input dimensions higher than 100).
	www.inf.ed.ac.uk /teaching/courses/dme/html/software2.html (2277 words)

	Machine Learning List: Vol. 10, No. 15 (Site not responding. Last check: 2007-10-09)
		Instead of defining metric vector spaces to be used with the self-organizing map (SOM) as is usually the case, symbols strings are organized on a SOM array.
		The algorithms described are the Soft Topographic Vector Quantization (STVQ) algorithm, the Kernel-based Soft Topographic Mapping (STMK) algorithm, and the Soft Topographic Mapping for Proximity data (STMP) algorithm.
		C.M. Bishop, M. Svensn, and C.K.I. Williams present Developments of the generative topographic mapping (GTM) which is an enhancement of the standard SOM algorithm with a number of advantages.
	www.ics.uci.edu /~mlearn/MLlist/v10/15.html (3934 words)

	Bayesian Sampling and Ensemble Learning in Generative Topographic Mapping (Site not responding. Last check: 2007-10-09)
		Generative topographic mapping (GTM) is a statistical model to extract a hidden smooth manifold from data, like the self-organizing map (SOM).
		Although a deterministic search algorithm for the hyperparameters regulating the smoothness of the manifold has been proposed previously, it is based on approximations that are valid only on abundant data.
		From the result of an experimental comparison of these algorithms, an efficient method for reliable estimation in GTM is suggested.
	staff.aist.go.jp /utsugi-a/bselgtm.html (140 words)

	Other research (Site not responding. Last check: 2007-10-09)
		A project led by the Institute of Neurology is concerned with the characterisation of the firing patterns measured from single cells in the basal ganglia, using self-organised maps and Hidden Markov modelling.
		Generative Topographic Map (GTM) of single cell recordings from the basal ganglia, taken in the periods immediately preceding and following conscious limb movements.
		Detailed GTM locations for individual cells in GPie, showing that they appear to have distinct firing patterns.
	www.cms.livjm.ac.uk /research/snc/other.htm (190 words)

	ABC-Dir: Topographic
		Historical topographic maps of US East Coast states from 19th and early 20th century, scanned from original US Geological Survey...
		Topographic map of ancient Mesopotamia from Syracuse University.
		Specializing in digital USGS topographic maps for most of the United States, all sizes and scales.
	www.abc-directory.com /view/topographic (172 words)

	1999 Projects in Artificial Intelligence (Site not responding. Last check: 2007-10-09)
		The purpose of this project is to use self organising artificial neural networks to facilitate the mapping of sensory perceptions, and to use that mapping as a joint point of reference in collaborative robotics.
		In general, games are interesting test beds for reinforcement learning algorithms, where one has to learn the value of moves made throughout the game, but the feedback comes only at the end of the game.
		Generating natural language is an active research area, in which the problems are (at least partly) understood, and progress is being made towards their solution.
	www.cs.man.ac.uk /ugrad/projects/year99/ai.html (3838 words)

	Topographic Mapping - VIP Maps
		Contacts The mission of the Cooperative Topographic Mapping (CTM) Program is to provide the Nation with access to current, accurate, and consistent base geographic data...
		...GTM, which stands for..generative topographic mapping, is a model for density.....GTM can be found in..
		GTM: The Generative Topographic Mapping, PhD thesis by Markus.....Map.
	www.vipmaps.com /topographic-mapping (188 words)

	Topographic algorithms (Site not responding. Last check: 2007-10-09)
		Change detection and integration of topographic updates from ATKIS to...
		Inclusion of topographic variables in an unsupervised classification of satellit...
		Topographic Maps Based on Kohonen Self Organizing Maps...
	www.scienceoxygen.com /signal/258.html (371 words)

	Abstract for reinhard_tr308
		On this subspace, we attempt a parametric modelling of the trajectory, and compute a distance metric to perform classification of diphones.
		We use the principal curves method of Hastie and Stuetzle and the Generative Topographic map (GTM) technique of Bishop, Svenson and Williams to describe the temporal evolution in terms of latent variables.
		We have attempted to provide automatically generated PDF copies of documents for which only PostScript versions have previously been available.
	svr-www.eng.cam.ac.uk /reports/abstracts/reinhard_tr308.html (321 words)

	GTM---Thesis by Markus Svensén (Site not responding. Last check: 2007-10-09)
		This thesis describes the Generative Topographic Mapping (GTM) --- a non-linear latent variable model, intended for modelling continuous, intrinsically low-dimensional probability distributions, embedded in high-dimensional spaces.
		When the target distribution is very different to that, the aim of maintaining an `interpretable' structure, suitable for visualizing data, may come in conflict with the aim of providing a good density model.
		Furthermore, this framework provides solid ground for extending the GTM to wider contexts than that of this thesis.
	www.ncrg.aston.ac.uk /GTM/thesis.html (389 words)

	Bibliography
		Bishop, C. M., Svensen, M., and Williams, C. Gtm: The generative topographic map.
		MacKay, D. and Oldfield, M. Generalization error and the number of hidden units in a multilayer perceptron.
		Sammon, J. A nonlinear mapping for data structures analyses a nonlinear mapping for data structures sanalyses.
	www.fe.up.pt /~jcard/publicacoes/tese_html/node220.html (2309 words)

	MACP: phd-thesis (Site not responding. Last check: 2007-10-09)
		We show that their log-likelihood surface has no singularities, unlike other mixture models, which makes EM estimation practical; and that their theoretical non-identifiability is rarely realised in actual estimates, which makes them interpretable.
		We discuss the advantages of the method over previous work based on the conditional mean or on universal mapping approximators (including ensembles and recurrent networks), conditional distribution estimation, vector quantisation and statistical analysis of missing data.
		We describe the possible application of the method to several well-known reconstruction or inversion problems: decoding of neural population activity for hippocampal place cells; wind field retrieval from scatterometer data; inverse kinematics and dynamics of a redundant manipulator; acoustic-to-articulatory mapping; audiovisual mappings for speech recognition; and recognition of occluded speech.
	www.dcs.shef.ac.uk /~miguel/papers/phd-thesis.html (714 words)

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