GTM: The Generative Topographic Mapping

By Charles M. Bishop, Markus Svensén, Christopher K. I. Williams. 1998

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Deep Unsupervised Learning using Nonequilibrium Thermodynamics (2015, background): “There is additionally significant work learning flexible generative mappings from simple latent distributions to data distributions – early examples including (MacKay, 1995) where neural networks are introduced as generative models, and (Bishop et al., 1998) where a stochastic manifold mapping is le”
f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization (2016, methodology): “Such probabilistic feedforward neural network models were first considered in [22] and [3], here we call these models generative neural samplers.”
Distance Metric Learning: A Comprehensive Survey (2006, methodology): “• Generative methods This group of methods adopts generative topology models [44, 45, 46], and hypothesizes that observed data are generated from the evenly spaced low dimensional latent nodes.”
Content-based organization and visualization of music archives (2002, methodology): “Methods with similar abilities include Principial Component Analysis [11], Multi-Dimensional Scaling [15], Sammon s mapping [27], or the Generative Topographic Mapping [3].”
Redundancy reduction revisited (2001, background): “…a network that determines simplifying beliefs, Hinton and Zemel (1994) suggest minimum description length and vector quantization methods for ﬁnding latent variables and Bishop et al (1998) describe a method that uses nonlinear transformations but is otherwise analogous to factor analysis.”
Connectionist multivariate density-estimation and its application to speech synthesis (2016, methodology): “Low-dimensional latent spaces can be sampled in a regular grid, in which case an expectation-maximization algorithm can be used for training (Bishop et al., 1998).”
Mathematical Aspects of Divergence Based Vector Quantization Using Fr´ echet-Derivatives (2009, background): “[18],[20],[19], Generative Topographic Mapping (GTM) [ 4 ], Soft Topographic Map-”
Pattern Recognition and Machine Learning (2006, unknown): “The generative topographic mapping, or GTM (Bishop et al., 1996; Bishop et al., 1997a; Bishop et al., 1998b) uses a latent distribution that is defined by a finite regular grid of delta functions over the (typically two-dimensional) latent space.”
Local discriminant embedding and its variants (2005, background): “Some algorithms resolve this kind of difficulty by finding a mapping for the whole data space, not just for the training data, e.g., [1], [ 4 ], [9], [12], [18].”
Hybrid and ensemble-based soft computing techniques in bankruptcy prediction: a survey (2010, unknown): “…(Tenenbaum et al. 2000), datadriven high-dimensional scaling (Lespinats et al. 2007), Sammon mapping (Sammon 1969), generative topographic mapping (Bishop et al. 1998), self-organizing maps (Kohonen 1990), curvilinear component analysis (CCA) (Demartines and Herault 1997; Lee et al. 2004),…”
Decision Forests for Classification, Regression, Density Estimation, Manifold Learning and Semi-Supervised Learning (2011, background): “A generative, probabilistic model for learning a latent manifold is discussed in [6].”
Dimensionality Reduction: A Comparative Review (2008, methodology): “The comparative review does not include self-organizing maps [73] and their probabilistic extension GTM [19], because these techniques combine a dimensionality reduction technique with clustering, as a result of which they do not fit in the dimensionality reduction framework that we discussed in Sec”
Intrinsic Dimension Estimation Using Packing Numbers (2002, methodology): “Another general scheme in the family of projection techniqu es is to turn the dimensionality reduction algorithm from an embedding technique into a prob abilistic, generative model [8], and optimize the dimension as any other parameter by usi ng cross-validation in a maximum likelihood setting.”