GTM: The Generative Topographic Mapping

Bishop, Christopher M.; Svensén, Markus; Williams, Christopher K. I.

doi:10.1162/089976698300017953

Cited by 1,079 publications

(834 citation statements)

References 18 publications

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“…Another possible way to define TDDs was to make use of subspace and low dimensional manifold produced by such dimensionality reduction techniques as PCA and generative topographic mapping (GTM). [48] Like Mishima et al [49] and Takeda et al [50] succeeded to propose novel chemical structures corresponding to a target area on the GTM manifold, taking TDDs into account through subspace might give a better chance to find de novo chemical structures.…”

Section: Distances Among Chemical Structures In Gdb11mentioning

confidence: 99%

Finding Chemical Structures Corresponding to a Set of Coordinates in Chemical Descriptor Space

Miyao

Funatsu

2017

Mol. Inf.

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When chemical structures are searched based on descriptor values, or descriptors are interpreted based on values, it is important that corresponding chemical structures actually exist. In order to consider the existence of chemical structures located in a specific region in the chemical space, we propose to search them inside training data domains (TDDs), which are dense areas of a training dataset in the chemical space. We investigated TDDs' features using diverse and local datasets, assuming that GDB11 is the chemical universe. These two analyses showed that considering TDDs gives higher chance of finding chemical structures than a random search-based method, and that novel chemical structures actually exist inside TDDs. In addition to those findings, we tested the hypothesis that chemical structures were distributed on the limited areas of chemical space. This hypothesis was confirmed by the fact that distances among chemical structures in several descriptor spaces were much shorter than those among randomly generated coordinates in the training data range

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Section: Distances Among Chemical Structures In Gdb11mentioning

confidence: 99%

Finding Chemical Structures Corresponding to a Set of Coordinates in Chemical Descriptor Space

Miyao

Funatsu

2017

Mol. Inf.

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“…It is true that the neural-computing community re-discovered some statistical concepts already in existence, but this influx of participants has created new ideas and refined existing ones. These benefits include the learning of sequences by time delay and partial recurrence [23], and the creation of powerful visualization techniques, such as generative topographic mapping [24]. Thus the ANN movement has resulted in statisticians having available to them a collection of techniques to add to their repertoire.…”

Section: Multilayer Perceptronsmentioning

confidence: 99%

Perspectives and Prospects

Mareschal¹

2016

Introduction to Drug Disposition and Pharmacokinetics

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In 1998, over 400 papers on artificial neural networks (ANNs) were published in the context of medicine, but why is there this interest in ANNs? And how do ANNs compare with traditional statistical methods? We propose some answers to these questions, and go on to consider the 'black box' issue. Finally, we briefly look at two directions in which ANNs are likely to develop, namely the use of Bayesian statistics and knowledgedata fusion.

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“…First, compute a kernel density estimate from the 6 Figures 5 and 6 may require to be viewed in colour to appreciate the different basins. 7 Or any other model that results in it, such as the generative topographic mapping (Bishop et al, 1998) or kernel density estimation. .…”

Section: Clusteringmentioning

confidence: 99%

On the Number of Modes of a Gaussian Mixture

Carreira-Perpiñán

Williams

2003

Scale Space Methods in Computer Vision

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We consider a problem intimately related to the creation of maxima under Gaussian blurring: the number of modes of a Gaussian mixture in D dimensions. To our knowledge, a general answer to this question is not known. We conjecture that if the components of the mixture have the same covariance matrix (or the same covariance matrix up to a scaling factor), then the number of modes cannot exceed the number of components. We demonstrate that the number of modes can exceed the number of components when the components are allowed to have arbitrary and different covariance matrices.We will review related results from scale-space theory, statistics and machine learning, including a proof of the conjecture in 1D. We present a convergent, EM-like algorithm for mode finding and compare results of searching for all modes starting from the centers of the mixture components with a brute-force search. We also discuss applications to data reconstruction and clustering.

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GTM: The Generative Topographic Mapping

Cited by 1,079 publications

References 18 publications

Finding Chemical Structures Corresponding to a Set of Coordinates in Chemical Descriptor Space

Finding Chemical Structures Corresponding to a Set of Coordinates in Chemical Descriptor Space

Perspectives and Prospects

On the Number of Modes of a Gaussian Mixture

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