A Sparse Grid Based Generative Topographic Mapping for the Dimensionality Reduction of High-Dimensional Data

Michael Griebel () and Alexander Hullmann ()
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Michael Griebel: University of Bonn, Institute for Numerical Simulation
Alexander Hullmann: University of Bonn, Institute for Numerical Simulation

A chapter in Modeling, Simulation and Optimization of Complex Processes - HPSC 2012, 2014, pp 51-62 from Springer

Abstract: Abstract Most high-dimensional data exhibit some correlation such that data points are not distributed uniformly in the data space but lie approximately on a lower-dimensional manifold. A major problem in many data-mining applications is the detection of such a manifold from given data, if present at all. The generative topographic mapping (GTM) finds a lower-dimensional parameterization for the data and thus allows for nonlinear dimensionality reduction. We will show how a discretization based on sparse grids can be employed for the mapping between latent space and data space. This leads to efficient computations and avoids the ‘curse of dimensionality’ of the embedding dimension. We will use our modified, sparse grid based GTM for problems from dimensionality reduction and data classification.

Keywords: Latent Space; Regularization Term; Sparse Grid; Locally Linear Embedding; Kernel Principal Component Analysis (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-09063-4_5

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DOI: 10.1007/978-3-319-09063-4_5

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