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#### Initialisation and training of the GLLiM model
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The Gaussian Locally Linear Mapping (GLLiM) model is a parametric statistical model closely related to Gaussian mixtures. It can describe the direct and inverse interaction between X and Y by a combination of local affine transformations and is adapted to solving inversion regression problems in a Bayesian framework. We refer the reader to [Kugler et al. 2020 and Deleforge et al., 2014] for a definition and detailed description of the model.
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The Gaussian Locally Linear Mapping (GLLiM) model is a parametric statistical model closely related to Gaussian mixtures and mixtures of expert models. It can describe the direct and inverse interaction between X and Y by a combination of local affine transformations and is adapted to solving inversion regression problems in a Bayesian framework. We refer the reader to [Kugler et al. 2020 and Deleforge et al., 2014] for a definition and detailed description of the model.
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The local transformation function $`\tau_k`$ from X to Y is given by:
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