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In this paper, we propose an auto-encoder based generative neural network model whose encoder compresses the inputs into vectors in the tangent space of a special Lie group manifold: upper triangular positive definite affine transform matrices (UTDATs).
Gradient-based learning applied to document recognition
Lecun, Y., Bottou, L., Bengio, Y., and Haffner, P · 1998
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Lie Groups Beyond an Introduction
Knapp, A. W · 2002
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Reducing the Dimensionality of Data with Neural Networks
Hinton, G. E. and Salakhutdinov, R. R · 2006
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Yeh, R., Liu, Z., Goldman, D. B., and Agarwala, A · 2016
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Zhang, H., Goodfellow, I., Metaxas, D., and Odena, A · 2018
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