Yubei Chen and Dylan Paiton and Bruno Olshausen

EECS Department, University of California, Berkeley

Technical Report No. UCB/EECS-2018-167

December 11, 2018

We present a signal representation framework called the sparse manifold transform that combines key ideas from sparse coding, manifold learning, and slow feature analysis. It turns non-linear transformations in the primary sensory signal space into linear interpolations in a representational embedding space while maintaining approximate invertibility. The sparse manifold transform is an unsupervised and generative framework that explicitly and simultaneously models the sparse discreteness and low-dimensional manifold structure found in natural scenes. When stacked, it also models hierarchical composition. We provide a theoretical description of the transform and demonstrate properties of the learned representation on both synthetic data and natural videos.

Advisors: Bruno Olshausen and Pieter Abbeel

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BibTeX citation:

@mastersthesis{Chen:EECS-2018-167,
    Author= {Chen, Yubei and Paiton, Dylan and Olshausen, Bruno},
    Title= {The Sparse Manifold Transform},
    School= {EECS Department, University of California, Berkeley},
    Year= {2018},
    Month= {Dec},
    Url= {http://www2.eecs.berkeley.edu/Pubs/TechRpts/2018/EECS-2018-167.html},
    Number= {UCB/EECS-2018-167},
    Abstract= {We present a signal representation framework called the sparse manifold transform that combines key ideas from sparse coding, manifold learning, and slow feature analysis. It turns non-linear transformations in the primary sensory signal space into linear interpolations in a representational embedding space while maintaining approximate invertibility. The sparse manifold transform is an unsupervised and generative framework that explicitly and simultaneously models the sparse discreteness and low-dimensional manifold structure found in natural scenes. When stacked, it also models hierarchical composition. We provide a theoretical description of the transform and demonstrate properties of the learned representation on both synthetic data and natural videos.},
}

EndNote citation:

%0 Thesis
%A Chen, Yubei 
%A Paiton, Dylan 
%A Olshausen, Bruno 
%T The Sparse Manifold Transform
%I EECS Department, University of California, Berkeley
%D 2018
%8 December 11
%@ UCB/EECS-2018-167
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/2018/EECS-2018-167.html
%F Chen:EECS-2018-167