The sparse manifold transform

Published in Neural Information Processing Systems, 2018

Paper link

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.

Recommended citation:
Yubei Chen, Dylan M. Paiton, and Bruno A. Olshausen. “The sparse manifold transform.” Advances in neural information processing systems. 2019.

 author={Chen, Yubei and Paiton, Dylan and Olshausen, Bruno},
 booktitle={Advances in Neural Information Processing Systems},
 editor={S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett},
 publisher={Curran Associates, Inc.},
 title={The Sparse Manifold Transform},