An Overcomplete Sparse Code to explain visual cortical nonlinearities

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An Overcomplete Sparse Code to explain visual
cortical nonlinearities
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Common algorithms limitations
PCA
ICA
ideal algorithm
Non-Orthogonal
Overcomplete
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ICA (linear)
Natural images
Ls
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The algorithm (quadratic sparse coding)
1. Using gray-scale natural images
2. Extract patches (8x8, 64 dim.)
3. Compute pairwise products (2080)
4. Dimensionality reduction (256)
5. whiten the data
6. Sparse code (or use ICA)
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L problem quad. sparse forms
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L problem spatiotemporal
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Embedded L problem
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Summary
Overcomplete, sparse codes reveal more relevant
structure
Even the simplest spatial and temporal
transformations necessitate such codes
Implications for relating natural images/video
encoding to early visual cortical cell responses.
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Acknowledgements

• David Field
• Damon Chandler
• Daniel Graham

Funding NSF nonlinear systems IGERT
Computation Cornell Center for Applied
Math, National Geospatial-Intelligence Agency