Title: An Overcomplete Sparse Code to explain visual cortical nonlinearities
1An Overcomplete Sparse Code to explain visual
cortical nonlinearities
2Common algorithms limitations
PCA
ICA
ideal algorithm
Non-Orthogonal
Overcomplete
3ICA (linear)
Natural images
Ls
4The 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)
5L problem quad. sparse forms
6L problem spatiotemporal
7Embedded L problem
8Summary
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.
9Acknowledgements
- David Field
- Damon Chandler
- Daniel Graham
Funding NSF nonlinear systems IGERT
Computation Cornell Center for Applied
Math, National Geospatial-Intelligence Agency