@article{3731,
  title = {Factorial coding of natural images: how effective are linear models in removing higher-order dependencies?},
  journal = {Journal of the Optical Society of America A},
  abstract = {The performance of unsupervised learning models for natural images is evaluated quantitatively by means of information theory. We estimate the gain in statistical independence (the multi-information reduction) achieved with independent component analysis (ICA), principal
  component analysis (PCA), zero-phase whitening, and predictive coding. Predictive coding is translated into the transform coding
  framework, where it can be characterized by the constraint of a triangular filter matrix. A randomly sampled whitening basis and the
  Haar wavelet are included into the comparison as well. The comparison of all these methods is carried out for different patch sizes, ranging from 2x2 to 16x16 pixels. In spite of large differences in the shape of the basis functions, we find only small differences in the multi-information between all decorrelation transforms (5% or less) for all patch sizes. Among the second-order methods, PCA is optimal for small patch sizes and predictive coding performs best for large patch sizes. The extra gain achieved with ICA is always less than 2%. In conclusion, the `edge filters‘ found with ICA lead only to a surprisingly small improvement in terms of its
  actual objective.},
  volume = {23},
  number = {6},
  pages = {1253-1268},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = jun,
  year = {2006},
  slug = {3731},
  author = {Bethge, M.},
  month_numeric = {6}
}