  Sparse coding has been proposed as a theory of visual cortex and as an
unsupervised algorithm for learning representations. We show empirically with
the MNIST dataset that sparse codes can be very sensitive to image distortions,
a behavior that may hinder invariant object recognition. A locally linear
analysis suggests that the sensitivity is due to the existence of linear
combinations of active dictionary elements with high cancellation. A nearest
neighbor classifier is shown to perform worse on sparse codes than original
images. For a linear classifier with a sufficiently large number of labeled
examples, sparse codes are shown to yield higher accuracy than original images,
but no higher than a representation computed by a random feedforward net.
Sensitivity to distortions seems to be a basic property of sparse codes, and
one should be aware of this property when applying sparse codes to invariant
object recognition.
