  Deep learning models extract, before a final classification layer, features
or patterns which are key for their unprecedented advantageous performance.
However, the process of complex nonlinear feature extraction is not well
understood, a major reason why interpretation, adversarial robustness, and
generalization of deep neural nets are all open research problems. In this
paper, we use wavelet transformation and spectral methods to analyze the
contents of image classification datasets, extract specific patterns from the
datasets and find the associations between patterns and classes. We show that
each image can be written as the summation of a finite number of rank-1
patterns in the wavelet space, providing a low rank approximation that captures
the structures and patterns essential for learning. Regarding the studies on
memorization vs learning, our results clearly reveal disassociation of patterns
from classes, when images are randomly labeled. Our method can be used as a
pattern recognition approach to understand and interpret learnability of these
datasets. It may also be used for gaining insights about the features and
patterns that deep classifiers learn from the datasets.
