Analysis of convolutional neural network image classifiers in a rotationally symmetric model
This provides theoretical justification for CNN performance in image classification, though it's incremental as it builds on existing CNN frameworks.
The paper analyzes the convergence rate of convolutional neural network classifiers for binary image classification, showing they can circumvent the curse of dimensionality under rotational symmetry assumptions, with results validated on simulated and real data.
Convolutional neural network image classifiers are defined and the rate of convergence of the misclassification risk of the estimates towards the optimal misclassification risk is analyzed. Here we consider images as random variables with values in some functional space, where we only observe discrete samples as function values on some finite grid. Under suitable structural and smoothness assumptions on the functional a posteriori probability, which includes some kind of symmetry against rotation of subparts of the input image, it is shown that least squares plug-in classifiers based on convolutional neural networks are able to circumvent the curse of dimensionality in binary image classification if we neglect a resolution-dependent error term. The finite sample size behavior of the classifier is analyzed by applying it to simulated and real data.