Pattern recognition at different scales: A statistical perspective

• We introduce two typical statistical scales affecting the performance of a pattern recognition algorithm.
• We describe the dependence of such scales on the image resolution.
• We recover the results of the statistical analysis by using Support Vector Machines algorithm.
• We discuss the effect of averaging the performance of a Support Vector Machine over different training samples.

In this paper we borrow concepts from Information Theory and Statistical Mechanics to perform a pattern recognition procedure on a set of X-ray hazelnut images. We identify two relevant statistical scales, whose ratio affects the performance of a machine learning algorithm based on statistical observables, and discuss the dependence of such scales on the image resolution. Finally, by averaging the performance of a Support Vector Machines algorithm over a set of training samples, we numerically verify the predicted onset of an “optimal” scale of resolution, at which the pattern recognition is favoured.