Trimming Prototypes of Handwritten Digit Images with Subset Infinite Relational Model

This paper proposes a nonparametric Bayesian model for constructing a trimmed prototype representation of handwritten digit images. We assume that all images are resized to the same size. At each pixel point, we count the number of occurrences of grayscaled colors over multiple images. Then we obtain a color histogram at each pixel location. When we conduct this counting over images of the same category, e.g. images of handwritten digit “5”, the obtained set of histograms can be regarded as a prototype of the category. After normalizing each histogram to a probability distribution over colors, we can calculate a likelihood of an unknown image by multiplying the probability of the color appearing at each pixel. We regard this method as the baseline and compare it with a method using a probabilistic model called Multinomialized Subset Infinite Relational Model (MSIRM), which constructs a prototype by clustering pixel columns and rows. While MSIRM can determine the number of clusters flexibly based on Chinese restaurant process, its interesting feature is that it can detect columns and rows irrelevant for constructing a prototype. In the experiment, we compared our method with the baseline and also with a histogram clustering by Dirichlet process mixture of multinomial. It was revealed that MSIRM could detect irrelevant columns and rows accurately at peripheral part of handwritten digit images. This means that MSIRM could provide trimmed prototypes. We could speed up testing processes by skipping irrelevant columns and rows with only a small degrade in accuracy.