A Rational Model of Dimension-reduced Human Categorization

Humans tend to categorize objects based on a few key features. We propose a rational model of categorization that utilizes a mixture of probabilistic principal component analyzers (mPPCA). This model represents each category with reduced feature dimensions and allows local features to be shared across categories to facilitate few-shot learning. Theoretically, we identify the necessary and sufficient condition for dimension-reduced representation to outperform full-dimension representation. We then show the superior performance of mPPCA in predicting human categorization over exemplar and prototype models in a behavioral experiment. When combined with the convolutional neural network, the mPPCA classifier with a single principal component dimension for each category achieves comparable performance to ResNet with a linear classifier on the ${\tt CIFAR-10H}$ human categorization dataset.