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.

翻译：人类倾向于基于少数关键特征对物体进行分类。我们提出了一种利用混合概率主成分分析（mPPCA）的理性分类模型。该模型以降低的特征维度表示每个类别，并允许类别间共享局部特征以促进少样本学习。理论上，我们确定了降维表示优于全维表示的必要且充分条件。随后，通过行为实验证明了mPPCA在预测人类分类方面优于范例模型和原型模型的表现。当与卷积神经网络结合时，每个类别仅使用单个主成分维度的mPPCA分类器在${\tt CIFAR-10H}$人类分类数据集上达到了与使用线性分类器的ResNet相当的性能。