In categorization processes explored in cognitive science, representation of categories is based on central tendencies, category boundaries, or exemplar memory. Here we explore a probabilistic representation in which categories are abstracted using a probability density function. This representation is compatible with the prototype theory as well as the exemplar theory and encompasses the category boundaries theory. We examine how affine transforms can be applied to perceived exemplars that are distorted instances of the category and how accurately category membership can be assessed. Simulations demonstrate that category retrieval is near perfect with rotation, translation and contraction or expansion on distorted exemplars.