Identification of Novel Modes in Generative Models via Fourier-based Differential Clustering

Abstract: An interpretable comparison of generative models requires the identification of sample types produced more frequently by each of the involved models. While several quantitative scores have been proposed in the literature to rank different generative models, such score-based evaluations do not reveal the nuanced differences between the generative models in capturing various sample types. In this work, we attempt to solve a differential clustering problem to detect sample types expressed differently by two generative models. To solve the differential clustering problem, we propose a method called Fourier-based Identification of Novel Clusters (FINC) to identify modes produced by a generative model with a higher frequency in comparison to a reference distribution. FINC provides a scalable stochastic algorithm based on random Fourier features to estimate the eigenspace of kernel covariance matrices of two generative models and utilize the principal eigendirections to detect the sample types present more dominantly in each model. We demonstrate the application of the FINC method to large-scale computer vision datasets and generative model frameworks. Our numerical results suggest the scalability of the developed Fourier-based method in highlighting the sample types produced with different frequencies by widely-used generative models. Code is available at \url{https://github.com/buyeah1109/FINC}