Before revision:   Compared with existing state-of-the-art indices on a beta-mixture distribution, we show that RRH more accurately detects the number of distinct mixture components. We also show that RRH can measure heterogeneity in natural images whose semantically relevant features must be abstracted using deep generative models. We further show that RRH can uniquely capture heterogeneity caused by distinct components in mixture distributions. Our novel approach will enable measurement of heterogeneity in disciplines where a priori categorical partitions of observable data are not possible, or where semantically relevant features must be inferred using latent variable models .
After revision:  Compared with existing state-of-the-art indices on a beta-mixture distribution, we show that RRH responds more appropriately to changes in mixture component separation and weighting. Finally, we demonstrate the measurement of RRH in disciplines where a priori categorical partitions of observable data are not possible, or where semantically relevant features must be inferred using latent variable models .