Before revision:  Unfortunately, numbers equivalent heterogeneity measures for non-categorical data require a priori (A) categorical partitioning and (B) pairwise distance measurement on the space of observable data . This precludes their application to problems in disciplines where categories are ill-defined  or where semantically relevant features must be learned as abstractions from some data.
After revision:  Unfortunately, numbers equivalent heterogeneity measures for non-categorical data require a priori (A) categorical partitioning and (B) pairwise distance measurement on the observable data space, thereby precluding application to problems in disciplines where categories are ill-defined or where semantically relevant features must be learned as abstractions from some data.