Several natural language processing (NLP) tasks are defined as a classification problem in its most complex form: Multi-label Hierarchical Extreme classification, in which items may be associated with multiple classes from a set of thousands of possible classes organized in a hierarchy and with a highly unbalanced distribution both in terms of class frequency and the number of labels per item. We analyze the state of the art of evaluation metrics based on a set of formal properties and we define an information theoretic based metric inspired by the Information Contrast Model (ICM). Experiments on synthetic data and a case study on real data show the suitability of the ICM for such scenarios.