We introduce a decision scheme for optimally choosing a classifier, which segments the cosmic web into different structure types (voids, sheets, filaments, and clusters). Our framework, based on information theory, accounts for the design aims of different classes of possible applications: (i) parameter inference, (ii) model selection, and (iii) prediction of new observations. As an illustration, we use cosmographic maps of web-types in the Sloan Digital Sky Survey to assess the relative performance of the classifiers T-web, DIVA and ORIGAMI for: (i) analyzing the morphology of the cosmic web, (ii) discriminating dark energy models, and (iii) predicting galaxy colors. Our study substantiates a data-supported connection between cosmic web analysis and information theory, and paves the path towards principled design of analysis procedures for the next generation of galaxy surveys. We have made the cosmic web maps, galaxy catalog, and analysis scripts used in this work publicly available.
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