Providing a fast and accurate (exact or approximate) access to large-scale multidimensional data is a ubiquitous problem and dates back to the early days of large-scale Information Systems. Similarity search, requiring to resolve nearest neighbor (NN) searches, is a fundamental tool for structuring information space. Permutation-based Indexing (PBI) is a reference-based indexing scheme that accelerates NN search by combining the use of landmark points and ranking in place of distance calculation. In this paper, we are interested in understanding the approximation made by the PBI scheme. The aim is to understand the robustness of the scheme created by modeling and studying by quantifying its invariance properties. After discussing the geometry of PBI, in relation to the study of ranking, from empirical evidence, we make proposals to cater for the inconsistencies of this structure.