Revisiting Colocalization from the Perspective of Similarity

Given two or more concentrations, an interesting and important related issue concerns the quantification of how strongly they are spatially interrelated. The concept of colocalization has been frequently considered as an indication of the tendency of the values of two concentrations to spatially vary together. While this frequently adopted approach presents several interesting characteristics, being a suitable choice for several situations, in the present work we study how multiset similarity indices can be applied for similar purposes, possibly allowing a complementation, in the sense of taking into account shared portions of the concentrations, of the colocalization characterization provided by the Pearson correlation methodology. The problem of colocalization is first addressed in terms of possible underlying mathematical models, and then the Pearson correlation coefficient-based approach, as well as the standardization procedure which is its intrinsic part, are presented and discussed. The particularly important issue of how to define the baseline of the concentrations is also approached and illustrated. The minmax alternative normalization scheme is presented next, followed by the description of the three considered multiset simiarlity indices -- namely the interiority, Jaccard, and coincidence similarity approaches. The characteristics of each of these methods is then illustrated respectively to 1D, and then to 2D concentrations under presence of several interesting and relevant effects including spatial displacement, as well as sharpening, presence of unrelated effects. The similarity indices, and in particular the coincidence approach, are found to present some interesting features when applied to the quantification of the colocalization between two or more concentrations, suggesting that it can provided complementary information when performing colocalization analysis.