Statistical analysis of NOMAO customer votes for spots of France

We investigate the statistical properties of votes of customers for spots of France collected by the startup company NOMAO. The frequencies of votes per spot and per customer are characterized by a power law distributions which remain stable on a time scale of a decade when the number of votes is varied by almost two orders of magnitude. Using the computer science methods we explore the spectrum and the eigenvalues of a matrix containing user ratings to geolocalized items. Eigenvalues nicely map to large towns and regions but show certain level of instability as we modify the interpretation of the underlying matrix. We evaluate imputation strategies that provide improved prediction performance by reaching geographically smooth eigenvectors. We point on possible links between distribution of votes and the phenomenon of self-organized criticality.