Statistical analysis of NOMAO customer votes for spots of France

TL;DR

This paper analyzes the voting patterns of NOMAO customers for French spots, revealing stable power-law distributions over a decade and exploring spectral properties of user ratings to improve prediction and understand underlying phenomena.

Contribution

It introduces a detailed statistical analysis of voting data, examines spectral properties of rating matrices, and evaluates imputation methods to enhance prediction accuracy.

Findings

Vote distributions follow stable power laws over ten years.

Eigenvalues of rating matrices correspond to geographic regions.

Imputation strategies improve prediction with geographically smooth eigenvectors.

Abstract

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.