k-Co-occurrences Density Map Estimation

Detecting and visualizing structures in spatial and spatio-temporal information is often the primer interest of the data scientist before going further into a statistical modeling. For labeled point patterns data, multiple co-occurrences based entropy and distance-ratios based entropy indices have proven to be useful to a global assessment or as providing hot-spot maps when localizing the statistical indices. As local information, the co-occurrences of the labeled points or of a statistic of interest (e.g., distance-ratios) are nonetheless the crucial information. This paper focuses on estimating the spatial or spatio-temporal distribution of these multiple co-occurrences. A non-parametric estimation of the co-occurrence density for sample data from a qualitative or quantitative process is built from the multivariate kernel density framework introducing a penalization linked to a co-occurring event. Direct applications as well as potential uses in spatial or spatio-temporal regression are briefly explored with examples using Twitter data on health related to seasonal diseases and using citizen science data on invasive species.