# Understanding the cross K-function [interactive visualization]

!!!UPDATE!!!
Since this post is still getting a lot of views, some of you might be interested in the
outcomes of my experiments with the cross K-function. I used the function in 2 recent
papers. Links to the articles are found on the Publications page.

Juhász, L. and Hochmair, H. H. (2017). Where to catch ‘em all? – a geographic analysis
of Pokémon Go locations. Geo-spatial Information Science. 20 (3): pp. 241-251

Hochmair, H.H., Juhász, L., and Cvetojevic, S. (2018). Data Quality of Points of
Interest in Selected Mapping and Social Media Platforms. Kiefer P., Huang H., Van de
Weghe N., Raubal M. (Eds.) Progress in Location Based Services 2018. LBS 2018.
Lecture Notes in Geoinformation and Cartography (pp. 293-313) Berlin: Springer.

One of the research papers I’ve submitted recently (yes, about Pokémons!) dealt with spatial point pattern analysis. Visually it seemed that two of my point sets prefer to cluster around each other, in other words I suspected that Pokéstops have a preference of being close to Pokémon Gyms. Check the map below to see what I mean. Pokémon locations (cyan dots) are all over the place as opposed to Pokéstops (orange) that almost exclusively appear to be in the proximity of gyms (red).

To confirm what’s obvious from the map, I used the bivariate version or Ripley’s K-function (a.k.a. the cross-K function) that can help us characterize two point patterns. As it turns out, it’s not as easy to interpret as I though it would be (at least with real world data) and I was trying to get my head around it for quite some time. As a result, I came up with a simple interactive visualization of this function to illustrate what it really means. If you’re anything like me and try to understand your stats instead of just reporting the results, you might want to read on more for some musings about the cross K-function.

# Sneak peek

If you like playing with data, chances are you’ve come across D3.js, Data-Driven Documents. Here are two of the first visualizations I made with it. I’m going to write up a more detailed blog post about it later. In the meantime – without commentary -just enjoy.

!! UPDATE: check out my post about Mapillary’s Rhythm !!

And the second one (without attempting to scale it to the screen):