Figueira

Triangles have mighty properties for geospatial queriesPhoto by Pawel Czerwinski on UnsplashTriangles are shapes with many practical geometric properties. In this article, I illustrate using such properties when performing opportunistic optimizations while solving a particular geospatial problem: the recovery of missing map-matched information.I started exploring the Extended Vehicle Energy Dataset¹ (EVED) a while ago to search for compelling geospatial data analysis opportunities in a city road network context. This…

How can we quickly find overlapping trajectories?Photo by Jens Lelie on UnsplashWhile traveling through space, an object describes a trajectory. We can think about a trajectory as a function of time that outputs positions in space. Conceptually, trajectories are continuous functions, although we pragmatically use their discrete versions. A discrete trajectory is a time-ordered collection of points in space where we implicitly assume a linear interpolation between each point. This representation makes storing discrete…

This article explains how to use optimization to perform stratified K-Fold cross-validation on a grouped datasetPhoto by Nicolas COMTE on UnsplashCross-validation is a common resampling technique to get more mileage from your dataset. The procedure involves taking repeated independent samples from the original dataset and fitting them to the desired model. Cross-validation is helpful for model selection, as it provides better generalization performance estimates than the holdout method. The resampling process ensures that…

This article explains how to estimate travel times using known speed vectors indexed by quadkeysPhoto by Dino Reichmuth on UnsplashHow long is your road trip going to last? If you are like me, you go to Google maps or Here maps and query the route directly. You will not only get the fastest or shortest paths, but you will also get estimates of your travel times. These services report the most common speeds according to the learned time patterns and live traffic information and do so for the typical vehicles on the…

How can we determine the equivalent DBSCAN ε parameter for HDBSCAN-generated clusters?The image above depicts the minimum spanning tree of distances in an HDBSCAN-generated cluster. Image by the author made with the Folium package and OpenStreetMap imagery.HDBSCAN is a hierarchical density-based clustering algorithm that works under simple assumptions. At a minimum, it only requires the data points to cluster and the minimum number of observations per cluster. The algorithm accepts a distance matrix if the data has a…

This article explains how to create geofences with square partitionsThe picture above displays a hierarchical square discretization of continental Portugal using the algorithm described here. Image by the author made with the Folium package and OpenStreetMap imagery.A geofence is a virtual border delimiting an arbitrary geographic region. We use these constructs to classify whether an object lies inside the area of interest, like when we want to determine if a car has entered a specific parking lot. Geofences do not have…