Dear all,

I just came across a very useful, fast and efficient function for matching points in one data frame to their nearest neighbours in another data frame. Of course, I’d like to share my newly acquired pearls of wisdom with you.

I’d like to outline the problem definition by providing a specific example of application: I wanted to match numerous GPS-tracks (about 200 GPX files indicating bike routes in Austria) to an underlying road graph covering all roads in Austria. Having read the track points from the GPX files, I had two simple feature collections of geometry type `POINT` I wanted to match:

• object `road_graph`, which is an `sf` object containing a graph of the Austrian road network (`frc` between `000` and `005`) in intervals of 50 meters (coordinates refer to the mean of each segment)
• object `bike_graph`, which is an `sf` object containing the gps waypoints of the bike tracks

Basically, one could use the function `snapPointsToLines()` from the package`maptools` or the `rgeos` implementation of `gDistance()` to perform this task. However, these functions are extremely inefficient if you have large data sets, since you have to calculate all distances between all possible pairs of points and subsequently select the nearest point based on the minimum distance.

This is where the function `nn2()` from the package `RANN` comes into play.

```# libraries
library(dplyr)
library(sf)
library(RANN)

# get coordinate matrices
bike_coords <- do.call(rbind, st_geometry(bike_graph))
bike_coords <- cbind(moto_coords, 1:nrow(bike_coords))

# fast nearest neighbour search
closest <- nn2(bike_coords[,1:2], graph_coords, k = 1, searchtype = "radius", radius = 0.001)
closest <- sapply(closest, cbind) %>% as_tibble

# create logical vector indicating bike routes and add it to the road graph
road_graph\$bikeroute <-ifelse(closest\$nn.idx == 0, FALSE, TRUE)

# define smoother function via run length encoding
track_smoother <- function(route, smooth_length=100){
r <- rle(route)
index <- r\$lengths < smooth_length
r\$values[index] <- 1
return(inverse.rle(r))
}

# apply smoother on all tracks across all roads
mutate(bikeroute_smooth = track_smoother(bikeroute))
```

Some explanatory remarks on the `nn2()` function:

• The function uses a kd-tree to find the k number of near neighbours for each point. Specifying `k = 1` yields only the ID of the nearest neighbor.
• Since I basically simply wanted to flag bike routes, I used `searchtype = "radius"` to only searches for neighbours within a specified radius of the point. If no waypoints (i.e. bike routes) lie within this radius,  `nn.idx` will contain 0 and `nn.dists` will contain 1.340781e+154 for that point. I used this information to establish a logical vector indicating bike routes in the subsequent ifelse-statement.
• Note that the radius is the distance based on the decimal between lon/lat coordinates. Having had a look at the Wikipedia page on decimal degrees (mpre precisely: the table about degree precision versus length), we can see that 3 decimal places (0.001 degrees) correspond to 111.32 m in N/S and 78.71 m E/W at 45N/S. Thus, `radius = 0.001` will search for the nearest point within approx. 110 in N/S direction and approx. 75 meters in W/E direction in Austria.

Here are the results in a simple visualization via QGIS. The grey dots are the underlying road graph, blue stars indicate the GPS waypoints, red dots indicate the fitted segments lying within the radius of the GPS tracks and the green dots indicate the smoothed bike tracks: Best regards,
Matthias