Binning points

Section 4.1 Binning points

In GIS it is often difficult to present point-based data because in many instances there are several different points and data symbologies that need to be shown. As the number of different data points grows, they can become complicated to interpret and manage, which can result in convoluted and sometimes inaccurate maps. This becomes an even larger problem in web maps that are able to be depicted at different scales because smaller scale maps need to show more area and more data. This makes the maps convoluted if multiple data points are included.

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In many maps there are so many data points included that little can be interpreted from them. In order to reduce congestion on maps, many GIS users and cartographers have turned to a process known as binning. Binning allows researchers and practitioners a way to systematically divide a region into equal-sized portions. As well as making maps with many points easier to read, binning data into regions can help identify spatial influence of neighbourhoods, and can be an essential step in developing systematic sampling designs.

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This approach to binning generates an array of repeating shapes over a user specified area. These shapes can be hexagons, squares, rectangles, triangles, circles or points, and they can be generated with any directional orientation. These are sometimes called ’grids’ or ’fishnets’ and lots of other spatial analysis (e.g., map algebra) can be done with such files.

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Subsection 4.1.1 The binning process

Binning is a data modification technique that changes the way data is shown at small scales. It is done in the pre-processing stage of data analysis to convert the original data values into a range of small intervals, known as a bin. These bins are then replaced by a value that is representative of the interval to reduce the number of data points.

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Spatial binning (also called spatial discretization) discretizes the location values into a small number of groups associated with geographical areas or shapes. This approach to binning generates an array of repeating shapes over a user-specified area. These shapes can be hexagons, squares, rectangles, triangles, circles or points, and they can be generated with any directional orientation. The assignment of a location to a group can be done by any of the following methods:

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Using the coordinates of the point to identify which “bin” it belongs to.
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Using a common variable in the attribute table of the bin and the point layers.
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Subsection 4.1.2 Different binning techniques

Binning itself is a general term used to describe the grouping of a dataset’s values into smaller groups ([Johnson, 2011]). The bins can be based on a variety of factors and attributes such as spatial and temporal and can thus be used for many different projects.

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Subsubsection 4.1.2.1 Choropleth maps

You might be thinking, “grouping points into a larger spatial unit, haven’t we already done this when making choropleth maps?”. In a way you are right. Choropleth maps are a type of map that uses binning. Proportional symbol and choropleth maps group similar data points together to show a range of data instead of many individual points. We’ve covered this extensively, and it is often the best approach to consider spatial grouping of your point variables, because the polygons (shapes) to which you are aggregating your points are meaningful. You can group into LSOAs, as we did in previous chapters, because you want to show variation in neighbourhoods. Or you can group into police force areas because you want to look at differences between those units of analysis. But sometimes there is just not a geography present to meet your needs.

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Let’s say you are conducting some days of action in Manchester city centre, focusing on antisocial behaviour. You are going to put up some information booths and staff them with officers to engage with the local population about antisocial behaviour. For these to be most effective, as an analyst you decide that they should go into the areas with the highest count of antisocial behaviour. You want to be very specific about where you focus your operational attention and, thus, the LSOA level may be too large. One approach can be to split central Manchester into some smaller polygons, and just calculate the number of antisocial behaviour incidents recorded in each. That way you can then decide to put your information booths somewhere inside the top 5 highest count bins.

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Subsubsection 4.1.2.2 Rectangular binning

The aggregation of incident point data to regularly shaped grids is used for many reasons such as normalizing geography for mapping or to mitigate the issues of using irregularly shaped polygons created arbitrarily (such as county boundaries or block groups that have been created from a political process). Regularly shaped grids can only be comprised of equilateral triangles, squares, or hexagons, as these three polygon shapes are the only that can tessellate (repeating the same shape over and over again, edge to edge, to cover an area without gaps or overlaps) to create an evenly spaced grid. Rectangular binning is the simplest binning method and as such it is heavily used. However, there are some reasons why rectangular bins are less preferable over hexagonal bins. Before we cover this, let’s have a look at hexagonal bins.

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Subsubsection 4.1.2.3 Hexagonal binning

In many applications binning is done using a technique called hexagonal binning. This technique uses hexagon shapes to create a grid of points and develops a spatial histogram that shows different data points as a range or group of pairs with common distances and directions. In hexagonal binning the number of points falling within a particular hexagon in a gridded surface is what makes the different colors to easily visualize data ([Smith, 2014]). Hexagonal binning was first developed in 1987 and today “hexbinning” is conducted by laying a hexagonal grid on top of two-dimensional data ([Johnson, 2011]). Once this is done users can conduct data point counts to determine the number of points for each hexagon ([Johnson, 2011]). The bins are then symbolized differently to show meaningful patterns in the data.

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So how can we use hexbinning to solve our antisocial behaviour days of action task? Well let’s say we split Manchester city centre into hexagons, and count the number of antisocial behaviour instances in these. We can then identify the top hexagons, and locate our booths somewhere within these.

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Subsection 4.1.3 A practical binning example

First, make sure you have the appropriate packages loaded. Also let’s get some data. You could go and get this data yourself from police.uk, but as we’ve been through a few times now, a tidied set of data is ready for you within the data provided with the book (see Preamble). This data is one year’s worth of antisocial behaviour from the police.uk data, from May 2016 to May 2017, for the borough of Manchester.

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manchester_asb <- read_csv("data/manchester_asb.csv")

This is currently just a text dataframe, so we need to let R know that actually this is a spatial object; the geometry can be found in its longitude and latitude coordinates. As we have long/lat we can assume it’s in WGS84 projection.

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ma_spatial <- st_as_sf(manchester_asb,
                       coords = c("Longitude", "Latitude"),
                       crs = 4326,
                       agr = "constant")

Now one thing that this does is it consumes our Longitude and Latitude columns into a geometry attribute. This is generally OK, but for the binning we will do, we would like to have them as separate coordinates. To do this, we can use the st_coordinates() function from the sf package. For example, if we look at the first row:

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ma_spatial %>%
  slice(1) %>%
  st_coordinates()

##        X     Y
## 1 -2.229 53.53

We have our longitude (X) and latitude (Y). We can select the first and second element of this to get only one or the other. To go through our whole dataframe, we can use the mutate() function, and assign each element to a longitude and latitude column respectively:

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ma_spatial <- ma_spatial %>%
  mutate(longitude = st_coordinates(.)[,1],
         latitude = st_coordinates(.)[,2])

As a first step, we can plot antisocial behaviour in the borough of Manchester using simple ggplot, as demonstrated in Chapter 1. We can plot our points first:

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A plot of points with the vertical axis being latitude, and the horizontal axis longitude. Black points cover most of an area shaped like Manchester. Only a small amount of the white background is not covered, in patches to the northeast and east, and towards the south. — Figure 4.1.1. Point map of ASB in Manchester
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We see our nice map of Manchester, as outlined by ASB incidents across the Local Authority. However, it is hard to tell from this map where these incidents might occur more frequently and where they are just a few one-off incidents. A binned map may help us better understand. To create such a map, we must first create the grid (or fishnet) of tessellating shapes.Once we have this grid, we can overlay it on top of our map, and count the number of ASB incidents (points) which fall into each grid shape (polygon). We can use the ggplot library to achieve this. To map a hexbinned version of our point data of antisocial behaviour, we can use the stat_binhex() function as a layer added on to our ggplot object. We can also recreate the thematic map element, using the frequency of points in each hex to shade each hexbin from white (least number of incidents) to red (most number of incidents). So let’s have a go:

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The shape of Manchester is tiled into hexagonal cells. To the right, a legend is labeled ’Frequency’, and shows a gradient of red to white with numbered notches. The deepest red is above the notch numbered four thousand, with a notch at every thousand, ending at one thousand, a very light red. Most of the hexagonal cells are nearly white, with one darker red towards the middle left. A few of the nearby cells are a light red as well. — Figure 4.1.2. Hexbin map of ASB in Manchester
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Neat, but it doesn’t quite tell us where that really dark hexbin actually is. So it would be much better if we could do this with a basemap as the background. For this we use the function annotation_map_tile() from the ggspatial package. We can also set the opacity of the binhex layer, so we can see our basemap, with the alpha parameter.

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The shading of hexagonal cells from the previous figure is now partially transparent, and overlaid onto a street map of Manchester. The darker hex can be identified as central Manchester. — Figure 4.1.3. Hexbin map of ASB in Manchester with basemap
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Note: you might get the following prompt when you run this code: “The hexbin package is required for stat_binhex(). Would you like to install it?” - if you do, just choose “Yes” or quit the action and install the hexbin package separately, and then try running the code again. Similarly if you get “Warning: Computation failed in stat_binhex()” the solution might be to install this hexbin package.

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Adding this basemap provides us with a bit more context. And combined with the hexbin map, it is much easier to see where antisocial-behaviour concentrates (as opposed to with the point map!). Above we used a hexagon shape for our binning; however, you might choose other shapes as well. We will illustrate in a moment the approach to use rectangular binning, but first, we want to highlight why hexagon might still be your ideal choice. Here are some thoughts, summarised from ([ArcGIS Pro, 2021]):

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Hexagons reduce sampling bias due to edge effects ([Rengert and Lockwood, 2009]) of the grid shape.
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As hexagons are circular, they represent curves in the patterns of your data more naturally than square grids.
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When comparing polygons with equal areas, the more similar to a circle the polygon is, the closer to the centroid the points near the border are.
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Hexagons are preferable when your analysis includes aspects of connectivity or movement paths. Due to the linear nature of rectangles, fishnet grids can draw our eyes to the straight, unbroken, parallel lines which may inhibit the underlying patterns in the data.
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If you are working over a large area, a hexagon grid will suffer less distortion due to the curvature of the earth than the shape of a fishnet grid.
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You will find more neighbours with hexagons than square grids, if you’re using a distance band, since the distance between centroids is the same in all six directions with hexagons (see image below).
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A comparison of a circle over a square grid, with a circle over a hexagonal grid. The circle has the same size in both, a radius of the width of one grid or cell. In the first image, the circle is centred in the centre of a square cell, completely engulfing that cell which is shaded dark red, and partially the four adjacent cells, which are light red. The circle barely touches the four cells at corners to the middle cell. In the second image, the circle is centred in the centre of a hexagonal cell, completly engulfing that cell which is shaded dark red, and partially the six adjacent cells. — Figure 4.1.4. Hexagonal bins will have more neighbors included in the calculations for each feature as opposed to a fishnet grid
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To illustrate the differences of different approaches. Like we did in earlier chapters, we can assign each map to an object, and then print them all side-by-side. Let’s start with rectangular binning:

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rectangular_bin_map <- ggplot(ma_spatial, aes(x = longitude, y = latitude)) +
  annotation_map_tile() +
  stat_bin2d(binwidth = c(.015, .01), alpha=0.7) +
  scale_fill_gradientn(colours = c("white","red"),
                       name = "Frequency") +
  theme_void()

Now map a map using hexagonal binning:

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hexagonal_bin_map <- ggplot(ma_spatial, aes(x = longitude, y = latitude)) +
  annotation_map_tile() +
  stat_binhex(binwidth = c(.015, .01), alpha=0.7) +
  scale_fill_gradientn(colours = c("white","red"),
                       name = "Frequency") +
  theme_void()

And finally for comparison a simple “heatmap” (we will discuss these more thoroughly in Chapter 7):

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heatmap <- ggplot(ma_spatial, aes(x = longitude, y = latitude)) +
  annotation_map_tile() + 
  stat_density2d(aes(fill = ..level.., # value corresponding to 
                                       # discretized density estimates 
                     alpha = ..level..), 
                 geom = "polygon") +  # creates the bands of 
                                      # different colours
  ## Configure the colours, transparency and panel
  scale_fill_gradientn(colours = c("white","red"), 
                       name = "Frequency") + 
  scale_alpha(guide = "none") + 
  theme_void()

Now we can print them all side-by-side using the plot_grid() function from the cowplot package to compare.

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Three different semi-transparent shadings are overlaid onto three street maps of Manchester, with labels A, B, and C. Their legends all have the same label ’Frequency’, and gradient from red to white, but the maximum values differ; over three thousand in A, over four thousand in B, and a little over one thousand in C. In the first one, the shading is broken into single-coloured squares. One square is dark red, with its bottom and right neighbours also noticeably darker than the rest. In the second one, single-coloured hexagons tile the map, with just one being a much darker red than the rest. In the third one, no shape constrains the colours, and there is just a small blotch of red fading to white near the city centre. — Figure 4.1.5. Comparing rectangular (A), hexagonal (B), and heat maps (C)
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Subsection 4.1.4 Benefits of binning

Because of the plethora of data types available and the wide variety of projects being done in GIS, binning is a popular method for mapping complex data and making it meaningful. Binning is a good option for map makers as well as users because it makes data easy to understand and it can be both static and interactive on many different map scales. If every different point were shown on a map, it would have to be a very large scale map to ensure that the data points did not overlap and were easily understood by people using the maps. According to Kenneth Field, an Esri Research Cartographer:

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Data binning is a great alternative for mapping large point-based data sets which allows us to tell a better story without interpolation. Binning is a way of converting point-based data into a regular grid of polygons so that each polygon represents the aggregation of points that fall within it ([Field, 2012]).
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Binning creates maps that are easier to understand, more accurate and more visually appealing. Hexbin plots can be viewed as an alternative to scatter plots. The hexagon-shaped bins were introduced to plot densely packed sunflower plots. They can be used to plot scatter plots with high-density data.

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