K-means clustering of bivariate polar plots

Function for identifying clusters in bivariate polar plots (polarPlot()); identifying clusters in the original data for subsequent processing.

Usage

polarCluster(
  mydata,
  pollutant = "nox",
  x = "ws",
  wd = "wd",
  n.clusters = 6,
  after = NA,
  cols = "Paired",
  angle.scale = 315,
  units = x,
  auto.text = TRUE,
  plot = TRUE,
  plot.data = FALSE,
  ...
)

Arguments

mydata: A data frame minimally containing a decimal wind direction, another variable to plot in polar coordinates (the default is a column "ws" — wind speed) and a pollutant. Should also contain date if plots by time period are required.
pollutant: Mandatory. A pollutant name corresponding to a variable in a data frame should be supplied e.g. pollutant = "nox". Only one pollutant can be chosen.
x: Name of variable to plot against wind direction in polar coordinates, the default is wind speed, “ws”.
wd: The name of the column in mydata representing the decimal wind direction, 0 to 360 where 0/360 are North and 180 is South. Defaults to "wd".
n.clusters: Number of clusters to use. If n.clusters is more than length 1, then a faceted plot will be output showing the clusters identified for each one of n.clusters.
after: The function can be applied to differences between polar plot surfaces (see polarDiff for details). If an after data frame is supplied, the clustering will be carried out on the differences between after and mydata in the same way as polarDiff.
cols: Colours to use for plotting. Can be a pre-set palette (e.g., "turbo", "viridis", "tol", "Dark2", etc.) or a user-defined vector of R colours (e.g., c("yellow", "green", "blue", "black") - see colours() for a full list) or hex-codes (e.g., c("#30123B", "#9CF649", "#7A0403")). Alternatively, can be a list of arguments to control the colour palette more closely (e.g., palette, direction, alpha, etc.). See openColours() and colourOpts() for more details.
angle.scale: In radial plots (e.g., polarPlot()), the radial scale is drawn directly on the plot itself. While suitable defaults have been chosen, sometimes the placement of the scale may interfere with an interesting feature. angle.scale can take any value between 0 and 360 to place the scale at a different angle, or FALSE to move it to the side of the plots.
units: The units shown on the polar axis scale.
auto.text: Either TRUE (default) or FALSE. If TRUE titles and axis labels will automatically try and format pollutant names and units properly, e.g., by subscripting the "2" in "NO2". Passed to quickText().
plot: When openair plots are created they are automatically printed to the active graphics device. plot = FALSE deactivates this behaviour. This may be useful when the plot data is of more interest, or the plot is required to appear later (e.g., later in a Quarto document, or to be saved to a file).
plot.data: By default, the data component of polarCluster() contains the original data frame appended with a new "cluster" column. When plot.data = TRUE, the data component instead contains data to reproduce the clustered polar plot itself (similar to data returned by polarPlot()). This may be useful for re-plotting the polarCluster() plot in other ways.
...: Other arguments passed on to polarPlot().

Value

an openair object. The object includes four main components: call, the command used to generate the plot; data, by default the original data frame with a new field cluster identifying the cluster, clust_stats giving the contributions made by each cluster to number of measurements, their percentage and the percentage by pollutant; and plot, the plot itself. Note that any rows where the value of pollutant is NA are ignored so that the returned data frame may have fewer rows than the original.

If the clustering is carried out considering differences, i.e., an after data frame is supplied, the output also includes the after data frame with cluster identified.

Details

Bivariate polar plots generated using the polarPlot function provide a very useful graphical technique for identifying and characterising different air pollution sources. While bivariate polar plots provide a useful graphical indication of potential sources, their location and wind-speed or other variable dependence, they do have several limitations. Often, a `feature' will be detected in a plot but the subsequent analysis of data meeting particular wind speed/direction criteria will be based only on the judgement of the investigator concerning the wind speed-direction intervals of interest. Furthermore, the identification of a feature can depend on the choice of the colour scale used, making the process somewhat arbitrary.

polarCluster applies Partition Around Medoids (PAM) clustering techniques to polarPlot() surfaces to help identify potentially interesting features for further analysis. Details of PAM can be found in the cluster package (a core R package that will be pre-installed on all R systems). PAM clustering is similar to k-means but has several advantages e.g. is more robust to outliers. The clustering is based on the equal contribution assumed from the u and v wind components and the associated concentration. The data are standardized before clustering takes place.

The function works best by first trying different numbers of clusters and plotting them. This is achieved by setting n.clusters to be of length more than 1. For example, if n.clusters = 2:10 then a plot will be output showing the 9 cluster levels 2 to 10.

The clustering can also be applied to differences in polar plot surfaces (see polarDiff()). On this case a second data frame (after) should be supplied.

Note that clustering is computationally intensive and the function can take a long time to run — particularly when the number of clusters is increased. For this reason it can be a good idea to run a few clusters first to get a feel for it e.g. n.clusters = 2:5.

Once the number of clusters has been decided, the user can then run polarCluster to return the original data frame together with a new column cluster, which gives the cluster number as a character (see example). Note that any rows where the value of pollutant is NA are ignored so that the returned data frame may have fewer rows than the original.

Note that there are no automatic ways in ensuring the most appropriate number of clusters as this is application dependent. However, there is often a-priori information available on what different features in polar plots correspond to. Nevertheless, the appropriateness of different clusters is best determined by post-processing the data. The Carslaw and Beevers (2012) paper discusses these issues in more detail.

Note that unlike most other openair functions only a single type “default” is allowed.

References

Carslaw, D.C., Beevers, S.D, Ropkins, K and M.C. Bell (2006). Detecting and quantifying aircraft and other on-airport contributions to ambient nitrogen oxides in the vicinity of a large international airport. Atmospheric Environment. 40/28 pp 5424-5434.

Carslaw, D.C., & Beevers, S.D. (2013). Characterising and understanding emission sources using bivariate polar plots and k-means clustering. Environmental Modelling & Software, 40, 325-329. doi:10.1016/j.envsoft.2012.09.005

Author

David Carslaw

Examples

if (FALSE) { # \dontrun{
# plot 2-8 clusters. Warning! This can take several minutes...
polarCluster(mydata, pollutant = "nox", n.clusters = 2:8)

# basic plot with 6 clusters
results <- polarCluster(mydata, pollutant = "nox", n.clusters = 6)

# get results, could read into a new data frame to make it easier to refer to
# e.g. results <- results$data...
head(results$data)

# how many points are there in each cluster?
table(results$data$cluster)

# plot clusters 3 and 4 as a timeVariation plot using SAME colours as in
# cluster plot
timeVariation(subset(results$data, cluster %in% c("3", "4")),
  pollutant = "nox",
  group = "cluster", col = openColours("Paired", 6)[c(3, 4)]
)
} # }