Function for identifying clusters in bivariate polar plots
(polarPlot); identifying clusters in the original data for subsequent
processing.
polarCluster(
mydata,
pollutant = "nox",
x = "ws",
wd = "wd",
n.clusters = 6,
after = NA,
cols = "Paired",
angle.scale = 315,
units = x,
auto.text = TRUE,
...
)As well as generating the plot itself, polarCluster also
returns an object of class ``openair''. The object includes three main
components: call, the command used to generate the plot;
data, the original data frame with a new field cluster
identifying the cluster; 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.
An openair output can be manipulated using a number of generic operations,
including print, plot and summary.
A data frame minimally containing wd, 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.
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.
Name of variable to plot against wind direction in polar coordinates, the default is wind speed, “ws”.
Name of wind direction field.
Number of clusters to use. If n.clusters is more
than length 1, then a lattice panel plot will be output showing the
clusters identified for each one of n.clusters.
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.
Colours to be used for plotting. Useful options for categorical
data are avilable from RColorBrewer colours --- see the
openair openColours function for more details. Useful
schemes include “Accent”, “Dark2”, “Paired”,
“Pastel1”, “Pastel2”, “Set1”, “Set2”,
“Set3” --- but see ?brewer.pal for the maximum useful
colours in each. For user defined the user can supply a list of colour
names recognised by R (type colours() to see the full list). An
example would be cols = c("yellow", "green", "blue").
The wind speed scale is by default shown at a 315 degree
angle. Sometimes the placement of the scale may interfere with an
interesting feature. The user can therefore set angle.scale to
another value (between 0 and 360 degrees) to mitigate such problems. For
example angle.scale = 45 will draw the scale heading in a NE
direction.
The units shown on the polar axis scale.
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.
Other graphical parameters passed onto polarPlot,
lattice:levelplot and cutData. Common axis and title
labelling options (such as xlab, ylab, main) are
passed via quickText to handle routine formatting.
David Carslaw
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.
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
polarPlot
if (FALSE) {
# load example data from package
data(mydata)
## 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)])
}
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