R: K-means clustering of bivariate polar plots

polarCluster {openair} | R Documentation

## K-means clustering of bivariate polar plots

### Description

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,
      ...
    )

### Arguments

`mydata` | 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.
`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` | Name of wind direction field.
`n.clusters` | 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`.
`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 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")`.
`angle.scale` | 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.
`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.
`...` | 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.

### 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.

### Value

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`.

### Author(s)

David Carslaw

### 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

### See Also

`polarPlot`

### Examples

    ## Not run:
    # 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)])

    ## End(Not run)

[Package openair version 2.8-5 Index]