# Zone delineation

    library(paar)
    library(sf)
    require(ggplot2)

Multivariate zone delineation can be done using `kmspc` function, whereas univariate zone delineation can be done with `fyzzy_k_means` function.

Multivariate function implements the protocol proposed by Córdoba et al. (2016), which performs a clustering with the `kmeans` function using as an input the spatial principal components (sPC) of the data. The function requires an `sf` object with the data to be clustered, and more than one numeric variable. The function by default returns a list with the following components: - `summaryResults`: a `data.frame` with - `indices`: a `data.frame` with indices to help to chose the optimal number of clusters. - `cluster`: the cluster number assigned to each observation.

For this example we will use the `wheat` dataset that comes with the `paar` package. The `data.frame` has apparent electrical conductivity (ECa) measured at two depths, elevation data, soil depth, and wheat gran yield. All variables have been interpolated to an unique grid and then merged in a single `data.frame`.

    data(wheat, package = 'paar')

    wheat_sf <- st_as_sf(wheat,
                         coords = c('x', 'y'),
                         crs = 32720)

    plot(wheat_sf)

The function `kmspc` requires the `sf` object with the data to be clustered, and the number of clusters (zones) to be delineated. For the sPC process, is necessary to specify the distance in which observations will be considered neighbors. The `ldist` and `udist` arguments specify the lower and upper distance thresholds, respectively. The `explainedVariance` argument specifies the minimum value of explained variance that the Principal Component to be used for the cluster process should explain. The `center` argument specifies if the data should be centered before the sPC process (default `TRUE`).

    # Run the kmspc function
    kmspc_results <-
      kmspc(wheat_sf,
            number_cluster = 2:4,
            explainedVariance = 70,
            ldist = 0,
            udist = 40,
            center = TRUE)
    #> Warning: All numeric Variables will be used to make clusters

To help the user to chose the optimal number of clusters, the function returns a `data.frame` with indices (`Xie Beni`, `Partition Coefficient`, `Entropy of Partition`, and `Summary Index`). The `Summary Index` is a combination of the indices to obtain a measure of the information reported by each index. In this example, the optimum number of cluster is 2. For each index, lower the value better the clustering. More information can be found in Paccioretti, Córdoba, and Balzarini (2020).

    kmspc_results$indices
    #>   Num. Cluster     Xie Beni Partition Coefficient Entropy of Partition
    #> 1            2 3.520969e-05             0.9611980           0.06490063
    #> 2            3 5.479312e-05             0.9391129           0.10430447
    #> 3            4 5.826727e-05             0.9292922           0.12352853
    #>   Summary Index
    #> 1      1.281088
    #> 2      1.597451
    #> 3      1.713101

The cluster for each observation can be found in the `cluster` component of the `kmspc` object. The `cluster` component is a `data.frame` with the cluster number assigned to each observation.

    head(kmspc_results$cluster)
    #>      Cluster_2 Cluster_3 Cluster_4
    #> [1,] "1"       "3"       "3"
    #> [2,] "1"       "3"       "3"
    #> [3,] "1"       "3"       "3"
    #> [4,] "1"       "1"       "3"
    #> [5,] "1"       "1"       "3"
    #> [6,] "1"       "1"       "3"

The clusters can be combined to the original data using the `cbind` function.

    wheat_clustered <- cbind(wheat_sf, kmspc_results$cluster)

This cluster can be plotted with the `plot` function.

    plot(wheat_clustered[, "Cluster_2"])

Also, ggplot can be used to plot the clusters.

    ggplot(wheat_clustered) +
      geom_sf(aes(color = Cluster_2)) +
      theme_minimal()

Córdoba, Mariano, Cecilia Bruno, José Luis Costa, Nahuel Peralta, and Mónica Balzarini. 2016. “Protocol for Multivariate Homogeneous Zone Delineation in Precision Agriculture.” Biosystems Engineering 143 (March): 95–107. https://doi.org/10.1016/j.biosystemseng.2015.12.008.
Paccioretti, P., M. Córdoba, and M. Balzarini. 2020. “FastMapping: Software to Create Field Maps and Identify Management Zones in Precision Agriculture.” Computers and Electronics in Agriculture 175 (August). https://doi.org/10.1016/j.compag.2020.105556.