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https://github.com/mpadge/spatialcluster

spatially-constrained clustering in R
https://github.com/mpadge/spatialcluster

cluster clustering-algorithm r spatial

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spatially-constrained clustering in R

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README 

        
---

output: github_document

---



```{r, echo = FALSE}

knitr::opts_chunk$set(

  collapse = TRUE,

  comment = "#>",

  fig.path = "man/figures/README-"

)

```



[![R build status](https://github.com/mpadge/spatialcluster/workflows/R-CMD-check/badge.svg)](https://github.com/mpadge/spatialcluster/actions?query=workflow%3AR-CMD-check)

[![Project Status: WIP](http://www.repostatus.org/badges/latest/wip.svg)](http://www.repostatus.org/#wip)

[![codecov](https://codecov.io/gh/mpadge/spatialcluster/branch/master/graph/badge.svg)](https://codecov.io/gh/mpadge/spatialcluster)



# spatialcluster



An **R** package for spatially-constrained clustering using either distance or

covariance matrices. "*Spatially-constrained*" means that the data from which

clusters are to be formed also map on to spatial reference points, and the

constraint is that clusters must be spatially contiguous.



The package includes both an implementation of the

REDCAP collection of efficient yet approximate algorithms described in [D. Guo's

2008 paper, "Regionalization with dynamically constrained agglomerative

clustering and

partitioning."](https://www.tandfonline.com/doi/abs/10.1080/13658810701674970)

(pdf available

[here](https://pdfs.semanticscholar.org/ead1/7df8aaa1aed0e433b3ae1ec1ec5c7e785b2b.pdf)),

with extension to covariance matrices, and a new technique for computing

clusters using complete data sets. The package is also designed to analyse

matrices of spatial interactions (counts, densities) between sets of origin and

destination points. The spatial structure of interaction matrices is able to be

statistically analysed to yield both global statistics for the overall spatial

structure, and local statistics for individual clusters.



## Installation



The easiest way to install `spatialcluster` is be enabling the [corresponding

`r-universe`](https://mpadge.r-universe.dev/):



```{r r-univ, eval = FALSE}

options(repos = c(

                  mpadge = 'https://mpadge.r-universe.dev',

                  CRAN = 'https://cloud.r-project.org'))

```



The package can then be installed as usual with,



```{r install, eval = FALSE}

install.packges ("spatialcluster")

```



Alternatively, the package can also be installed using any of the following

options:



```{r gh-installation, eval = FALSE}

# install.packages("remotes")

remotes::install_git("https://codeberg.org/mpadge/spatialcluster")

remotes::install_git("https://git.sr.ht/~mpadge/spatialcluster")

remotes::install_bitbucket("mpadge/spatialcluster")

remotes::install_gitlab("mpadge/spatialcluster")

remotes::install_github("mpadge/spatialcluster")

```



## Usage



The two main functions, `scl_redcap()` and `scl_full()`, implement different

algorithms for spatial clustering. The former implements the algorithms of

REDCAP collection of efficient yet approximate algorithms described in [D.

Guo's 2008 paper, "Regionalization with dynamically constrained agglomerative

clustering and

partitioning."](https://www.tandfonline.com/doi/abs/10.1080/13658810701674970)

(pdf available

[here](https://pdfs.semanticscholar.org/ead1/7df8aaa1aed0e433b3ae1ec1ec5c7e785b2b.pdf)),

yet also here allowing covariance matrices to be submitted to clustering

routines. These algorithms are computationally efficient yet generate only

*approximate* estimates of underlying clusters. The latter function,

`scl_full()`, trades computational efficiency for accuracy, through generating

clustering schemes using all available data.



In short:



- `scl_full()` should always be preferred as long as it returns results within

  a reasonable amount of time

- `scl_redcap()` should be used only where data are too large for `scl_full()`

  to be run in a reasonable time.



Both of these functions require three main arguments:



1. A rectangular matrix of coordinates of points to be clustered (`n` rows; at

   least 2 columns);

2. An `n`-by-`n` square matrix quantifying relationships between those points;

3. A single value (`ncl`) specifying the desired number of clusters.



Usage can be demonstrated with some simple fake data:

```{r}

set.seed (1)

n <- 100

xy <- matrix (runif (2 * n), ncol = 2)

dmat <- matrix (runif (n ^ 2), ncol = n)

```



The load the package and call the function:



```{r full-single, echo = TRUE, eval = TRUE}

library (spatialcluster)

scl <- scl_full (xy, dmat, ncl = 8)

plot (scl)

```



The `scl` object is a `list` with the following components:



```{r list-components}

names (scl)

```



- `tree` details distances and cluster numbers for all pairwise comparisons

  between objects.

- `merges` details increasing distances at which each pair of objects was

  merged into a single cluster.

- `ord` provides the ...

- `nodes` records the spatial coordinates of each point (node) of the input

  data.

- `pars` retains the parameters used to call the clustering function.

- `statsiticss` returns the clustering statistics, both for individual clusters

  and an overall global statistic for the clustering scheme as a whole.



## A Cautionary Note



The following plot compares the results of applying four different clustering

algorithms to the same data.



```{r cautionary, eval = TRUE, fig.width = 7, fig.height = 7}

library (ggplot2)

library (gridExtra)

scl <- scl_full (xy, dmat, ncl = 8, linkage = "single")

p1 <- plot (scl) + ggtitle ("full-single")

scl <- scl_redcap (xy, dmat, ncl = 8, linkage = "single")

p2 <- plot (scl) + ggtitle ("redcap-single")

scl <- scl_redcap (xy, dmat, ncl = 8, linkage = "average")

p3 <- plot (scl) + ggtitle ("redcap-average")

scl <- scl_redcap (xy, dmat, ncl = 8, linkage = "complete")

p4 <- plot (scl) + ggtitle ("redcap-complete")



grid.arrange (p1, p2, p3, p4, ncol = 2)

```



This example illustrates the universal danger in all clustering algorithms: they

can not fail to produce results, even when the data fed to them are definitely

devoid of any information as in this example. Clustering algorithms should only

be applied to reflect a very specific hypothesis for why data should be

clustered in the first place; spatial clustering algorithms should only be

applied to reflect two very specific hypothesis for (i) why data should be

clustered at all, and (ii) why those clusters should manifest a spatial

pattern.