Types of spatial patterns’ signatures

Jakub Nowosad

2024-08-23

Source: vignettes/articles/v2_signatures.Rmd

The fundamental element of the pattern-based spatial analysis is a numerical description of spatial patterns (so-called signature). This vignette shows how to derive spatial signatures using the lsp_signature() function on example datasets. Let’s start by attaching necessary packages:

library(motif)
library(stars)
#> Loading required package: abind
#> Loading required package: sf
#> Linking to GEOS 3.11.0, GDAL 3.5.3, PROJ 9.1.0; sf_use_s2() is TRUE
library(sf)

For this vignette, we use several spatial objects. The first one is a "raster/landcover2015.tif" file.

landcover = read_stars(system.file("raster/landcover2015.tif", package = "motif"))

This file contains a land cover data for New Guinea, with seven possible categories: (1) agriculture, (2) forest, (3) grassland, (5) settlement, (6) shrubland, (7) sparse vegetation, and (9) water.

landcover = droplevels(landcover)
plot(landcover, key.pos = 4, key.width = lcm(5), main = NULL)
#> downsample set to 12

The second one is a "raster/landform.tif" file.

landform = read_stars(system.file("raster/landform.tif", package = "motif"))

It has fourteen landform categories (plus surface water) for the same area.

landform = droplevels(landform)
plot(landform, key.pos = 4, key.width = lcm(8), main = NULL)
#> downsample set to 12

The third example object is random_ndvi.

set.seed(222)
random_ndvi = landcover
random_ndvi$ndvi = runif(length(random_ndvi[[1]]), min = 1, max = 10)
random_ndvi$ndvi[is.na(random_ndvi$landcover2015.tif)] = NA
random_ndvi$landcover2015.tif = NULL

It is an artificial dataset representing numerical weights for each cell for the same area as the datasets above.

plot(random_ndvi)
#> downsample set to 12

A co-occurrence matrix ("coma") representation - one layer

The first type of signature is a co-occurrence matrix ("coma"). It requires just one layer (one attribute in a stars object).

coma_output = lsp_signature(landcover, type = "coma", window = 100)
coma_output
#> # A tibble: 1,080 × 3
#>       id na_prop signature    
#>  * <int>   <dbl> <list>       
#>  1     5  0.357  <int [7 × 7]>
#>  2     6  0.0398 <int [7 × 7]>
#>  3     7  0.114  <int [7 × 7]>
#>  4     8  0.465  <int [7 × 7]>
#>  5     9  0.884  <int [7 × 7]>
#>  6    76  0.645  <int [7 × 7]>
#>  7    77  0.480  <int [7 × 7]>
#>  8    78  0.164  <int [7 × 7]>
#>  9    79  0      <int [7 × 7]>
#> 10    80  0      <int [7 × 7]>
#> # ℹ 1,070 more rows

The output is an object of class lsp with three columns:

  • id - an id of each window (area)
  • na_prop - share (0-1) of NA cells for each window
  • signature - a list-column containing with calculated signatures

We can see a signature for selected local landscape extracting it from the signature column:

coma_output$signature[[1]]
#>   1     2 3 4 5 6   7
#> 1 0     5 0 2 0 0   0
#> 2 5 24258 0 7 0 0 114
#> 3 0     0 0 0 0 0   0
#> 4 2     7 0 4 0 0   0
#> 5 0     0 0 0 0 0   0
#> 6 0     0 0 0 0 0   0
#> 7 0   114 0 0 0 0 822

Co-occurrence vector ("cove") is rearrangement of a co-occurrence matrix into one-dimensional object:

cove_output = lsp_signature(landcover, type = "cove", window = 100)
cove_output
#> # A tibble: 1,080 × 3
#>       id na_prop signature     
#>  * <int>   <dbl> <list>        
#>  1     5  0.357  <dbl [1 × 28]>
#>  2     6  0.0398 <dbl [1 × 28]>
#>  3     7  0.114  <dbl [1 × 28]>
#>  4     8  0.465  <dbl [1 × 28]>
#>  5     9  0.884  <dbl [1 × 28]>
#>  6    76  0.645  <dbl [1 × 28]>
#>  7    77  0.480  <dbl [1 × 28]>
#>  8    78  0.164  <dbl [1 × 28]>
#>  9    79  0      <dbl [1 × 28]>
#> 10    80  0      <dbl [1 × 28]>
#> # ℹ 1,070 more rows

This representation can be used to compare different local landscapes.

Learn more about these representations at https://nowosad.github.io/comat/articles/coma.html.

A weighted co-occurrence matrix (wecoma) representation - two layers

The next type of signature is a weighted co-occurrence matrix ("wecoma"). It requires two layers - a stars object with two attributes. The first one is a categorical raster data, while the second one is a continuous raster data containing weights.

wecoma_output = lsp_signature(c(landcover, random_ndvi), 
                               type = "wecoma", window = 100)
wecoma_output
#> # A tibble: 1,080 × 3
#>       id na_prop signature    
#>  * <int>   <dbl> <list>       
#>  1     5  0.357  <dbl [7 × 7]>
#>  2     6  0.0398 <dbl [7 × 7]>
#>  3     7  0.114  <dbl [7 × 7]>
#>  4     8  0.465  <dbl [7 × 7]>
#>  5     9  0.884  <dbl [7 × 7]>
#>  6    76  0.645  <dbl [7 × 7]>
#>  7    77  0.480  <dbl [7 × 7]>
#>  8    78  0.164  <dbl [7 × 7]>
#>  9    79  0      <dbl [7 × 7]>
#> 10    80  0      <dbl [7 × 7]>
#> # ℹ 1,070 more rows

Weighted co-occurrence vector ("wecove") is rearrangement of a weighted co-occurrence matrix into one-dimensional object:

wecove_output = lsp_signature(c(landcover, random_ndvi),
                               type = "wecove", window = 100)
wecove_output
#> # A tibble: 1,080 × 3
#>       id na_prop signature     
#>  * <int>   <dbl> <list>        
#>  1     5  0.357  <dbl [1 × 28]>
#>  2     6  0.0398 <dbl [1 × 28]>
#>  3     7  0.114  <dbl [1 × 28]>
#>  4     8  0.465  <dbl [1 × 28]>
#>  5     9  0.884  <dbl [1 × 28]>
#>  6    76  0.645  <dbl [1 × 28]>
#>  7    77  0.480  <dbl [1 × 28]>
#>  8    78  0.164  <dbl [1 × 28]>
#>  9    79  0      <dbl [1 × 28]>
#> 10    80  0      <dbl [1 × 28]>
#> # ℹ 1,070 more rows

Learn more about these representations at https://nowosad.github.io/comat/articles/wecoma.html.

An integrated co-occurrence matrix (incoma) representation - two or more layers

The next type of signature is an integrated co-occurrence matrix (incoma). It requires two or more layers - a stars object with two or more attributes. All layers must be categorical raster data.

incoma_output = lsp_signature(c(landcover, landform),
                               type = "incoma", window = 100)

Integrated co-occurrence vector ("incove") is rearrangement of an integrated co-occurrence matrix into one-dimensional object:

incove_output = lsp_signature(c(landcover, landform),
                               type = "incove", window = 100)

Learn more about these representations at https://nowosad.github.io/comat/articles/incoma.html

A composition representation ("composition") - one layer

A composition signature describes proportions of categories in a local landscape. It requires one layer (a stars object with one attribute).

composition_output = lsp_signature(landcover, 
                                    type = "composition", window = 100)
composition_output
#> # A tibble: 1,080 × 3
#>       id na_prop signature    
#>  * <int>   <dbl> <list>       
#>  1     5  0.357  <dbl [1 × 7]>
#>  2     6  0.0398 <dbl [1 × 7]>
#>  3     7  0.114  <dbl [1 × 7]>
#>  4     8  0.465  <dbl [1 × 7]>
#>  5     9  0.884  <dbl [1 × 7]>
#>  6    76  0.645  <dbl [1 × 7]>
#>  7    77  0.480  <dbl [1 × 7]>
#>  8    78  0.164  <dbl [1 × 7]>
#>  9    79  0      <dbl [1 × 7]>
#> 10    80  0      <dbl [1 × 7]>
#> # ℹ 1,070 more rows

By default, it is normalized to sum to 1:

composition_output$signature[[1]]
#>                 1         2 3            4 5 6          7
#> [1,] 0.0003110904 0.9581583 0 0.0007777259 0 0 0.04075284

To get an actual number of cells of each category, the normalization should be set to "none":

composition_output2 = lsp_signature(landcover, 
                                    type = "composition", window = 100,
                                    normalization = "none")
composition_output2$signature[[1]]
#>      1    2 3 4 5 6   7
#> [1,] 2 6160 0 5 0 0 262

User-defined functions - one or more layers

The motif package also allows calculating signature based on a user-defined function. This function should accept only one argument, which is a list containing one or more matrices. For example my_fun() below counts how many non-NA cells exist in each local landscape.

my_fun = function(x){
  sum(!is.na(c(x[[1]])))
}

Importantly, we need to set normalization = "none" to prevent the normalization of the output.

my_fun_output = lsp_signature(landcover, 
                               type = my_fun, window = 100,
                               normalization = "none")
my_fun_output
#> # A tibble: 1,080 × 3
#>       id na_prop signature
#>  * <int>   <dbl> <list>   
#>  1     5  0.357  <int [1]>
#>  2     6  0.0398 <int [1]>
#>  3     7  0.114  <int [1]>
#>  4     8  0.465  <int [1]>
#>  5     9  0.884  <int [1]>
#>  6    76  0.645  <int [1]>
#>  7    77  0.480  <int [1]>
#>  8    78  0.164  <int [1]>
#>  9    79  0      <int [1]>
#> 10    80  0      <int [1]>
#> # ℹ 1,070 more rows

We can see that in the first local landscape we have 6429 non-NA cells.

my_fun_output$signature[[1]]
#> [1] 6429