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1. blockCV introduction: how to create block cross-validation folds

Roozbeh Valavi, Jane Elith, José Lahoz-Monfort and Gurutzeta Guillera-Arroita

2024-11-01

Introduction

The package blockCV offers a range of functions for generating train and test folds for k-fold and leave-one-out (LOO) cross-validation (CV). It allows for separation of data spatially and environmentally, with various options for block construction. Additionally, it includes a function for assessing the level of spatial autocorrelation in response or raster covariates, to aid in selecting an appropriate distance band for data separation. The blockCV package is suitable for the evaluation of a variety of spatial modelling applications, including classification of remote sensing imagery, soil mapping, and species distribution modelling (SDM). It also provides support for different SDM scenarios, including presence-absence and presence-background species data, rare and common species, and raster data for predictor variables.

Please cite blockCV by: Valavi R, Elith J, Lahoz-Monfort JJ, Guillera-Arroita G. blockCV: An R package for generating spatially or environmentally separated folds for k-fold cross-validation of species distribution models. Methods Ecol Evol. 2019; 10:225–232. doi: 10.1111/2041-210X.13107

New updates of the version 3.0

The latest version blockCV (v3.0) features significant updates and changes. All function names have been revised to more general names, beginning with cv_*. Although the previous functions (version 2.x) will continue to work, they will be removed in future updates after being available for an extended period. It is highly recommended to update your code with the new functions provided below.

Some new updates:

Installation

The blockCV is available in CRAN and the latest update can also be downloaded from GitHub. It is recommended to install the dependencies of the package. To install the package use:

# install stable version from CRAN
install.packages("blockCV", dependencies = TRUE)

# install latest update from GitHub
remotes::install_github("rvalavi/blockCV", dependencies = TRUE)
# loading the package
library(blockCV)
## blockCV 3.1.5

Package data

The package contains the raw format of the following data:

These data are used to illustrate how the package is used. The raster data include several bioclimatic variables for Australia. The species data include presence-absence records (binary) of a simulated species.

To load the package raster data use:

library(sf) # working with spatial vector data
library(terra) # working with spatial raster data
library(tmap) # plotting maps

# load raster data
# the pipe operator |> is available for R version 4.1 or higher
rasters <- system.file("extdata/au/", package = "blockCV") |>
  list.files(full.names = TRUE) |>
  terra::rast()

The presence-absence species data include 243 presence points and 257 absence points.

# load species presence-absence data and convert to sf
points <- read.csv(system.file("extdata/", "species.csv", package = "blockCV"))
head(points)
##            x        y occ
## 1  1313728.4 -2275453   0
## 2  1176795.0 -1916003   0
## 3 -1741599.3 -3927213   1
## 4  1099769.9 -4124055   1
## 5  1279495.1 -3901538   0
## 6   928603.1 -1342594   0

The appropriate format of species data for the blockCV package is simple features (from the sf package). The data is provide in GDA2020 / GA LCC coordinate reference system with "EPSG:7845" as defined by crs = 7845. We convert the data.frame to sf as follows:

pa_data <- sf::st_as_sf(points, coords = c("x", "y"), crs = 7845)

Let’s plot the species data using tmap package:

tm_shape(rasters[[1]]) +
  tm_raster(legend.show = FALSE, n = 30, palette = gray.colors(10)) +
  tm_shape(pa_data) +
  tm_dots(col = "occ", style = "cat", size = 0.1)

Block cross-validation strategies

The blockCV stores training and testing folds in three different formats. The common format for all three blocking strategies is a list of the indices of observations in each fold. For cv_spatial and cv_cluster (but not cv_buffer and cv_nndm), the folds are also stored in a matrix format suitable for the biomod2 package and a vector of fold’s number for each observation. This is equal to the number of observation in spatial sample data (argument x in functions). These three formats are stored in the cv objects as folds_list, biomod_table and folds_ids respectively.

Spatial blocks

The function cv_spatial creates spatial blocks/polygons then assigns blocks to the training and testing folds with random, checkerboard pattern or a systematic way (with the selection argument). When selection = "random", the function tries to find evenly distributed records in training and testing folds. Spatial blocks can be defined either by size or number of rows and columns.

Consistent with other functions, the distance (size) should be in metres, regardless of the unit of the reference system of the input data. When the input map has geographic coordinate system (i.e. decimal degrees), the block size is calculated based on dividing size by 111325 (the standard distance of a degree in metres, on the Equator) to change metre to degree. In reality, this value varies by a factor of the cosine of the latitude. So, an alternative sensible value could be cos(mean(sf::st_bbox(x)[c(2,4)]) * pi/180) * 111325.

The offset argument can be used to shift the spatial position of the blocks in horizontal and vertical axes, respectively. This only works when the block have been built based on size, and the extend option allows user to enlarge the blocks ensuring all points fall inside the blocks (most effectve when rows_cols is used). The blocks argument allows users to define an external spatial polygon as blocking layer.

Here are some spatial block settings:

sb1 <- cv_spatial(x = pa_data,
                  column = "occ", # the response column (binary or multi-class)
                  k = 5, # number of folds
                  size = 350000, # size of the blocks in metres
                  selection = "random", # random blocks-to-fold
                  iteration = 50, # find evenly dispersed folds
                  biomod2 = TRUE) # also create folds for biomod2

The output object is an R S3 object and you can get its elements by a $. Explore sb1$folds_ids, sb1$folds_list, and sb1$biomod_table for the three types of generated folds from the cv_spatial object sb1. Use the one suitable for you modelling practice to evaluate your models. See the explanation of all other outputs/elements of the function in the help file of the function.

The same setting from previous code can be used to create square blocks by using hexagon = FALSE. You can optionally add a raster layer (using r argument) for to be used for creating blocks and be used in the background of the plot (raster can also be added later only for visualising blocks using cv_plot).

sb2 <- cv_spatial(x = pa_data,
                  column = "occ",
                  r = rasters, # optionally add a raster layer
                  k = 5, 
                  size = 350000, 
                  hexagon = FALSE, # use square blocks
                  selection = "random",
                  progress = FALSE, # turn off progress bar for vignette
                  iteration = 50, 
                  biomod2 = TRUE)
## 
##   train_0 train_1 test_0 test_1
## 1     214     197     43     46
## 2     218     211     39     32
## 3     216     198     41     45
## 4     194     208     63     35
## 5     186     158     71     85

The assignment of folds to each block can also be done in a systematic manner using selection = "systematic", or a checkerboard pattern using selection = "checkerboard". The blocks can also be created by number of rows and columns when no size is supplied by e.g. rows_cols = c(12, 10).

# systematic fold assignment 
# and also use row/column for creating blocks instead of size
sb3 <- cv_spatial(x = pa_data,
                  column = "occ",
                  rows_cols = c(12, 10),
                  hexagon = FALSE,
                  selection = "systematic")
## 
##   train_0 train_1 test_0 test_1
## 1     227     203     30     40
## 2     204     232     53     11
## 3     215     125     42    118
## 4     194     220     63     23
## 5     188     192     69     51

The function’s output report reveals that setting the selection to ‘random’ results in a more even distribution of presence/absence instances between the train and test folds compared to ‘systematic’. This is because the random assignment process is repeated multiple times, controlled by the iteration parameter, to ensure that the folds are evenly distributed.

# checkerboard block to CV fold assignment
sb4 <- cv_spatial(x = pa_data,
                  column = "occ",
                  size = 350000,
                  hexagon = FALSE,
                  selection = "checkerboard")
## 
##   train_0 train_1 test_0 test_1
## 1     125     143    132    100
## 2     132     100    125    143

Let’s visualise the checkerboard blocks with tmap:

tm_shape(sb4$blocks) +
  tm_fill(col = "folds", style = "cat")

Spatial and environemntal clustering

The function cv_cluster uses clustering methods to specify sets of similar environmental conditions based on the input covariates. Species data corresponding to any of these groups or clusters are assigned to a fold. Alternatively, the clusters can be based on spatial coordinates of sample points (the x argument).

Using spatial coordinate values for clustering:

# spatial clustering
set.seed(6)
scv <- cv_cluster(x = pa_data,
                  column = "occ", # optional: counting number of train/test records
                  k = 5)
##   train_0 train_1 test_0 test_1
## 1     230     240     27      3
## 2     171     142     86    101
## 3     232     228     25     15
## 4     203     227     54     16
## 5     192     135     65    108

The clustering can be done in environmental space by supplying r. Notice, this could be an extreme case of cross-validation as the testing folds could possibly fall in novel environmental conditions than what the training points are (check cv_similarity for testing this). Note that the input raster layer should cover all the species points, otherwise an error will rise. The records with no raster value should be deleted prior to the analysis or a different raster be used.

# environmental clustering
set.seed(6)
ecv <- cv_cluster(x = pa_data,
                  column = "occ",
                  r = rasters,
                  k = 5, 
                  scale = TRUE)
##   train_0 train_1 test_0 test_1
## 1     249     172      8     71
## 2     215     234     42      9
## 3     211     211     46     32
## 4     216     145     41     98
## 5     137     210    120     33

When r is supplied, all the input rasters are first centred and scaled to avoid one raster variable dominate the clusters using scale = TRUE option.

By default, the clustering will be done based only on the values of the predictors at the sample points. In this case, and the number of the folds will be the same as k. If raster_cluster = TRUE, the clustering is done in the raster space. In this approach, the clusters will be consistent throughout the region and across species (in the same region). However, this may result in cluster(s) that cover none of the species records especially when species data is not dispersed throughout the region (or environmental ranges) or the number of clusters (k or folds) is high.

Buffering LOO (also known as Spatial LOO)

The function cv_buffer generates spatially separated training and testing folds by considering buffers of specified distance around each observation point. This approach is a form of leave-one-out (LOO) cross-validation. Each fold is generated by excluding nearby observations around each testing point within the specified distance (ideally the range of spatial autocorrelation). In this method the test set never directly abuts a training set.

Using buffering to create CV folds:

bloo <- cv_buffer(x = pa_data,
                  column = "occ",
                  size = 350000)

When using species presence-background data (or presence and pseudo-absence), you need to supply the column and set presence_bg = TRUE. In this case, only presence points (1s) are considered as target points. For more information read the details section in the help of the function (i.e. help(cv_buffer)).

For species presence-absence data and any other types of data (such as continuous, counts, and multi-class targets) keep presence_bg = FALSE (default). In this case, all sample points other than the target point within the buffer are excluded, and the training set comprises all points outside the buffer.

Nearest Neighbour Distance Matching (NNDM) LOO

The cv_nndm is a fast implementation of the Nearest Neighbour Distance Matching (NNDM) algorithm (Milà et al., 2022) in C++. Similar to cv_buffer, this is a variation of leave-one-out (LOO) cross-validation. It tries to match the nearest neighbour distance distribution function between the test and training data to the nearest neighbour distance distribution function between the target prediction and training points (Milà et al., 2022).

nncv <- cv_nndm(x = pa_data,
                column = "occ",
                r = rasters,
                size = 350000,
                num_sample = 5000, 
                sampling = "regular",
                min_train = 0.1,
                plot = TRUE)
##     train_0         train_1          test_0          test_1     
##  Min.   :210.0   Min.   :146.0   Min.   :0.000   Min.   :0.000  
##  Mean   :244.4   Mean   :221.2   Mean   :0.514   Mean   :0.486  
##  Max.   :257.0   Max.   :243.0   Max.   :1.000   Max.   :1.000

Visualising the folds

You can visualise the generate folds for all block cross-validation strategies. You can optionally add a raster layer as background map using r option. When r is supplied the plots might be slightly slower.

Let’s plot spatial clustering folds created in previous section (using cv_cluster):

cv_plot(cv = scv, 
        x = pa_data)

When cv_buffer is used for plotting, only first 10 folds are shown. You can choose any set of CV folds for plotting. If remove_na = FALSE (default is TRUE), the NA in the legend shows the excluded points.

cv_plot(cv = bloo,
        x = pa_data,
        num_plots = c(1, 50, 100)) # only show folds 1, 50 and 100

If you do not supply x when plotting a cv_spatial object, only the spatial blocks are plotted.

cv_plot(cv = sb1,
        r = rasters,
        raster_colors = terrain.colors(10, alpha = 0.5),
        label_size = 4)

Check similarity

The cv_similarity function can check for environmental similarity between the training and testing folds and thus possible extrapolation in the testing folds. It computes multivariate environmental similarity surface (MESS) as described in Elith et al. (2010). MESS represents how similar a point in a testing fold is to a training fold (as a reference set of points), with respect to a set of predictor variables in r. The negative values are the sites where at least one variable has a value that is outside the range of environments over the reference set, so these are novel environments.

cv_similarity(cv = ecv, # the environmental clustering
              x = pa_data, 
              r = rasters, 
              progress = FALSE)
## Warning: The following aesthetics were dropped during statistical transformation:
## colour.
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

Estimating size: the effective range of spatial autocorrelation

To support a first choice of block size, prior to any model fitting, package blockCV includes the option for the user to look at the existing autocorrelation in the response or predictors (as an indication of landscape spatial structure). This tool does not suggest any absolute solution to the problem, but serves as a guide to the user. It provides information about the effective range of spatial autocorrelation which is the range over which observations are independent.

When only r is supplied, the cv_spatial_autocor function works by automatically fitting variograms to each continuous raster and finding the effective range of spatial autocorrelation. Variogram is a fundamental geostatistical tool for measuring spatial autocorrelation (O’Sullivan and Unwin, 2010).

sac1 <- cv_spatial_autocor(r = rasters, 
                           num_sample = 5000)

The plotted block size is based on the median of the spatial autocorrelation ranges. This could be as the minimum block size for creating spatially separated folds. Variograms are computed taking a number of random points (5000 as default) from each input raster file. The variogram fitting procedure is done using automap package (Hiemstra et al., 2009), using the isotropic variogram and assuming the data meets the geostatistical criteria e.g. stationarity.

The output object of this function is an cv_spatial_autocor object, an object of class S3.

# class of the output result
class(sac1)
## [1] "cv_spatial_autocor"

To see the details of the fitted variograms:

# summary statistics of the output
summary(sac1)
## Summary statistics of spatial autocorrelation ranges of all input layers:
## Length  Class   Mode 
##      0   NULL   NULL 
## NULL

Alternatively, only use the response data using x and column. This could be a binary or continuous variable provided in as a column in the sample points sf object. This could be the response or the residuals of a fitted model.

sac2 <- cv_spatial_autocor(x = pa_data, 
                           column =  "occ")

To visualise them (this needs the automap package to be loaded):

library(automap)

plot(sac2$variograms[[1]])

Package blockCV also provides a visualisation tool for assisting in block size selection. This tool is developed as local web applications using R package shiny. With cv_block_size, the user can choose among block sizes in a specified range, visualise the resulting blocks interactively, viewing the impact of block size on number and arrangement of blocks in the landscape (and optionally on the distribution of sample points in those blocks).

Using only raster data:

cv_block_size(r = rasters)

Or use only spatial sample data:

cv_block_size(x = pa_data,
              column = "occ") # optionally add the response

Or add both raster and samples (also define a min/max size):

cv_block_size(x = pa_data,
              column = "occ",
              r = rasters,
              min_size = 2e5,
              max_size = 9e5)

Note that the interactive plots cannot be shown here, as they require opening an external window or web browser. When using cv_block_size, slide to the selected block size, and click Apply Changes to change the block size.

References:

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