Spatial Cross-Validation Methods

Concept

Spatial block CV divides the study area into a grid of rectangular blocks. Observations are assigned to folds based on which block they fall into. This ensures spatial separation between training and test sets.

When to Use

• Data with relatively uniform spatial distribution
• When you want to ensure geographic coverage
• When computational efficiency is important
• As a default spatial CV method

Basic Usage

# Create spatial block folds
folds_block <- spatial_folds(
  data = sample_spatial_data,
  x = "longitude",
  y = "latitude",
  k = 5,
  method = "block",
  seed = 123
)

print(folds_block)

## Spatial Cross-Validation Folds
## ==============================
## Method: spatial_block 
## Number of folds: 5 
## Observations: 200 
## CRS: Not defined 
## Has duplicate coordinates: FALSE 
## Seed: 123 
## 
## Fold sizes:
##   Fold 1: 155 train, 45 test
##   Fold 2: 150 train, 50 test
##   Fold 3: 150 train, 50 test
##   Fold 4: 168 train, 32 test
##   Fold 5: 177 train, 23 test

Controlling Block Size

You can control the spatial resolution using either block size or number of blocks:

# Specify block size
folds_block_size <- spatial_block_folds(
  data = sample_spatial_data,
  x = "longitude",
  y = "latitude",
  k = 5,
  block_size = c(200, 200),  # 200x200 unit blocks
  seed = 123
)

# Specify number of blocks
folds_n_blocks <- spatial_block_folds(
  data = sample_spatial_data,
  x = "longitude",
  y = "latitude",
  k = 5,
  n_blocks = c(5, 5),  # 5x5 grid
  seed = 123
)

Assignment Strategies

Blocks can be assigned to folds using different strategies:

# Systematic assignment (default)
folds_systematic <- spatial_block_folds(
  data = sample_spatial_data,
  x = "longitude",
  y = "latitude",
  k = 5,
  assignment = "systematic",
  seed = 123
)

# Random assignment
folds_random_assign <- spatial_block_folds(
  data = sample_spatial_data,
  x = "longitude",
  y = "latitude",
  k = 5,
  assignment = "random",
  seed = 123
)

Concept

Buffered CV ensures that for each test observation, no training observation falls within a specified buffer radius. This provides strict control over the minimum spatial separation.

When to Use

• When you need precise control over train/test distance
• For point-based data with irregular sampling
• When buffer distance has ecological/physical meaning
• For conservative performance estimates

Basic Usage

# Create buffered folds
folds_buffer <- spatial_buffer_folds(
  data = sample_spatial_data,
  x = "longitude",
  y = "latitude",
  k = 5,
  buffer_radius = 100,  # 100 unit buffer
  seed = 123
)

print(folds_buffer)

## Spatial Cross-Validation Folds
## ==============================
## Method: spatial_buffer 
## Number of folds: 5 
## Observations: 
## CRS:  
## Has duplicate coordinates: 
## 
## Fold sizes:
##   Fold 1: 160 train, 40 test
##   Fold 2: 160 train, 40 test
##   Fold 3: 160 train, 40 test
##   Fold 4: 160 train, 40 test
##   Fold 5: 160 train, 40 test

Important Notes

• Buffered CV requires a projected CRS for accurate distance calculations
• Using geographic coordinates (longitude/latitude) will produce approximate distances
• Larger buffer radii reduce the size of training sets
• This method is computationally more intensive than block CV

Concept

Spatial clustering CV groups spatially proximate observations using clustering algorithms (k-means), then assigns clusters to folds. This is useful for data with complex spatial structure.

When to Use

• Data with irregular or clustered spatial patterns
• When natural spatial groupings exist
• For heterogeneous spatial distributions
• When block boundaries would be arbitrary

Basic Usage

# Create clustering folds
folds_cluster <- spatial_cluster_folds(
  data = sample_spatial_data,
  x = "longitude",
  y = "latitude",
  k = 5,
  n_clusters = 10,  # Number of spatial clusters
  seed = 123
)

print(folds_cluster)

## Spatial Cross-Validation Folds
## ==============================
## Method: spatial_cluster 
## Number of folds: 5 
## Observations: 
## CRS:  
## Has duplicate coordinates: 
## 
## Fold sizes:
##   Fold 1: 143 train, 57 test
##   Fold 2: 173 train, 27 test
##   Fold 3: 161 train, 39 test
##   Fold 4: 158 train, 42 test
##   Fold 5: 165 train, 35 test

Understanding Cluster Assignment

# Examine cluster centers
folds_cluster$parameters$cluster_centers

##    x_coords y_coords
## 1  532.7197 565.9710
## 2  887.9961 696.9285
## 3  434.2980 318.7487
## 4  233.6940 125.0067
## 5  148.7116 397.2902
## 6  608.2099 878.5329
## 7  843.4232 400.2357
## 8  886.7498 125.1667
## 9  619.4220 116.1783
## 10 235.5819 827.2978

Concept

Random spatial split performs standard random k-fold cross-validation without spatial constraints. This serves as a baseline to demonstrate the impact of spatial dependence.

When to Use

• As a baseline for comparison
• When spatial dependence is minimal
• For initial exploratory analysis
• To demonstrate the value of spatial CV

Basic Usage

# Create random folds
folds_random <- spatial_split(
  data = sample_spatial_data,
  x = "longitude",
  y = "latitude",
  k = 5,
  seed = 123
)

print(folds_random)

## Spatial Cross-Validation Folds
## ==============================
## Method: random 
## Number of folds: 5 
## Observations: 
## CRS:  
## Has duplicate coordinates: 
## 
## Fold sizes:
##   Fold 1: 160 train, 40 test
##   Fold 2: 160 train, 40 test
##   Fold 3: 160 train, 40 test
##   Fold 4: 160 train, 40 test
##   Fold 5: 160 train, 40 test

Decision Flowchart

1. Start with spatial block CV - Good default choice
2. Need precise distance control? → Use buffered CV
3. Complex spatial patterns? → Use clustering CV
4. Compare with random CV → Always include baseline

Method Comparison

Start Simple

Begin with spatial block CV using default parameters:

# Default spatial block CV
folds_default <- spatial_folds(
  data = sample_spatial_data,
  x = "longitude",
  y = "latitude",
  k = 5
)

Adjust Based on Data Characteristics

• Dense data: Use larger blocks or more clusters
• Sparse data: Use smaller blocks or fewer clusters
• Strong spatial patterns: Consider clustering CV
• Precise distance requirements: Use buffered CV

Always Compare with Random CV

# Compare spatial vs random
folds_spatial <- spatial_folds(sample_spatial_data, "longitude", "latitude", 
                               k = 5, method = "block", seed = 123)
folds_random <- spatial_folds(sample_spatial_data, "longitude", "latitude", 
                             k = 5, method = "random", seed = 123)

# Analyze spatial leakage for both
leakage_spatial <- detect_spatial_leakage(sample_spatial_data, folds_spatial, 
                                           "longitude", "latitude")
leakage_random <- detect_spatial_leakage(sample_spatial_data, folds_random, 
                                          "longitude", "latitude")

print(leakage_spatial)

## Spatial Leakage Detection
## =========================
## Method: spatial_block 
## Overall Risk Level: LOW 
## Distance Threshold: 53.04 
## 
## Summary Statistics:
##   Min distance: 11.24
##   Mean distance: 521.24
##   Median distance: 530.91
##   Proportion below threshold: 0.1%
## 
## Fold Analysis:
##   Fold 1: LOW risk (0.1% below threshold)
##   Fold 2: LOW risk (0.0% below threshold)
##   Fold 3: LOW risk (0.1% below threshold)
##   Fold 4: LOW risk (0.2% below threshold)
##   Fold 5: LOW risk (0.1% below threshold)
## 
## Recommendations:
##   - Spatial separation appears adequate. 
##   - Current cross-validation setup should provide reliable performance estimates. 
##   - Consider increasing spatial separation if you need more conservative estimates.

print(leakage_random)

## Spatial Leakage Detection
## =========================
## Method: random 
## Overall Risk Level: LOW 
## Distance Threshold: 51.27 
## 
## Summary Statistics:
##   Min distance: 2.21
##   Mean distance: 512.67
##   Median distance: 504.43
##   Proportion below threshold: 0.8%
## 
## Fold Analysis:
##   Fold 1: LOW risk (0.7% below threshold)
##   Fold 2: LOW risk (0.8% below threshold)
##   Fold 3: LOW risk (0.8% below threshold)
##   Fold 4: LOW risk (0.7% below threshold)
##   Fold 5: LOW risk (0.8% below threshold)
## 
## Recommendations:
##   - Spatial separation appears adequate. 
##   - Current cross-validation setup should provide reliable performance estimates. 
##   - Consider increasing spatial separation if you need more conservative estimates.

Issue: Too few observations per fold

Solution: Reduce k or use fewer blocks/clusters

# Reduce number of folds
folds_k3 <- spatial_folds(sample_spatial_data, "longitude", "latitude", k = 3)

Issue: Uneven fold sizes

Solution: This is normal for spatial methods; consider using stratified approaches if class imbalance is severe

Issue: Geographic gaps in training data

Solution: Increase block size or number of clusters to improve coverage