# Conducting Cross-Validation With k-folds in R (Example Code)

In this article, you’ll learn how to conduct cross-validation with k-folds in the R programming language.

## Setting up the Example

We use three packages: data.table, class, and caret.

install.packages(data.table) # Install data.table package library("data.table") install.packages(class) # Install class package library("class") install.packages(caret) # Install caret package library("caret") |

install.packages(data.table) # Install data.table package library("data.table") install.packages(class) # Install class package library("class") install.packages(caret) # Install caret package library("caret")

For an illustrative example of cross-validation, we use the built-in iris dataset.

data(iris) # Load iris data set head(iris) # Print head of data # Sepal.Length Sepal.Width Petal.Length Petal.Width Species # 1 5.1 3.5 1.4 0.2 setosa # 2 4.9 3.0 1.4 0.2 setosa # 3 4.7 3.2 1.3 0.2 setosa # 4 4.6 3.1 1.5 0.2 setosa # 5 5.0 3.6 1.4 0.2 setosa # 6 5.4 3.9 1.7 0.4 setosa prop.table(table(iris$Species)) * 100 # Proportions of species in iris # setosa versicolor virginica # 33.33333 33.33333 33.33333 |

data(iris) # Load iris data set head(iris) # Print head of data # Sepal.Length Sepal.Width Petal.Length Petal.Width Species # 1 5.1 3.5 1.4 0.2 setosa # 2 4.9 3.0 1.4 0.2 setosa # 3 4.7 3.2 1.3 0.2 setosa # 4 4.6 3.1 1.5 0.2 setosa # 5 5.0 3.6 1.4 0.2 setosa # 6 5.4 3.9 1.7 0.4 setosa prop.table(table(iris$Species)) * 100 # Proportions of species in iris # setosa versicolor virginica # 33.33333 33.33333 33.33333

In the iris data, the three species are balanced, each accounting for 1/3 of the total number of observations.

## Example: Cross-Validation With k Folds

We want to implement a k-nearest neighbor (kNN) algorithm for classifying new observations as one of the three iris species classes. For general information on kNN, see this post from RPubs.

In kNN, we have to choose the number of nearest neighbors k. We can use k-fold cross validation to estimate how well kNN works under different values of k, and thereby determine which k to choose.

nr_neighbors <- c(1, 5, 10) # Setting the number of neighbors to consider |

nr_neighbors <- c(1, 5, 10) # Setting the number of neighbors to consider

We normalize the features.

f_norm <- function (x) { ( x - min(x) ) / ( max(x) - min(x) ) } # Function for normalizing data iris_X <- apply(iris[, 1:4], 2, f_norm ) # Normalizing the data |

f_norm <- function (x) { ( x - min(x) ) / ( max(x) - min(x) ) } # Function for normalizing data iris_X <- apply(iris[, 1:4], 2, f_norm ) # Normalizing the data

For the cross-validation, we decide to go with 6 folds.

nr_folds <- 6 # Choosing the number of folds for cross-validation |

nr_folds <- 6 # Choosing the number of folds for cross-validation

The iris data is partitioned into 6 folds of roughly equal size.

data_folds <- sample(rep(1:nr_folds, each = nrow(iris)/nr_folds), nrow(iris)) # Creating data folds |

data_folds <- sample(rep(1:nr_folds, each = nrow(iris)/nr_folds), nrow(iris)) # Creating data folds

Now we conduct the cross-validation. We use each fold as validation data and the rest 5 folds as training data. Based on the validation data, we predict the species via kNN and compare the predicted classes with the actual classes in the validation data. For the evaluation, we calculate the F1 score for each of the three classes of species in iris. For information on the F1 score, see e.g. Aggarwal (2015) Data Mining, Chapter 10.

result_cv <- lapply(1:nr_folds, # 5-fold cross-validation function (k) { IDs_for_training <- (1:nrow(iris))[data_folds != k] # IDs for training data IDs_for_validation <- (1:nrow(iris))[data_folds == k] # IDs for test data results_choices_neighbors <- sapply(nr_neighbors, # Calculating kNN with "nr_neighbors" neighbors function (i) { kNN_out <- class::knn(train = iris_X[IDs_for_training, ], test = iris_X[IDs_for_validation, ], cl = iris$Species[IDs_for_training], k = i) confMat <- caret::confusionMatrix(reference = iris$Species[IDs_for_validation], # Model performance data = kNN_out) confMat$byClass[,"F1"] # Return accuracy }) colnames(results_choices_neighbors) <- paste0(nr_neighbors, "_neighbors") results_choices_neighbors }) |

result_cv <- lapply(1:nr_folds, # 5-fold cross-validation function (k) { IDs_for_training <- (1:nrow(iris))[data_folds != k] # IDs for training data IDs_for_validation <- (1:nrow(iris))[data_folds == k] # IDs for test data results_choices_neighbors <- sapply(nr_neighbors, # Calculating kNN with "nr_neighbors" neighbors function (i) { kNN_out <- class::knn(train = iris_X[IDs_for_training, ], test = iris_X[IDs_for_validation, ], cl = iris$Species[IDs_for_training], k = i) confMat <- caret::confusionMatrix(reference = iris$Species[IDs_for_validation], # Model performance data = kNN_out) confMat$byClass[,"F1"] # Return accuracy }) colnames(results_choices_neighbors) <- paste0(nr_neighbors, "_neighbors") results_choices_neighbors })

Calculate the mean value of the species-specific F1 scores over the folds.

round(Reduce('+', result_cv) / nr_folds, digits = 3) # Averaging the results over the k folds # 1_neighbors 5_neighbors 10_neighbors # Class: setosa 1.000 1.000 1.000 # Class: versicolor 0.934 0.949 0.940 # Class: virginica 0.922 0.929 0.937 |

round(Reduce('+', result_cv) / nr_folds, digits = 3) # Averaging the results over the k folds # 1_neighbors 5_neighbors 10_neighbors # Class: setosa 1.000 1.000 1.000 # Class: versicolor 0.934 0.949 0.940 # Class: virginica 0.922 0.929 0.937

You can see the estimates of the F1 scores for kNN with 1, 5, and 10 neighbors. There is no clear winner in this example. Try a different setting, e.g. a different number of k neighbors or different number of folds!

**Note:** This article was created in collaboration with Anna-Lena Wölwer. Anna-Lena is a researcher and programmer who creates tutorials on statistical methodology as well as on the R programming language. You may find more info about Anna-Lena and her other articles on her profile page.