Balanced Accuracy

baccuracy.factor

R Documentation

Description

A generic function for the (normalized) balanced accuracy. Use weighted.baccuracy() for the weighted balanced accuracy.

Usage

## S3 method for class 'factor'
baccuracy(actual, predicted, adjust = FALSE, na.rm = TRUE, ...)

## S3 method for class 'factor'
weighted.baccuracy(actual, predicted, w, adjust = FALSE, na.rm = TRUE, ...)

## S3 method for class 'cmatrix'
baccuracy(x, adjust = FALSE, na.rm = TRUE, ...)

## Generic S3 method
baccuracy(
  ...,
  adjust = FALSE,
  na.rm  = TRUE
)

## Generic S3 method
weighted.baccuracy(
  ...,
  w,
  adjust = FALSE,
  na.rm  = TRUE
)

Arguments

actual	A vector of with length \(n\), and \(k\) levels
predicted	A vector of with length \(n\), and \(k\) levels
adjust	A logical value (default: FALSE). If TRUE the metric is adjusted for random chance \(\frac{1}{k}\).
na.rm	A logical value (default: TRUE). If TRUE calculation of the metric is based on valid classes.
…	micro = NULL, na.rm = TRUE Arguments passed into other methods
w	A <numeric>-vector of length \(n\). NULL by default
x	A confusion matrix created cmatrix()

Value

A numeric-vector of length 1

Definition

Let \(\hat{\alpha} \in [0, 1]\) be the proportion of correctly predicted classes. If adjust == false, the balanced accuracy of the classifier is calculated as,

\[ \hat{\alpha} = \frac{\text{sensitivity} + \text{specificity}}{2} \]

otherwise,

\[ \hat{\alpha} = \frac{\text{sensitivity} + \text{specificity}}{2} \frac{1}{k} \]

Where:

• \(k\) is the number of classes

• \(\text{sensitivity}\) is the overall sensitivity, and

• \(\text{specificity}\) is the overall specificity

Examples

# 1) recode Iris
# to binary classification
# problem
iris$species_num <- as.numeric(
  iris$Species == "virginica"
)

# 2) fit the logistic
# regression
model <- glm(
  formula = species_num ~ Sepal.Length + Sepal.Width,
  data    = iris,
  family  = binomial(
    link = "logit"
  )
)

# 3) generate predicted
# classes
predicted <- factor(
  as.numeric(
    predict(model, type = "response") > 0.5
  ),
  levels = c(1,0),
  labels = c("Virginica", "Others")
)

# 3.1) generate actual
# classes
actual <- factor(
  x = iris$species_num,
  levels = c(1,0),
  labels = c("Virginica", "Others")
)

# 4) evaluate the
# model
cat(
  "Balanced accuracy", baccuracy(
    actual    = actual,
    predicted = predicted
  ),
  
  "Balanced accuracy (weigthed)", weighted.baccuracy(
    actual    = actual,
    predicted = predicted,
    w         = iris$Petal.Length/mean(iris$Petal.Length)
  ),
  sep = "\n"
)