How to calculate Imbalance Accuracy Metric in multi-class classification

Question

I am sorry to bother, but I found an interesting article "Mortaz, E. (2020). Imbalance accuracy metric for model selection in multi-class imbalance classification problems. Knowledge-Based Systems, 210, 106490" (https://www.sciencedirect.com/science/article/pii/S0950705120306195) and there they calculate this measure (IAM) (the formula is in the paper, and I understood it), but I would like to ask: how can I replicate it on R?

I apologise in advance for the dumb question. Thank you for your attention!

Answer 1

The IAM formula provided in the article is: IAM formula

Where cij is the element (i,j) in the classifier's confusion matrix (c). k is referred to the number of classes in the classification (k>=2). It is shown that this metric can be used as a solo metric in multi-class model selection.

The code to implement the IAM (Imbalance Accuracy Metric) in python provided below:

def IAM(c):
  '''
  c is a nested list presenting the confusion matrix of the classifier (len(c)>=2)
  '''
  l  = len(c)
  iam = 0

  for i in range(l):
      sum_row = 0
      sum_col = 0
      sum_row_no_i = 0
      sum_col_no_i = 0
      for j in range(l):
          sum_row += c[i][j]
          sum_col += c[j][i]
          if j is not i:
              sum_row_no_i += c[i][j] 
              sum_col_no_i += c[j][i]
      iam += (c[i][i] - max(sum_row_no_i, sum_col_no_i))/max(sum_row, sum_col)
  return   iam/l

c = [[2129,   52,    0,    1],
     [499,   70,    0,    2],
     [46,   16,    0,   1],
     [85,   18,    0,   7]]

IAM(c) = -0.5210576475801445

The code to implement the IAM (Imbalance Accuracy Metric) in R provided below:

IAM <- function(c) {

 # c is a matrix representing the confusion matrix of the classifier.

  l <- nrow(c)
  result = 0
  
  for (i in 1:l) {
  sum_row = 0
  sum_col = 0
  sum_row_no_i = 0
  sum_col_no_i = 0

    for (j in 1:l){
          sum_row = sum_row + c[i,j]
          sum_col = sum_col + c[j,i]
          if(i != j)  {
              sum_row_no_i = sum_row_no_i + c[i,j] 
              sum_col_no_i = sum_col_no_i + c[j,i]
          }
    }
    result = result + (c[i,i] - max(sum_row_no_i, sum_col_no_i))/max(sum_row, sum_col)
  }
  return(result/l)
}

c <- matrix(c(2129,52,0,1,499,70,0,2,46,16,0,1,85,18,0,7), nrow=4, ncol=4)

IAM(c) = -0.5210576475801445

Another example from the iris dataset (3 class problem) and sklearn:

from sklearn.datasets import load_iris
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import confusion_matrix

X, y = load_iris(return_X_y=True)
clf = LogisticRegression(max_iter = 1000).fit(X, y)
pred = clf.predict(X)
c = confusion_matrix(y, pred)
print('confusion matrix:')
print(c)
print(f'accuarcy : {clf.score(X, y)}')
print(f'IAM : {IAM(c)}')

confusion matrix:
[[50  0  0]
 [ 0 47  3]
 [ 0  1 49]]
accuarcy : 0.97
IAM : 0.92