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machine-learningdeep-learningconfusion-matrixmulticlass-classification

calculation of performance metrics in the multi-class classification

I am using XGBoost classifier that classify X-ray images into 3 classes. My problem is that when I calculate these values manually (by hand) using the confusion matrix, it shows me values that are not as they are in the classification report. Even though I used all the equations to calculate those. Please I need a help on how I can make a calculation by hand to find these values (accuracy, precision and recall).

here is the classification report

    precision    recall  f1-score   support

           0     1.0000    0.9052    0.9502       116
           1     0.8267    0.9180    0.8700       317
           2     0.9627    0.9357    0.9490       855

accuracy                             0.9286      1288
macro avg        0.9298    0.9196    0.9231      1288
weighted avg     0.9326    0.9286    0.9297      1288

and this is the confusion matrix

[0.90     0.05     0.04

 0        0.91     0.08

 0        0.06     0.93]
Solution

  • enter image description here

    Accuracy

    How many of the correct predictions are made in total? (Closer to 1)

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    TP plus TN, divided by the sum of all

    Recall

    In a sample that is actually positive, the proportion of samples that are determined to be positive

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    How many of the total things I'm trying to get right? (Closer to 1)

    Precision

    If it is predicted to be positive, moderate positive. How accurate the positive prediction is

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    How many correct answers are correct among the questions you solved? (Closer to 1 is better)

    Okay lets do 3 x 3 confusion matrix

    enter image description here

    class A precision = 15 / 24 = 0.625

    class B precision = 15 / 20 = 0.75

    class C precision = 45 / 56 = 0.80

    class A recall = 15 / 20 = 0.75

    class B recall = 15 / 30 = 0.5

    class C recall = 45 / 50 = 0.9

    Accuracy of classifier = (15 + 15 + 45) / 100 = 0.75

    Weighted Average Precision = Actual class A instances * precison of class A + Actual class B instances * precison of class B + Actual class C instances * precison of class C
    = 20 / 100 * 0.625 + 30 / 100 * 0.75 + 50 / 100 * 0.8 = 0.75

    Weighted Average Recall = Actual class A instances * Recall of class A + Actual class B instances * Recall of class B + Actual class C instances * Recall of class C
    = 20 / 100 * 0.75 + 30 / 100 * 0.5 + 50 / 100 * 0.9 = 0.75

    In your case

    enter image description here

    class A precision = 0.9 / 0.9 = 1

    class B precision = 0.91 / 1.02 = 0.89

    class C precision = 0.93 / 1.05 = 0.89

    class A recall = 0.9 / 0.99 = 0.91

    class B recall = 0.91 / 0.99 = 0.92

    class C recall = 0.93 / 0.99 = 0.94

    Accuracy of classifier = (0.9 + 0.91 + 0.93) / 2.97 = 0.92

    Weighted Average Precision = Actual class A instances * precison of class A + Actual class B instances * precison of class B + Actual class C instances * precison of class C = 0.99 / 2.97 * 1 + 0.99 / 2.97 * 0.89 + 0.99 / 2.97 * 0.89 = 0.93

    Weighted Average Recall = Actual class A instances * Recall of class A + Actual class B instances * Recall of class B + Actual class C instances * Recall of class C = 0.99 / 2.97 * 0.91 + 0.99 / 2.97 * 0.92 + 0.99 / 2.97 * 0.94 = 0.92