Understanding example of MultiClass Classification

Question

Hello, I am currently reading the module multiclass classification and would like to understand how was TN(true negative) value for Class 0 derived as 5 instead of 4 (Section : The confusion matrix for a multiclass classifier). Can some-one help me understand that?

https://learn.microsoft.com/en-us/training/modules/fundamentals-machine-learning/6-multiclass-classification

Thanks

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Answer 1

Hi DimpleM

Thank you for reaching out to Microsoft Q&A forum!

I understand that you would like to understand how the True Negative (TN__)__ value for Class 0 was derived as 5 instead of 4.

The confusion matrix represents the actual vs. predicted values:

Actual \ Predicted (y^\hat{y}y^)	0	1	2
Actual \ Predicted (y^\hat{y}y^)	0	1	2
0 (Actual 0)	2	0	0
1 (Actual 1)	0	2	0
2 (Actual 2)	0	1	2

TN Calculation for Class 0:

• True Negatives (TN) for Class 0 are the cases where the actual class is not 0 (i.e., the actual class is either 1 or 2), and the predicted class is also not 0 (i.e., predicted as 1 or 2).
• To compute TN for Class 0, we exclude:

            Row 0 (actual class 0)

            Column 0 (predicted class 0)

Extracting relevant values from the confusion matrix:

Actual \ Predicted (y^\hat{y}y^​)	1	2
1 (Actual 1)	2	0
1 (Actual 1)	2	0
2 (Actual 2)	1	2

The values contributing to TN for Class 0 are: 2, 0, 1, 2

Total TN for Class 0 = 2 + 0 + 1 + 2 = 5

Thus, TN for Class 0 is correctly calculated as 5 instead of 4.

Hope this helps. Do let us know if you any further queries.  

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