Question

Question 4 (10 Marks) Assuming a total sample of 1079 persons, among which 520 persons are having autism and 559 are healthy persons. When we pass the data of 520 autism patients into the KNN classifier, it correctly predicted “220” patients as autism category and the remaining patients into healthy category. Similarly, from 559 healthy persons, the KNN categorize “100” as autism patients and the remaining as healthy persons. In the above scenario, if “autism” is considered as “positive class” and “healthy person” is considered as negative class then find the:

a. True Positive

b. True Negative

c. False Positive

d. False Negative

e. Sensitivity (True positive rate)

f. Specificity (True negative rate)

g. Accuracy

h. Precision

i. Draw the confusion matrix

Answer 1

Given:

Autism Patients are considered as Positive (P)
Healthy patients are considered as Negative (N)

Total Persons = 1079
Total Positve persons (Autism) = 520
Total Negative persons (Healthy) = 559

Confusion Matrix is denoted as:

Predicted class P N Actual class P TP FN N FP TN

where,

P = Positve
N = Negative
TP = True Positive: The actual positve patients which are rightly predicted as positive.
FN = False Negative: The actual positve patients which wrongly are predicted as negative.
FP = False Positve: The negative positve patients which are wrongly predicted as positive.
TN = True Negative: The actual negative patients which are rightly predicted as negative.

Now, in the question:

• It correctly predicted 220 autism patients as Autism (positve) -> So, these are True Positive (Actual positive and Predicted Positive)
• Remaining (520 - 220) = 300 autism patients are predicted as Healthy(Negative) -> So, these are False Negative (Actual positive and Predicted Negative)
• It predicted 100 healthy(N) patients as Autism(P) patients -> So, these are False Positive (Actual Negative and Predicted Positive)
• Remaining (559 - 100) = 459 healthy(N) patients are predicted as Healthy(N) -> So, these are True Negative (Actual Negative and Predicted Negative)

Hence, the confusuin matrix will be:

Predicted class P N Actual class P 220 (TP) 300 (FN) N 100 (FP) 459 (TN)

a. True Positive = 220

b. True Negative = 459

c. False Positive = 100

d. False Negative = 300

e. Sensitivity (True positive rate) =

$\frac{TP}{P} = \frac{TP}{TP + FN} = \frac{220}{220 + 300} = \frac{220}{520} = 0.423$

f. Specificity (True negative rate) =

$\frac{TN}{N} = \frac{TN}{TN + FP} = \frac{459}{459 + 100} = \frac{459}{559} = 0.82$

g. Accuracy =

$\frac{TP + TN}{P + N} = \frac{TP + TN}{TP + TN + FP + FN}$

679 220 + 459 220 + 459 + 100 + 300 0.629 1079

h. Precision =

$\frac{TP}{TP + FP} = \frac{220}{220 + 100} = \frac{220}{320} = 0.6875$

i. Confusion Matrix =

Predicted class P N Actual class P 220 (TP) 300 (FN) N 100 (FP) 459 (TN)