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statistics

Getting various stats from confusion matrix This function takes in arguments a Confusion matrix i.e. a square matrix and returns Accuracy Recall Specificity and Precision

For 2X2 Confusion Matrix

				Positive					Negative

Positive		True Positive(tp)			False Negative(fn)
Negative		False Positive(fp)			True Negative(tn)

sensitivity = recall = tp / t = tp / (tp + fn)
specificity = tn / n = tn / (tn + fp)
precision = tp / p = tp / (tp + fp)

For NXN Confusion Matrix - We can convert it to 2X2 matrix for each class

For each row class there is recall specificity and precision as follows
(i,i)  represents ConfusionMatrix(i,i)
row(i) represents ConfusionMatrix(i,:)
col(i) represents ConfusionMatrix(:,i)
all    represents all values in ConfusionMatrix i.e. sum(ConfusionMatrix)

							Class1					not in Class1

Class1					(i,i)(tp)					row(i)-(i,i)(fn)
not in CLass1			col(i)-(i,i)(fp)			all - row(i) - col(i) + (i,i)(tn)

sensitivity = recall = tp / t = tp / (tp + fn) 	= 		(i,i)/row(i)
specificity = tn / n = tn / (tn + fp)     		=		 all-row(i)-col(i)+(ii)/all-row(i)
precision = tp / p = tp / (tp + fp)		  		= 		(i,i)/col(i)


Stats 			Matrix order
Accuracy  			1X1 
Recall 				NX1
Specificity 		NX1
Precision 			NX1

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