Evaluation of matrix in classification

Evaluation of the Matrix: Evaluation of the matrices provide a key role in the accuracy of the model. There are different evaluation matrices but here going to discuss only three i.e. Jaccard Index, F1 score Confusing Matrix, and Log loss.

1. Jaccard Index: Let us consider that y is actual labels and x is predicted labels. Then the Jaccard index is given by J(y,x)

J(y,x) = ratio of intersection by the union of the actual label and predicted labels

For example: y = [0,0,0,0,1,1,1,1] and    X = [1,1,0,0,0,1,1,1]

J (y,x) = 8 / 12 = 0.66

2.F1 Score Confusing Matrix: It is best for binary classification. Before defining the F1 Score, Let’s define some terms which are used in the definition.

	Positive	Negative
Positive	True Positive	False Positive
Negative	False Negative	True Negative

Precision: Ratio of true positive to the sum of a true and false positive.

Recall: Ratio of true positive to the sum of a true positive and false negative.

Now F1 Score is defined 2*((precision)*(recall)/(precision + recall))

3. Log-Loss: It defines the performance of the classifier where predicted output is a probability value between 0 and 1.

Log-loss = (1/N) * Σ [ (y log x) + (1 – y) log (1 – x) ]   

 It measures how far is the value from the actual value. The lower value of log-loss indicates better accuracy. Among all three, the F1 score is better.