Confusion Matrixis a matrix that illustrates the performance of a classification model when exposed to unseen data. This matrix helps us to identify how the model is performing on test set. From this matrix, many other scores are calculated such as Accuracy, Recall, Precision, F1-score, etc. It is important one should know where to use which type of score as it depends on the application.
There are two classes: Class 1 and Class 2
Class 1:Positive
Class 2: Negative
Positive: Observation is True (eg. Picture is a dog)
Negative: Observation is False (eg. Picture is not a dog)
T.P.(True Positive): Truth and Prediction both are Positive
T.N.(True Negative): Truth and Prediction both are Negative
F.P.(False Positive): Truth is Negative but Prediction is Positive
F.N.(False Negative): Truth is Positive but Prediction is Negative
Accuracy:
Accuracy is the ratio of sum of True Positive(T.P.) and True Negative(T.N.) to the sum of the matrix elements.
Precision:
Precision is defined as the ratio of True Positive(T.P) to the sum of True Positive(T.P) and False Positive(F.P)
Recall:
Recall is defined as the ratio of True Positive(T.P) to the sum of True Positive(T.P) and False Negative(F.N)
High recall, low precision:This means that most of the positive examples are correctly recognized (low FN) but there are a lot of false positives.
Low recall, high precision:This shows that we miss a lot of positive examples (high FN) but those we predict as positive are indeed positive (low FP)
F1-score:
Since we have two measures (Precision and Recall) it helps to have a measurement that represents both of them. We calculate an F-measure which uses Harmonic Mean in place of Arithmetic Mean as it punishes the extreme values more.
The F-Measure will always be nearer to the smaller value of Precision or Recall.
Exercise
Accuracy
Accuracy = (TP + TN) / (TP + TN + FP + FN) = (100 + 50) /(100 + 5 + 10 + 50) = 0.90Precision
Precision tells us about when it predicts yes, how often is it correct.Precision = TP / (TP + FP)=100/ (100+10) = 0.91
Recall
Recall gives us an idea about when it’s actually yes, how often does it predict yes.
Recall = TP / (TP + FN) = 100 / (100 + 5) = 0.95
F-score
F1-score = (2 * Recall * Precision) / (Recall + Presision) = (2 * 0.95 * 0.91) / (0.91 + 0.95) = 0.9Got any questions?
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The Art of Computer Programming, Volume 4, Fascicle 3
Donald E. Knuth / Addison-Wesley Professional / 2005-08-05 / USD 19.99
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