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Confusion Matrix

In Pattern Recognition , confusion matrix is used as the table of the output.

Patterns of Confusion Matrix

For Perfect Judgment

If the system is perfect, there values only in upper left and lower right space.

For Perfect Mistake

If the values only in lower left and upper right space, the system mistakes perfectly.

Need More Data

If "only in upper left" or "only in lower right", they are not perfect system.

In the real world, there are not enough data for 4 parts of the confusion matrix.

Evalation with Confusion Matrix

Differet fields use different ways for the evaluation with confusion matrix.

If Risk is Important

If risk is important, 2 types of risk is calcurated.
FP ratio = FP / (TN + FP)
FN ratio = FN / (TP + FN)

FP ratio and FN rario use same idea of Type I error and Type II error in Statistics .

If Positive is Importanr

FP ratio = FP / (TN + FP)
TP ratio = TP / (TP + FN)

This evaluation is used for screening. At screening, at first, TP ratio is maximized. Second, FP ratio is mimized.

ROC Curve and AUC are used for this evalation.

Relationship between Confusion Matrix and Threshold

If there is a data set and histgram below.

For example, if threshold is "3", confusion matrix is below.

For example, if threshold is "7", confusion matrix is below.

NEXT ROC Curve and AUC