# 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.

**F**P ratio = FP / (TN + FP)

**F**N 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

F**P** ratio = FP / (TN + FP)

T**P** 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