# Evaluation of a classifier by confusion matrix in data mining

**How to evaluate a classifier?**

The classifier can be evaluated by building the confusion matrix. Confusion matrix shows the total number of correct and wrong predictions.

Confusion Matrix for class label positive(+VE) and negative(-VE)is shown below;

Actual Class(Target) | |||||

+VE | -VE | ||||

Predicted Class (Model) | +VE | A = True +VE | B = False -VE | +VE prediction | P=A / (A+B) |

-VE | C = False +VE | D = True -VE | -VE prediction | D / (C + D) | |

Sensitivity | Specificity | Accuracy = A + D / (A + B + C + D) | |||

A / (A + C) | D / (B + D) |

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**Accuracy:**

Accuracy is the proportion of the total number of correct predictions.

e.g

Accuracy = A + D / (A + B + C + D)

**Error-Rate:**

Error Rate = 1 – Accuracy

**+VE predictions:**

+VE predictions are the proportion of the total number of correct positive predictions.

+VE predictions = A / (A+B)

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**-VE predictions:**

-VE predictions are the proportion of the total number of correct negative predictions.

-VE predictions = D / (C + D)

**Precision:**

Precision is the correctness that how much tuple are

- +VE and classifier predicted them as +VE
- -VE and classifier predicted them as -VE

Precision = A / P

# Recall:

Recall = A / Real positive

**Sensitivity (Recall):**

Sensitive is the total True +VE rate.

The correction of the actual positive cases that are correctly identified.

Sensitivity (Recall) = A / (A + C)

**F-Measure:**

# F-Measure is harmonic mean of recall and precision.

# F-Measure = 2 * Precision * Recall / Precision + Recall

**Specificity:**

Specificity is true -VE rate.

Specificity is the proportion of the actual -VE cases that are correctly identified.

Specificity = D / (B + D)

Note: Specificity of one class is same as the sensitivity of the other class.

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