Classification Matrix

TL;DR

• A tabular tool (often 2x2) that compares predicted vs actual class labels to evaluate a classifier.
• Summarizes counts of true positives, false positives, true negatives, and false negatives.
• Enables calculation of metrics like accuracy, precision, recall, and F1 score and helps identify error patterns (e.g., many false positives).

Definition

A classification matrix, also known as a confusion matrix, is a tool used in machine learning and data mining to evaluate the performance of a classification model. It is a table that presents the predicted and actual values of a classification model in a tabular format, allowing for interpretation and analysis of the model’s performance. The classification matrix is typically used in binary classification and is commonly presented as a 2x2 table with four cells representing combinations of predicted and actual values.

Explanation

The matrix displays how often the model’s predictions match the actual labels by counting occurrences for each outcome:

• True positive (TP): predicted positive and actually positive.
• False positive (FP): predicted positive but actually negative.
• True negative (TN): predicted negative and actually negative.
• False negative (FN): predicted negative but actually positive.

From these counts you can compute several performance metrics. For example, accuracy is the proportion of correct predictions:

$$\text{accuracy} = \frac{TP + TN}{TP + TN + FP + FN}$$

The classification matrix also helps identify where a model errs; for instance, a high number of false positives may indicate a need to adjust the model’s decision threshold.

Examples

Cancer diagnosis example

• True positive (TP): The model correctly predicts that the patient has cancer.
• False positive (FP): The model incorrectly predicts that the patient has cancer.
• True negative (TN): The model correctly predicts that the patient does not have cancer.
• False negative (FN): The model incorrectly predicts that the patient does not have cancer.

Use cases

• Evaluating the performance of binary classification models.
• Calculating metrics such as accuracy, precision, recall, and F1 score.
• Identifying areas for model improvement (for example, diagnosing an excess of false positives).

Notes or pitfalls

• A high number of false positives may require adjusting the model’s threshold to reduce incorrect positive predictions.

Related terms

• Confusion matrix (alternate name)
• Accuracy
• Precision
• Recall
• F1 score