ML0014 Confusion Matrix

A confusion matrix is a table that summarizes the performance of a classification model by comparing its predicted labels against the actual labels. For binary classification it is a 2×2 table with four cells: true positives (correctly predicted positive), false positives (negative predicted as positive), false negatives (positive predicted as negative), and true negatives (correctly predicted negative). Unlike a single scalar metric, it shows not only how many predictions were wrong but which kinds of errors were made. For multi-class problems, the matrix expands into a larger square table where cell counts the instances of actual class predicted as class ; off-diagonal clusters reveal which specific classes the model systematically confuses, guiding model refinement or relabeling.

(1) Structure: Rows are actual classes, columns are predicted classes; the diagonal holds all correct predictions.
(2) Binary Case: The four cells TP/FP/FN/TN feed every classification metric: accuracy, precision, recall, F1.
(3) Multi-Class Case: An matrix whose off-diagonal hotspots expose systematic class confusions.

Mathematical Formulation:

Where:

• is the count in row , column of the confusion matrix.
• is the true label of sample , its predicted label, and indexes the samples.
• is the indicator function: 1 when the condition holds, 0 otherwise.
• is the row-normalized version: row then shows the per-class recall distribution, which reads better under class imbalance.

Figure 1: A 3-class example: strong diagonal means healthy classification; the bright off-diagonal cell shows the model systematically confuses class 1 with class 2.