Confusion matrix

Background

The confusion matrix is the foundation of classification evaluation: entry $(i, j)$ counts how many examples of true class $i$ were predicted as class $j$. The diagonal holds the correct predictions; everything off-diagonal is a specific kind of mistake. Accuracy, precision, recall, and F1 are all read directly off it.

Problem statement

Implement confusion_matrix(y_true, y_pred, num_classes=None) returning the $C \times C$ matrix M where M[i, j] is the number of samples with true label $i$ and predicted label $j$. If num_classes is None, infer it as one more than the largest label observed.

Input

• y_true — array-like of integer labels (ground truth).
• y_pred — array-like of integer labels (predictions), same length.
• num_classes — optional int; if omitted, inferred from the data.

Output

Returns an np.ndarray of shape (C, C) of integer counts — rows index the true class, columns the predicted class.

Examples

Example 1

Input:  y_true = [1, 0, 1, 1, 0], y_pred = [1, 0, 0, 1, 1]
Output: [[1, 1], [1, 2]]

Explanation: of the true-0 samples, 1 was predicted 0 and 1 predicted 1 (top row); of the true-1 samples, 1 was predicted 0 and 2 predicted 1 (bottom row).

Constraints

• Rows index the true class, columns the predicted class (the sklearn convention).
• Entries are integer counts; the matrix is (C, C) with C = num_classes.
• Works for any number of classes, not only binary.

Notes

• Precision of class $j$ is $M_{jj} / \sum_i M_{ij}$ (down a column); recall of class $i$ is $M_{ii} / \sum_j M_{ij}$ (across a row).
• The grand total equals the number of samples, and the trace equals the number of correct predictions.