Binary Classification Outcome Matrix (Easy) — Practice with Code Visualizer

In machine learning and statistical classification, evaluating the performance of a binary classifier requires understanding how predictions align with actual outcomes. The Outcome Matrix (also known as an error matrix or classification outcome table) is a structured summary that captures the relationship between predicted labels and ground truth labels in a 2×2 tabular format.

For a binary classification task with two possible labels—positive (1) and negative (0)—the outcome matrix organizes prediction results into four distinct categories:

	Predicted Negative (0)	Predicted Positive (1)
Actual Negative (0)	True Negative (TN)	False Positive (FP)
Actual Positive (1)	False Negative (FN)	True Positive (TP)

Understanding Each Quadrant:

True Negatives (TN): Cases where the model correctly predicted the negative class. The actual label was 0, and the prediction was also 0.
False Positives (FP): Cases where the model incorrectly predicted positive. The actual label was 0, but the prediction was 1. Also called Type I errors or false alarms.
False Negatives (FN): Cases where the model incorrectly predicted negative. The actual label was 1, but the prediction was 0. Also called Type II errors or missed detections.
True Positives (TP): Cases where the model correctly predicted the positive class. The actual label was 1, and the prediction was also 1.

Why This Matters:

The outcome matrix forms the foundation for computing crucial classification metrics:

Accuracy = (TP + TN) / Total
Precision = TP / (TP + FP)
Recall (Sensitivity) = TP / (TP + FN)
Specificity = TN / (TN + FP)
F1 Score = 2 × (Precision × Recall) / (Precision + Recall)

Your Task:

Given a list of observation pairs where each pair contains [actual_label, predicted_label], construct and return the 2×2 outcome matrix. The matrix should be structured as:

[[TN, FP],
 [FN, TP]]

where the first row corresponds to actual negatives (0) and the second row corresponds to actual positives (1).

Analyzing each observation pair [actual, predicted]: • [1, 1] → Actual=1, Predicted=1 → True Positive (TP) • [1, 0] → Actual=1, Predicted=0 → False Negative (FN) • [0, 1] → Actual=0, Predicted=1 → False Positive (FP) • [0, 0] → Actual=0, Predicted=0 → True Negative (TN) • [0, 1] → Actual=0, Predicted=1 → False Positive (FP)

Tallying the counts: • TN = 1 (one case of actual=0, predicted=0) • FP = 2 (two cases of actual=0, predicted=1) • FN = 1 (one case of actual=1, predicted=0) • TP = 1 (one case of actual=1, predicted=1)

The outcome matrix [[TN, FP], [FN, TP]] = [[1, 2], [1, 1]]

This represents a perfect classifier with no errors: • [0, 0] → True Negative (count: 2) • [1, 1] → True Positive (count: 2)

No false positives or false negatives occurred. The diagonal entries (TN=2, TP=2) capture all correct predictions, while off-diagonal entries are zero, indicating flawless classification performance.

Result: [[2, 0], [0, 2]]

This represents the worst possible classifier—every prediction is wrong: • [0, 1] → False Positive (count: 2) • [1, 0] → False Negative (count: 2)

The classifier never makes a correct prediction. True negatives and true positives are both zero, while all errors are concentrated in the off-diagonal cells.

Result: [[0, 2], [2, 0]]