1. Definition

  • Single-label classification = each instance (sample) is assigned exactly one label from a set of classes.
  • Formal setting:
    • Input space: $X$ (features)
    • Label space: $Y = \{1,2,…,K\}$ (K classes)
    • Classifier outputs exactly one class $y \in Y$ for each input.

2. Examples

  • Email classification: spam vs not spam → (2 classes, each email must be 1 of them).
  • Image classification: dog / cat / horse → each image belongs to exactly one animal.
  • Medical diagnosis: predicting one disease type (assuming mutually exclusive outcomes).

3. Characteristics

  • Mutually exclusive labels: one sample cannot belong to two classes at the same time.
  • Evaluation metrics typically used:
    • Accuracy = % of correctly classified samples
    • Precision, Recall, F1 (binary or multiclass extensions: macro/micro/weighted)
    • AUROC / AUPRC for binary or extended multiclass settings

4. Comparison with Multi-label Classification

  • Single-label: one sample = one label
    • Example: An image is either “cat” or “dog” (but not both).
  • Multi-label: one sample = multiple labels possible
    • Example: A news article may be labeled both “politics” and “economy.”

5. Mathematical Form

In single-label classification, the classifier is:

$f: X \rightarrow Y$

Where $f(x) = \arg\max_{k} P(y=k \mid x)$ → the model picks the highest probability class.

In contrast, multi-label classification uses thresholding on each class probability.

Summary

  • Single-label classification = exactly one label per sample (mutually exclusive classes).
  • Most common type of classification in ML.
  • Different from multi-label classification, where a sample can belong to multiple classes.