📏 Single-label Classification

Single-label Classification#

Tasks where each instance is assigned exactly one label.

Important

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What it is#

In single-label classification every sample is assigned exactly one label from a set of \(K\) mutually exclusive classes. Formally the classifier maps an input to one label,

\[f : X \rightarrow Y, \qquad Y = \{1, 2, \dots, K\},\]

and typically picks the highest-probability class,

\[f(x) = \arg\max_{k}\, P(y = k \mid x).\]

This is the most common classification setting: spam vs not-spam, an image that is a cat or a dog or a horse (never two at once), a single diagnosis from mutually exclusive outcomes.

How it’s modelled#

The output layer is a softmax, so the predicted class probabilities sum to one and the classes compete — raising one lowers the others. Training uses categorical cross-entropy.

How it’s scored#

Because there is one prediction per sample, the natural metrics are accuracy plus precision, recall and F1 (with micro / macro / weighted averaging for the multi-class case) and AUROC / AUPRC via one-vs-rest. A useful identity: under single-label evaluation, micro precision, recall and F1 all equal accuracy.

vs multi-label#

The contrast is exclusivity. Single-label gives one label per sample (an image is cat or dog); multi-label allows any subset (a news story tagged politics and economy), uses independent sigmoids instead of a softmax, and needs set-based metrics like Hamming loss and Jaccard.

Pitfalls and edge cases#

The exclusivity assumption — if samples can truly belong to several classes, forcing one label loses information; use multi-label instead.
Calibrated probabilities — argmax discards confidence; keep the softmax scores if you need ranking, thresholds or AUROC.
Imbalance — plain accuracy flatters a majority-heavy dataset; prefer macro metrics when minority classes matter.

Theme: Classification & Averaging Metrics · All terminology

Hint

Mind map — connected ideas

Multi-label Classification · Micro F1 · Macro F1 · One-vs-Rest (OvR) AUROC

Hint

More in Classification & Averaging Metrics

Accuracy · AUC (Area Under the Curve) · Average Precision (AP) · Binary Classification · Classification Probability · Discriminatory Power · F1-score · Gini Coefficient · Harmonic Mean · Log Loss (also called Logarithmic Loss or Cross-Entropy Loss) · Macro AUC · Macro AUROC (Macro-Averaged AUROC) · Macro Averaging · Macro F1