Face Recognition

Definition

The task of verifying or identifying a person from their face image; framed as a metric learning problem where the model learns an embedding space where same-identity faces cluster together.

Intuition

Training a separate classifier per identity requires retraining when new identities are added. Metric learning instead trains an embedding where distance directly measures similarity — enabling one-shot recognition of unseen identities.

Formal Description

Verification vs identification:

• Verification: given two images, are they the same person? (binary)
• Identification: given a probe image, who is this person? (retrieval)

Embedding network $f:{\mathbb{R}}^{H\times W\times 3}\to {\mathbb{R}}^d$, typically $d=128$ or $512$; trained so $\Vert f(x_i)-f(x_j){\Vert }_2$ is small for same identity, large for different.

Triplet loss: anchor-positive-negative triplets with margin $\alpha$:

$$\mathcal{L}=\sum _i{\left[\Vert f(A_i)-f(P_i){\Vert }^2-\Vert f(A_i)-f(N_i){\Vert }^2+\alpha \right]}_{+}$$

Hard triplet mining (selecting difficult negatives) is critical for convergence.

Siamese networks: two branches with shared weights processing two images; outputs compared directly.

Deployment: compare probe embedding against gallery embeddings; threshold on distance for accept/reject.

Applications

Phone unlock, building access control, photo management (tagging), law enforcement (surveillance).

Trade-offs

• Requires large labeled datasets of identity pairs/triplets
• Hard triplet mining is critical for convergence
• Bias/fairness concerns (demographic performance disparities)
• Privacy implications

Links

• object_detection
• cnn_architecture
• Deep Learning
• negative metric learning
• SVD — embedding distance geometry, low-rank face spaces