Eigenfaces, for Facial Recognition

Abstraction: PCA-based eigenvector decomposition for facial recognition classification

Key points:

• Faces are represented as vectors in R^(n*m) face space; a 200x180 image yields a 36,000-dimensional vector
• The covariance matrix of difference faces is 36,000x36,000 but only ~76 eigenvectors with nonzero eigenvalues exist; computed via the smaller 76x76 matrix using the identity that if v is an eigenvector of A^T A, then Av is an eigenvector of AA^T with the same eigenvalue
• Eigenfaces are the eigenvectors of the covariance matrix visualized as ghostly face images, each representing directions of maximal variability in face space
• Recognition uses projection of a new face into the eigenface subspace, then nearest-neighbor distance to training samples
• Mahalanobis metric (inverse covariance-weighted distance) outperforms Euclidean distance because eigenface axes have different scales
• ~30 eigenfaces suffice for recognizable reconstruction from 76; empirically determined threshold of 25 units separates known from unknown subjects

Connections: Principal Component Analysis · Eigendecomposition · Covariance Matrix · Facial Recognition

Source: https://jeremykun.com/2011/07/27/eigenfaces/