eigenimage

One eigenvector of an image dataset's covariance matrix, reshaped back into picture form.

A dataset's covariance matrix $C$ measures how a set of images spreads out and along which directions. Since $C$ is symmetric, it diagonalizes into real eigenvalues and orthogonal eigenvectors -- this splitting apart into simpler pieces is the decomposition in "eigen-decomposition." Reshaping one of those eigenvectors back into an image (instead of leaving it as a plain list of numbers) produces an eigenimage. Ranking eigenimages by their eigenvalue and keeping only the largest few is dimensionality reduction: describing every image by a handful of numbers instead of its full pixel count.

Examples

The eigenimage with the single largest eigenvalue captures more of how a dataset's images differ from one another than any other single direction.