Eigenfaces 25 points We will now use the SVD and orthogonal matrices to build a simple classifier that detects whether a given image contains a face or not. We will do this by constructing a subspace of images of faces in the vector space of all gray-scale images using low-rank approximation. We can then use a distance measure to decide if an image shows a face or not Review: Facts about ortho To start, let's briefly review some facts about orthogonality and the SVD Approximation with low-dimensional subspaces Suppose you have a matrix A whose columns span an m-dimensional space V. Then A has rank m. Consider the SVD A-UEVT. The columns of U corresponding to non- zero singular values form the span of V. The subspace V of rank n (where n