Eigenfaces
Given a set of data points (or vectors), find a "good"
basis for them.
Here we have a collection of digital photographs, each has
374 x 486 pixels. They are in color, so each pixel actually
has a red value, a green value and a blue value. That means
that each digital photograph has 374 x 486 x 3 = 545,292
numbers (that is the dimension of our "face space").
Find the mean:
To find the basis, we first compute the mean of the data.
Here is the result. For fun, we
computed the Male mean and the Female mean separately, then
we also show the overall mean.
Find the basis vectors
The basis vectors are orthonormal (the coloring is from a
re-scaling/rounding of the values to be integers between 0
and 255). It is equally likely that a particular photo would
use either the positive of the vector or the negative.
Multiplication by -1 is the same as taking the photographic negative.
However, as we see below, it is hard to tell what features are
being represented by either a positive or negative.
Here are the basis vectors. Since
they are also eigenvectors, they have been called "Eigenfaces".
While it is tempting to "see" individuals in these pictures,
each basis vector is actually a composite of all of you.
Write each face in terms of the eigenfaces
Here we show the result of using a partial basis to reconstruct
each of your photos. That is, after you click on the
link below, find your face and click on your photo. You
will be taken to a page of partial reconstructions.
The first photo is the mean plus one basis vector. The
next photo is the mean plus two basis vectors, and so on.
Click Here to See Individual Faces.
Click on a face to see its partial reconstruction.
What you should see:
The basis vectors are in a particular order. They should
fill in your "big" features first, and as more and more
basis vectors are added, finer and finer features should
come into focus.
Think of the partial reconstructions as the (orthogonal) projection
of each face into a subspace of face space, as defined by
the orthonormal "eigenfaces".