FACE DETCTION Comparing PCA and isomap on face image detection Applying both PCA and Isomap to the 698 raw images to derive 2D principal components and a 2D embedding of the data's intrinsic geometric structure. Project both onto a 2D scatter plot, with a few superimposed face images on the associated samples.
ALOI BEAR Whatever your high-dimensional samples are, be they images, sound files, or thoughtfully collected attributes, they can all be considered single points in a high dimensional feature-space. Each one of your observations is just a single point. Even with a high dimensionality, it's possible that most or all your samples actually lie on a lower dimension surface. Isomap aims to capture that embedding, which is essentially the motion in the underlying, non-linear degrees of freedom. By testing isomap on a carefully constructed dataset, you will be able to visually confirm its effectiveness, and gain a deeper understanding of how and why each parameter acts the way it does. The ALOI, Amsterdam Library of Object Images, hosts a huge collection of 1000 small objects that were photographed in such a controlled environment, by systematically varying the viewing angle, illumination angle, and illumination color for each object separately. To really drive home how well isomap does what it claims, this lab will make use of two image sets taken from the ALOI's collection. Manifold extraction, and isomap specifically are really good with vision recognition problems, speech problems, and many other real-world tasks, such as identifying similar objects, or objects that have undergone some change. In the case of the 3D rotating object such as the office chair example from earlier, if every pixel is a feature, at the end of the day, the manifold surface is parametrizable by just the angle of the chair—a single feature!