The IUR (independent uniform random) plane probe is a random translation of a Grassmann manifold. ( A little jargon is not always bad.)
The Grassmann Manifold is simply the set of all subspaces such that in n dimensions G2,n is the space of all (centered) planes in n-space. This manifold of planes makes a good tool for visualizing objects in n-dimensions. A random walk through this manifold is called a grand tour when the n-dimensional object or data point set is projected onto these planes. The grand tour is thus closely related to the IUR probe discussed in Chapter 4.
Look at the animation above. It is a grand tour through some data as effected by a computer utility called ORCA.
( A little jargon is not always bad.)
The Grassmann Manifold is simply the set of all subspaces such that in n dimensions G2,n is the space of all (centered) planes in n-space. This manifold of planes makes a good tool for visualizing objects in n-dimensions. A random walk through this manifold is called a grand tour when the n-dimensional object or data point set is projected onto these planes. The grand tour is thus closely related to the IUR probe discussed in Chapter 4.