Graphics Reference
In-Depth Information
Figure
.
.
Some views of
-D grand tour paths in
dimensions (top let)and
dimensions(bottom).
he path consists of a sequence of points on a
-D and
-D sphere respectively. Each point corresponds
to a projection from
dimensions (or
dimensions) to
dimension. he solid circle indicates the first
point on the tour path corresponding to the starting frame, yielding the
-D data projection (top right)
shown for the
-D path. he solid square indicates the last point in the tour path, or the last projection
computed
in a projection: higher values correspond to more interesting structure in the pro-
jections. Used alone, PP seeks out low-dimensional projections that expose interest-
ing features of the high-dimensional point cloud. In conjunction with the interpola-
tion, a PP guided tour shows many projections to the viewer, in a smooth sequence.
Using a PP index function to navigate the high-dimensional data space has the ad-
vantage over the grand tour of increasing the proportion of interesting projections
visited.
he PPindex, f
,is optimized over all possible d-dimensional projections of
p-dimensional data, subject to orthonormality constraints on
A
. he optimization
(
XA
)