Higher Dimensions
Adding more dimensions in parallel coordinates (often abbreviated ||-coords or PCs) involves adding more axes. The value of parallel coordinates is that certain geometrical properties in high dimensions transform into easily seen 2D patterns. For example, a set of points on a line in n-space transforms to a set of polylines (or curves) in parallel coordinates all intersecting at n − 1 points. For n = 2 this yields a point-line duality pointing out why the mathematical foundations of parallel coordinates are developed in the Projective rather than Euclidean space. Also known are the patterns corresponding to (hyper)planes, curves, several smooth (hyper)surfaces, proximities, convexity and recently non-orientability. It is worth mentioning that since the process maps a k-dimensional data onto a lower 2D space, some loss of information is expected. The loss of information can be measured using Parseval's identity (or energy norm).
Read more about this topic: Parallel Coordinates
Famous quotes containing the words higher and/or dimensions:
“To higher or lower ends, they [the majority of mankind] move too often with something of a sad countenance, with hurried and ignoble gait, becoming, unconsciously, something like thorns, in their anxiety to bear grapes; it being possible for people, in the pursuit of even great ends, to become themselves thin and impoverished in spirit and temper, thus diminishing the sum of perfection in the world, at its very sources.”
—Walter Pater (1839–1894)
“The truth is that a Pigmy and a Patagonian, a Mouse and a Mammoth, derive their dimensions from the same nutritive juices.... [A]ll the manna of heaven would never raise the Mouse to the bulk of the Mammoth.”
—Thomas Jefferson (1743–1826)