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:
“The true thrift is always to spend on the higher plane; to invest and invest, with keener avarice, that he may spend in spiritual creation, and not in augmenting animal existence. Nor is the man enriched, in repeating the old experiments of animal sensation; nor unless through new powers and ascending pleasures he knows himself by the actual experience of higher good to be already on the way to the highest.”
—Ralph Waldo Emerson (1803–1882)
“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)