The main difficulty in handling high-dimensional data is its … high dimension. A data sample is high-dimensional if its elements may be seen as tuples with a usually high value for . Note however that may be considered high already when or since in these cases the data cannot be directly plotted on a screen. In the sequel, will denote the size of the .
Go have a look at the 'zoo', as Jeffrey Heer calls it (Heer is the creator of prefuse and Vizster). The zoo contains lots of images of layouts for high-dimensional data.
Scatterplots are basic graphical devices. They are nonetheless extremely relevant, useful and well understood.
We shall look at two different strategies to project high-dimensional data onto 2D space.
Parallel coordinates offer an alternative to scatterplot matrix by allowing the simultaneous visualization of multiple variables of a same dataset using polylines. In a nutshell: imagine the data has been laid out in an p-dimensional space, positioning an element e = (x_1, …, x_p) at this precise position in Euclidean space. Now, project each of the unit axis onto parallel lines in the 2D planes. What you get is a parallel coordinates view of your data.
Put differently, parallel coordinates view can be realized by using parallel vertical axis (positioned at x = i) each ranging over the range of the ith variable. For each element e = (x_1, …, x_p) we draw a polyline crossing the ith axis at y = x_i.