Is there a good and easy way to visualize high dimensional data?

Question

Can someone please tell me if there is a good (easy) way to visualize high dimensional data? My data is currently 21 dimensions but I would like to see how whether it is dense o

Answer 1

The buzzword I would search for is multidimensional scaling. It is a technique to develop a projection from the high dimensional space to a lower space (2 or 3 dimensional) in such a way that points which are close in the full space will be close in the projection.

It is often used for visualising the output of clustering algorithms (i.e. if your clusters are compact in the MDS projection there is a good chance they are also in the full space).

Edit: This wouldn't necessarily help with determining if the data is dense or sparse, because you lose the scale in the projection, but it would show whether it is uniform or clumpy (perhaps thats what you mean).