Representing a point in an n-dimensional space in a 2D geometrical shape

[Alan P Smith]

Is it possible for me to use a Voronoi diagram - or some other algorithm - to represent a point in an multidimensional space (between 5 and 10 dimensions) in a 2D geometrical shape? (And more interestingly, in a geometrical shape that is a) fairly small, and b) looks aesthetic.

I have a number of measurements in standard deviation units on different normal distributions. Say I have 8 standard deviation measurements on 8 different variables. This gives me the following numbers (one for each normal distribution):

1: -0.3
2: 1.2
3: 0.7
4: 2.1
5: 0.2
6: -1.3
7: -0.2
8: 1.9

Can I represent these 8 SD measures as a 2D geometrical shape (to encode them) in such a way that the 2D shapes distinguish between e.g. 10ths of a standard deviation unit (to a level of resolution as in this list)? What are my options here?

Thanks... Alan

 

[pat_connell]

.Yes, it is possible to use a Voronoi diagram or some other algorithm to represent a point in an multidimensional space in a 2D geometrical shape. You can use Voronoi diagrams to map high-dimensional points in 2D and 3D space. This means that your 8 standard deviation measurements can be represented as a 2D geometrical shape. You can also use other algorithms like Delaunay Triangulations, which can be used to represent even higher dimensional points in 2D or 3D space. Depending on the number of dimensions you are working with, and the level of accuracy you want, you can choose different algorithms to represent the points.