Represent multivariate data [closed]

Question

I am not sure if this is the best place for my question. Please delete if it is not, but I would really appreciate some suggestions.

I want to graphically represent multivariate data. I have 7 variables named s1,s2,s3,s4,s5,s6,s7. Each variable can have value 0,1 or 2. There are in total 3^7 = 2187 combinations, or entries in my data. Each combination s1,s2,s3,s4,s5,s6,s7 has a label which is a number from 1 to 9. For example:

s1 s2 s3 s4 s5 s6 s7 L

0 0 0 0 0 0 0 9

0 0 0 0 0 0 1 3

0 0 0 0 0 0 2 5

0 0 0 0 0 1 0 5

0 0 0 0 0 1 1 5

0 0 0 0 0 1 2 5

0 0 0 0 0 2 0 6

...

Any suggestion on how to represent the 2187 entries with its associated label in a human-readable format?

I tried a classification tree, but it is to large and not much interpretable. I was thinking on radar charts or spiders charts, but is does not look understandable too.

Any suggestion will be more than welcome!

Best regards.

Answer 1

Looking at the data I noticed that the labels can be encoded as two further ternary digits, yielding a width of nine digits that can be partitioned into 3 groups and interpreted as $(x,y,z)$ coordinates; I would suggest to make the digits related to the labels the most significant ones of the $z$-coordinate so that a side-view exhibits their distribution.
Further ideas would be to associate the digit values of the labels as rgb color codes e.g. 0<-->blue, 1<-->red, 2<-->green of which the first digit sets the lower 4 bits and the second one the higher 4 bits of the corresponding byte.
The multiplicity of data may then be depicted by the size of a marker, e.g. a colored sphere.

If one also wished to visualize properties of the sequence, then my suggestion would be consider the directed graph with the values as vertices and directed edges to all values that are successors; that graph can then be visualized as an adjacency matrix that again may be subjected to various matrix-reordering algorithms to get a "clearer" picture of the sequence of values.