How can i reduce the number of dimensions of an matrix without losing important information?

I have some input data on which i apply k-means. After this i want to plot3 the results, but my data has more than 3 dimensions. How can i reduce it to 3 dimensions without losing (topological) information. Should i use kohonen soms or pca or what? thank you in advance

[sorena mirzaie]

I have a problem like u...i used pca:

[pc,score,latent,tsquare] = princomp(X); 
red_dim = score(:,1:50);

bu t i dont know how to apply this to my input data :(

(my inputs data (X) has 320 feature and i want to reduce them to about 50 )

Answer 1

[Walter Roberson]

If non-redundant topological information is present in more than 3 dimensions, then it is not possible to reduce the data to 3 dimensions without losing topological information.

As a mental exercise, try reducing a triangular pyramid (3 dimensions) to 2 dimensions without the 4th vertex ending up "further away" from some of the 2D vertices than others of the vertices.

[Andrei]

i don't think i explained well enough what i wanted. I have some multidimensional points, which i cluster, and i want to be able to reduce those points to 3 dimensions, so i can plot. So there isn't something like Soms i can use to be able to plot them? The worst solution would be to just ignore the 4th, 5th etc dimensions and i would want that.

[Iain]

You can only present 3D information easily. You need to figure out how you want to get your x,y,z coordinates from you "n" dimensions, and then use the other dimensions, to, say, stick in the appropriate legend.

Alternatively, you can use the 4th/5th/etc. dimension in some way to control the colour/marker/etc. of the points you plot.

[Walter Roberson]

http://www.mathworks.com/matlabcentral/linkexchange/links/949-som-toolbox