# How to compare (statistically) matrices of different dimensions?

• Mar 14th 2014, 03:39 AM
shappi
How to compare (statistically) matrices of different dimensions?
Hi,I need to compare two sets of matrices related to two different classification systems X and Y. Each system is represented by a dendrogram having three levels.I have a matrix of overlap between each pair of entities (groups) at each level of dendrogram of each system (Overlap=s/[a+b-s], where "s" is the number of common members between groups a and b). I need to statistically compare matrices of the two systems at each level, say matrix X1 with Y1, and determine which system has greater overalp at any given level.The problem is that while matrices of both systems measure the same variable (overlap) among their respective groups, they have different dimensions, order, and sparsity. For instance, X1 is 8*8 and Y1 is 4*4 and their member groups are also different. Therefore, a measure of average (say, Mean), is not a valid measure of comparison. The problem gets worse at lower levels of dendrogram.Can anyone suggest a way to statistically compare matrix X1 with corresponding Y1?I shall be grateful for any help.Best regards,S
• Mar 14th 2014, 05:49 AM
shappi
Re: How to compare (statistically) matrices of different dimensions?
Hi,
I found one possible solution known as "T Method" (BMC Evolutionary Biology | Full text | A simple procedure for the comparison of covariance matrices) but I have yet to test it.

I shall be glad to know other possible options as well.

Best,
S
• Mar 14th 2014, 12:21 PM
shappi
Re: How to compare (statistically) matrices of different dimensions?
Quote:

Originally Posted by shappi
Hi,
I found one possible solution known as "T Method" (BMC Evolutionary Biology | Full text | A simple procedure for the comparison of covariance matrices) but I have yet to test it.

I shall be glad to know other possible options as well.

Best,
S

It is not applicable/relevant to this case...