# Clustering of set of matrices

I have 25 matrices 19x19 containing coherence measure between EEG electrodes. I want to divided them into some groups by clustering or any other method. I know how to deal with vectors, but I can't find anything about clustering of set of matrices. If it can help - I think we can use coherence as a distance between cells into matrix. So may be there are some method for clustering of distance matrices?

EDIT

Traditional clustering methods cluster vectors. In the vector space, the distance metric and other distance functions are well defined. The Euclidean distance between vectors $x_1$ and $x_2$ is $|x_1-x_2|_2$, the 2-norm of $x_1-x_2$. Analogously, to compare two matrices $M_1$ and $M_2$, we may want to compute $|| M_1-M_2||_p$, the p-norm of $M_1-M_2$.

EDIT

While there are two solution:

1. Compute distance between matrices as sum of squares of the difference matrix
2. Unwrap a triangle of each matrix into a vector

Is there something else?

• Take a look at this paper. The authors develop a method for cluster temporal gene expression matrices in which rows are time series for gene expression. – learner Feb 17 '13 at 21:38

• But, for example, linkage MATLAB function take Matrix with two or more rows. The rows represent observations, the columns represent categories or dimensions. But in my case observations is not 25 rows, is 25 matrices. Sorry for not clear question – sviter Feb 17 '13 at 19:50
• At 25 observations, there is nothing wrong in filling the 25x25 matrix by doing the n*(n-1)/2=300 dissimilarity computations yourself, and just writing them to the matrix. Then do the cluster analysis. In fact, it even is smart to compute the matrix only once, store it somewhere, so you can try different algorithms on it easily, as probably the similarity computation is much more expensive than the actual clustering. – Anony-Mousse Feb 18 '13 at 11:11