I have 100 data points and each data point has 3 measures and then I use them calculated the similarity matrix and want to know: the correlation among the 10 similarity matrix. I known that Mantel test can do something like this. Is there other ways to handle this?
An example like this:
Suppose: the data set is denoted as: $A1 \in R^{100 \times 10}$, and $A2 \in R^{100 \times 5}$, and $A3 \in R^{100 \times 15}$. And from A1, A2 and A3, I can obtain the similarity matrix based on the Gaussian kernel. That is, I have $S1 \in R^{100 \times 100}$, $S2 \in R^{100 \times 100}$ and $S3 \in R^{100 \times 100}$. Is there same ways to determine the correlation (coefficient or relationship) among these 3 similarity matrices from the same data points.
Or say, information from these 3 similarity matrices is complementary, overlap or others? what mathematical methods can test the relationship of theses kinds of similarity matrices?
Thanks.