Score matrix string similarity I have a load of documents, which have a load of key value pairs in them. The key might not be unique so there might be multiple keys of the same type with different values.

I want to compare the similarity of the keys between 2 documents. More specifically the string similarity of these values. I am thinking of using something like the Smith-Waterman Algorithm to compare the similarity.

So I've drawn a picture of how I'm thinking about representing the data - 



The values in the cells are the result of the smith-waterman algorithm (or some other string similarity metric).

Image that this matrix represents a key type of "things" I then need to add the "things" similarity score into a vector of 0 or 1. Thats ok.

What I can't figure out is how I determine if the matrix is similar or not similar - ideally I want to convert the matrix to an number between 0 and 1 and then I'll just set a threshold to score it as either 0 or 1.

Any ideas how I can create a score of the matrix? Does anyone know any algorithms that do this type of thing (obviously things like how smith waterman works is kind of applicable).
If your goal is to transform your matrix into a number (your similarity measure), you may want to use a matrix norm.

For instance, using the Frobenius norm on your example would return 1.488086.