The question might be improved so that the answer can be more specific by defining two things more rigorously.
- Strength of the connection
- What the automation must infer from that value
Learning, Correlation, Projection, and Maximizing Profitability
Guessing from the comments, it appears that the goal is to profile the user for business purposes. Two common applications of user profiling are
- To present buying options or
- To suggest friends in a social network.
Although it may appear that a learning program would serve both of these applications, they are actually two very different problems.
One is to optimize e-commerce profitability through increased sales per session. The other is to build a social network where there are some similarities and perhaps a few deliberate differences in the pairing of user profiles from which the friend suggestion comes.
The first of the two has to do with the projecting of the potential of a sale by matching the users and relying on the assumption that two people with like interests are more likely to mirror one another in purchasing patterns to some degree that could be projected with statistical analysis.
But approaching the project by immediately jumping to learning algorithms may not produce the best results after a month or a year of development.
One Reasonable Approach for Some Problems of This Type
Depending on the definitions of STRENGTH and AUTOMATICALLY in the question, it may be a simple application of a probability matrix or hypercube that will create a functional application of user profiling based on interests. To create a correlation between users via an ordered list of interests to place in one of the cells of the matrix or hypercube, the Spearman's Rank Order Correlation is a generalized yet effective method for such applications.
Learning Usually Begins With a Guess
First, you must determine what is (preferably in precise mathematical terms) what is a favorable product presentation or favorable potential friend introduction. After that is determined, one can develop a probability formula to project what would be favorable based on the correlation matrix or hypercube. Bayes's Theorem may be quite applicable in the development of a probability formula from the constraints and relationships of the application.
Once improved favorablility gained through the application of the correlations can be demonstrated, it would then be wise to apply a learning algorithm. The sequence is thus.
- Results gained by random selection of options to present the user
- Results gained by using the correlation matrix or hypercube
- Results gained by iteratively converging on an optimal presentation
- Tuning the iterative convergence track change and yet not oscillate
A multi-tier, back propagating Hopfield neural net could be one option for varying parameters in the use of the correlations (or the choice of correlations, since Spearman's is only one correlation model for ordered discrete interests). Neural networks are only one type of convergent approach too. Modelling with as a system of differential equations and using extensions of the Taylor Series to evaluate with a defined independent input vector is another.
To see how simple convergence can be and how primitive what appears to be a learning algorithm can become, think about the divide and average method of iteratively determining a square root.