Self Organizing Map - objective function?

Given a dataset, the self organizing map command in MATLAB will assign the data to different clusters if run several times due to the initial weights. If ran only own one can fix the random number generation seed (e.g. rng(seed)) and get reproducibility. My questions are:

• Is it possible to retrieve some kind of objective function the SOM minimizes, run SMOM several times and try to get rid of the effect of the initialization weights? How?
• Each time it runs, most of the points will be assigned to the same class (maybe with a different tag/name but same points will be assigned to the same group), some of them will not. Is it possible to use that distribution to obtain some kind of metric of the reliability of the overall procedure?

Thanks in advance.