Details on Umbrella approach Integration Testing

I have been researching on the Umbrella Integration testing approach and most of the sites I can across seem to have the exact same definition for it:

The umbrella approach requires testing along functional data and control-flow paths. First, the inputs for functions are integrated in the bottom-up pattern discussed above. The outputs for each function are then integrated in the top-down manner. The primary advantage of this approach is the degree of support for early release of limited functionality. It also helps minimize the need for stubs and drivers. The potential weaknesses of this approach are significant, however, in that it can be less systematic than the other two approaches, leading to the need for more regression testing.

However, this seems vague and I would like to have a better description as well as some advantages and disadvantages.

Some of the websites I came across:

http://ift.tt/2pAjmxH http://ift.tt/1VOqtzN