I am reading about minimal model of $A_\infty$ structure. So far, I find two different ways of the construction, given by Kadeishvili and Kontsevich, Soibelman.
1) The construction of these two minimal model looks quite different, although we know they should be quasi-isomorphic. Is there any direct homomorphism between this two model?
2) Is there any other algebraic construction of minimal model of $A_\infty$ structure?