In this talk, we shall describe a detailed construction of certain invariants associated with the data of a saturated Calabi-Yau $A_\infty$-category plus a choice of splitting of the non-commutative Hodge filtration, originally defined by Costello and Kontsevich (unpublished) back in 2003/2004. The new input here is the use of ribbon graphs which makes Costello's original definition explicitly computable and theoretically more approachable. This is a joint work with Andrei Caldararu and Kevin Costello.