One quick edit to this description : We (Ayasdi) have generalized the notion of Reeb Graph's - such that it is no longer limited to single scalar functions. Whi

One quick edit to this description : We (Ayasdi) have generalized the notion of Reeb Graph's - such that it is no longer limited to single scalar functions. While in the single scalar function the mapper algorithm is an (extremely efficient) approximation to the Reeb Graph, in the multiple scalar function case, it has no direct theoretical analogue (although the notion of Reeb Spaces is similar). We are generally not trying to lay claim to the phrase "Topological Data Analysis" and not going around suing people for using it. In fact we still support research in academia and actively publish in the field. TDA is the basis of what we do so it is the most efficient way of describing it.