Wittgenstein proposed in his later philosophy the concept of family resemblance to describe groups which cannot be defined by a single (or simple set) of common features but instead display (from the SEP):
There is no reason to look, as we have done traditionally—and dogmatically—for one, essential core in which the meaning of a word is located and which is, therefore, common to all uses of that word. We should, instead, travel with the word’s uses through “a complicated network of similarities overlapping and criss-crossing” (PI 66). Family resemblance also serves to exhibit the lack of boundaries and the distance from exactness that characterize different uses of the same concept. Such boundaries and exactness are the definitive traits of form—be it Platonic form, Aristotelian form, or the general form of a proposition adumbrated in the Tractatus. It is from such forms that applications of concepts can be deduced, but this is precisely what Wittgenstein now eschews in favor of appeal to similarity of a kind with family resemblance.
Now consider a typical pattern recognition/machine learning problem: We have a set of photos some of which are of trees and some which are not. We want to classify them into two groups "photos of trees" and "photos of other things". No single criterion ("trunk/no trunk", "leaves/no leaves" , "green/not green") exists for deciding whether the photo is that of a tree or not, but a suitable patter recognition algorithm such as a neural network or support vector machine will easily be able to separate the two classes of photos.
The thing about how such algorithms work: there is a sharp boundary between the two classes, it's just that it's too complicated to represent with a simple function or set of if-then rules. It can only be represented in a high dimension feature space which can't be visualized in 2D or 3D, but a sharp decision boundary still exists, otherwise the algorithms wouldn't work.
Based on this consideration, does Wittgenstein's family resemblance really boil down to a lack of sufficient knowledge?
Is Wittgenstein wrong when he says that no boundaries or exact distances can be described for such notions? They can, they are just too complex to be described in a simple fashion?
Or are there examples of family resemblance where no sharp boundary can be found no matter how complex the representation we use?