In order to shatter a given configuration of points, a classifier must be able to, for all possible assignments of positive and negative for the points, perfectly partition the plane such that positive points are separated from negative points. For a configuration of * n* points, there are

**2***possible assignments of positive or negative.*

**n**When choosing a classifier, we need to consider the type of data to be classified and this can be known by VC dimension of a classifier. It is defined as cardinality of the largest set of points that the classification algorithm i.e. the classifier can shatter. In order to have a VC dimension of *at* least **n**, a classifier must be able to shatter a single given configuration of **n** points.