What is shattering a set of points? Explain VC dimension.

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 2n possible assignments of positive or negative.

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.