Let's consider a dataset of points:
We assume that it's possible to find a criterion (not unique) so that each sample can be associated with a specific group:
Conventionally, each group is called a cluster and the process of finding the function G is called clustering. Right now, we are not imposing any restriction on the clusters; however, as our approach is unsupervised, there should be a similarity criterion to join some elements and separate other ones. Different clustering algorithms are based on alternative strategies to solve this problem, and can yield very different results. In the following figure, there's an example of clustering based on four sets of bidimensional samples; the decision to assign a point to a cluster depends only on its features and sometimes on the position of a set of other points (neighborhood):
In this book, we're going to discuss hard clustering techniques, where each element must belong to a single cluster. The alternative approach, called...