In this chapter, we introduced the fundamental clustering algorithms, starting with k-NN, which is an instance-based method that can be employed whenever it's helpful to retrieve the most similar samples given a query point. Then, we discussed the Gaussian mixture approach, focusing on its peculiarities and requirements, discussing how it's possible to use it whenever a soft-clustering is preferable than a hard method.
The natural evolution of Gaussian mixture with null covariances leads to the K-means algorithm, which is based on the idea of defining (randomly, or according to some criteria) k centroids that represent the clusters and optimize their position so that the sum of squared distances for every point in each cluster and the centroid is minimal. We have discussed different methods to find out the optimal number of clusters and, consequently, to evaluate...
