An important aspect of data science is clustering data. Clustering means partitioning data into groups. A common algorithm for clustering is the k-means algorithm. In this algorithm one must specify the number of cluster groups k.

Details of the algorithm are omitted. (to be added)

Here is an example data set.

For the remaining groupings, the convex hull is displayed as an outline. The convex hull is the set of points that, when connected, contain all points in the data set.

Here is the k-means grouping of the data set into 1 cluster.

Here is the k-means grouping of the data set into 2 clusters.

Here is the k-means grouping of the data set into 3 clusters.

Here is the k-means grouping of the data set into 4 clusters.

Here is the k-means grouping of the data set into 5 clusters.

Here is the k-means grouping of the data set into 6 clusters.

Here is the k-means grouping of the data set into 7 clusters.

Here is an animation of the clusters.

Whenever the number of desired clusters is known beforehand, the process is called parametric - since the parameter for number of clusters is known.

Whenever the number of desired clusters is not known beforehand, the process is called nonparametric - since the parameter for the number of clusters is not known (beforehand).