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Input data Initialization Assign Points (1) o w Recompute Centers (2) A Cluster 0 A Cluster 1 A Cluster 2 Figure 3-23. Input data and three steps of the k-means algorithm Cluster centers are shown as triangles, while data points are shown as circles. Colors indicate cluster membership. We specified that we are looking for three clusters, so the algorithm was initialized by declaring three data points randomly as cluster cen- ters (see “Initialization”). Then the iterative algorithm starts. First, each data point is assigned to the cluster center it is closest to (see “Assign Points (1)”). Next, the cluster centers are updated to be the mean of the assigned points (see “Recompute Centers (1)”). Then the process is repeated two more times. After the third iteration, the assignment of points to cluster centers remained unchanged, so the algorithm stops. Given new data points, k-means will assign each to the closest cluster center. The next example (Figure 3-24) shows the boundaries of the cluster centers that were learned in Figure 3-23: In[48]: mglearn.plots.plot_kmeans_boundaries() Clustering | 169