clusters (rightfailure cases of -means even if you know the "rightnumber of clusters for given datasetk-means might not always be able to recover them each cluster is defined solely by its centerwhich means that each cluster is convex shape as result of thisk-means can only capture relatively simple shapes -means also assumes that all clusters have the same "diameterin some senseit always draws the boundary between clusters to be exactly in the middle between the cluster centers that can sometimes lead to surprising resultsas shown in figure - in[ ]x_variedy_varied make_blobs(n_samples= cluster_std=[ ]random_state= y_pred kmeans(n_clusters= random_state= fit_predict(x_variedmglearn discrete_scatter(x_varied[: ]x_varied[: ]y_predplt legend(["cluster ""cluster ""cluster "]loc='best'plt xlabel("feature "plt ylabel("feature "clustering