ML 32: k-Means Finds k Pieces Whether or Not There Are Clusters
Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. Over ten draws of four simulated shapes, k-means recovered four separated round blobs (adjusted Rand index 1.00) and the silhouette chose k = 4 each time. On uniform noise, with no clusters, the silhouette also chose k = 4 each time, with a score of 0....