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We present a new clustering algorithm called k-means-u* which in many casesis able to significantly improve the clusterings found by k-means++, thecurrent de-facto standard for clustering in Euclidean spaces. First weintroduce the k-means-u algorithm which starts from a result of k-means++ andattempts to improve it with a sequence of non-local "jumps" alternated by runsof standard k-means. Each jump transfers the "least useful" center towards thecenter with the largest local error, offset by a small random vector. This iscontinued as long as the error decreases and often leads to an improvedsolution. Occasionally k-means-u terminates despite obvious remainingoptimization possibilities. By allowing a limited number of retries for thelast jump it is frequently possible to reach better local minima. The resultingalgorithm is called k-means-u* and dominates k-means++ wrt. solution qualitywhich is demonstrated empirically using various data sets. By construction thelogarithmic quality bound established for k-means++ holds for k-means-u* aswell.

The k-means-u* algorithm: non-local jumps and greedy retries improve k-means++ clustering