Local optima in K-means clustering: what you don't know may hurt you.

The popular K-means clustering method, as implemented in 3 commercial software packages (SPSS, SYSTAT, and SAS), generally provides solutions that are only locally optimal for a given set of data. Because none of these commercial implementations offer a reasonable mechanism to begin the K-means method at alternative starting points, separate routines were written within the MATLAB (Math-Works, 1999) environment that can be initialized randomly (these routines are provided at the end of the online version of this article in the PsycARTICLES database). Through the analysis of 2 empirical data sets and 810 simulated data sets, it is shown that the results provided by commercial packages are most likely locally optimal. These results suggest the need for some strategy to study the local optima problem for a specific data set or to identify methods for finding "good" starting values that might lead to the best solutions possible.