Understanding human personality has been a focus for philosophers and scientists for millennia. It is now widely accepted that there are about five major personality domains that describe the personality profile of an individual. In contrast to personality traits, the existence of personality types remains extremely controversial. Despite the various purported personality types described in the literature, small sample sizes and the lack of reproducibility across data sets and methods have led to inconclusive results about personality types. Here we develop an alternative approach to the identification of personality types, which we apply to four large data sets comprising more than 1.5 million participants. We find robust evidence for at least four distinct personality types, extending and refining previously suggested typologies. We show that these types appear as a small subset of a much more numerous set of spurious solutions in typical clustering approaches, highlighting principal limitations in the blind application of unsupervised machine learning methods to the analysis of big data.