The rapid expansion of the Slavic speakers in the second half of the first millennium CE remains a controversial topic in archaeology, and academic passions on the issue have long run high. Currently, there are three main hypotheses for this expansion. The aim of this paper was to test the so-called "hybrid hypothesis," which states that the movement of people, cultural diffusion and language diffusion all occurred simultaneously. For this purpose, we examined an archaeological Deep Data set with a machine learning method termed time series clustering and with emerging hot spot analysis. The latter required two archaeology-specific modifications: The archaeological trend map and the multiscale emerging hot spot analysis. As a result, we were able to detect two migrations in the Eastern Alps between c. 500 and c. 700 CE. Based on the convergence of evidence from archaeology, linguistics, and population genetics, we have identified the migrants as Alpine Slavs, i.e., people who spoke Slavic and shared specific common ancestry.