Atmospheric new-particle formation (NPF) is a very non-linear process that includes atmospheric chemistry of precursors and clustering physics as well as subsequent growth before NPF can be observed. Thanks to ongoing efforts, now there exists a tremendous amount of atmospheric data, obtained through continuous measurements directly from the atmosphere. This fact makes the analysis by human brains difficult but, on the other hand, enables the usage of modern data science techniques. Here, we calculate and explore the mutual information (MI) between observed NPF events (measured at Hyytiälä, Finland) and a wide variety of simultaneously monitored ambient variables: Trace gas and aerosol particle concentrations, meteorology, radiation and a few derived quantities. The purpose of the investigations is to identify key factors contributing to the NPF. The applied mutual information method finds that the formation events are strongly linked to sulfuric acid concentration and water content, ultraviolet radiation, condensation sink (CS) and temperature. Previously, these quantities have been well-established to be important players in the phenomenon via dedicated field, laboratory and theoretical research. The novelty of this work is to demonstrate that the same results are now obtained by a data analysis method which operates without supervision and without the need of understanding the physics deeply. This suggests that the method is suitable to be implemented widely in the atmospheric field to discover other interesting phenomena and their relevant variables.