The Rosette complex is a well studied region of the galactic plane which presents the apparent characteristics of a triggered star forming region. This is however still debated as no strong evidence corroborates this statement. We focus on characterizing the young stellar population in the Rosette complex to improve our understanding of the processes that regulate the star formation in this region. We propose an original method that relies on the joint analysis of the star color and density in the near-infrared. It leads to mapping the molecular cloud spatial distribution and detecting the embedded clusters with their characterization in terms of member number and age estimation. We have identified 13 clusters, 2 of which are new discoveries, and we estimate that the total number of young stellar objects in the Rosette ranges between 4000 and 8000 members. We find that the age distribution of the young clusters is not consistent with a general triggered scenario for the star formation in this molecular cloud. This study proves that the Rosette complex evolution is not governed by the influence of its OB star population. It suggests that the simple morphological appearance of an active region is not sufficient to conclude much about the triggering role in the star formation process. Our method of constraining the cluster properties using UKIDSS and WISE data has proven efficient, and studies of other regions of the galactic plane would definitely benefit from this approach.