Cyber attacks have recently gained momentum in the research community as a sharply concerning phenomenon further ignited by the proliferation of social networks, which unfold a variety of ways for cybercriminals to access compromised information of their users. This paper gravitates on impersonation attacks, whose motivation may go beyond economic interests of the attacker towards getting unauthorised access to information and contacts, as often occurs between teenagers and early users of social platforms. This manuscript proposes a meta-heuristically optimised learning model as the algorithmic core of a non-intrusive detection system that relies exclusively on connection time features to detect evidences of an impersonation attack. The proposed scheme hinges on the K-Means clustering approach applied to a set of time features specially tailored to characterise the usage of users, which are weighted prior to the clustering under detection performance maximisation criteria. The obtained results shed light on the potentiality of the proposed methodology for its practical application to real social networks.