This paper proposes to recognise the true (self-reported) personality from the learned simulation of the target subject's cognition. This approach builds on two following findings in cognitive science: (i) human cognition partially determines expressed behaviour and is directly linked to true personality traits; and (ii) in dyadic interactions individuals' nonverbal behaviours are influenced by their conversational partner's behaviours. In this context, we hypothesise that during a dyadic interaction, a target subject's facial reactions are driven by two main factors, i.e. their internal (person-specific) cognitive process, and the externalised nonverbal behaviours of their conversational partner. Consequently, we propose to represent the target subject's (defined as the listener) person-specific cognition in the form of a person-specific CNN architecture that has unique architectural parameters and depth, which takes audio-visual non-verbal cues displayed by the conversational partner (defined as the speaker) as input, and is able to reproduce the target subject's facial reactions. Each personspecific CNN is explored by the Neural Architecture Search (NAS) and a novel adaptive loss function, which is then represented as a graph representation for recognising the target subject's true personality. Experimental results not only show that the produced graph representations are well associated with target subjects' personality traits in both human-human and human-machine interaction scenarios, and outperform the existing approaches with significant advantages, but also demonstrate that the proposed novel strategies such as adaptive loss, and the end-to-end vertices/edges feature learning, help the proposed approach in learning more reliable personality representations. Building on our earlier version of this work, this paper further proposes: (i) assigning a unique depth for each CNN; (ii) a novel end-to-end graph vertex feature learning strategy; (iii) a transformer-based edge feature learning strategy; and (iv) evaluating the approach in human-machine interaction scenario.