Facebook is the largest and the most popular online social network that records the large amount of users’ behavior expressed in various activities such as Facebook Likes, status updates, posts, comments, photos, tags and shares. One of the major attractions of such a big data offered by Facebook relates to the predictability of individuals’ psychological traits from their digital footprints which helps researchers and service providers to improve personalized products and services. The goal of this research project is to investigate the predictability of Facebook users’ personality traits measured by BIG5 test as a function of their digital records of behavior such as Facebook Likes. This research is based on a dataset of 92,255 users who provided their Facebook Likes and the results of their BIG5 personality test. For preprocessing the Likes data including 600 attributes, the proposed model uses the R Package “fscaret” to automatically determine the importance level of the attributes as a function of the set of learning algorithms applied to this problem. Two supervised versions of the Multi-Layer Self-Organizing-Map (MLSOM) algorithm is used to visualize the data and predict the users’ personality profiles as a function of Facebook profiles. The model predicts Facebook users' BIG5 personality traits with mean squared error of at most 0.053 for neuroticism and correlation of at most 0.3 for openness.