In this work, we study the privacy risk due to profile matching across online social networks (OSNs), in which anonymous profiles of OSN users are matched to their real identities using auxiliary information about them. We consider different attributes that are publicly shared by users. Such attributes include both strong identifiers such as user name and weak identifiers such as interest or sentiment variation between different posts of a user in different platforms. We study the effect of using different combinations of these attributes to profile matching in order to show the privacy threat in an extensive way. The proposed framework mainly relies on machine learning techniques and optimization algorithms. We evaluate the proposed framework on three datasets (Twitter - Foursquare, Google+ - Twitter, and Flickr) and show how profiles of the users in different OSNs can be matched with high probability by using the publicly shared attributes and/or the underlying graphical structure of the OSNs. We also show that the proposed framework notably provides higher precision values compared to state-of-the-art that relies on machine learning techniques. We believe that this work will be a valuable step to build a tool for the OSN users to understand their privacy risks due to their public sharings.