The document presents a methodology for modeling word usage similarity (Usim) in social media texts without supervision. It uses Latent Dirichlet Allocation (LDA) topic modeling to represent tweets containing target words as topic distribution vectors and evaluate models on a dataset of manually annotated Usim scores. LDA outperforms a baseline and benchmark, and expanding documents with hashtags improves performance. The study concludes LDA is suitable for modeling Usim in tweets.