We represented the thesaurus as two matrices where T syn is the synonym graph and T ant is the antonym graph. The signed graph can then be written in matrix form asŴ = γW + β ant T ant W +β syn T syn W , where computes Hadamard product (element-wise multiplication). The parameters γ, β syn , and β ant are tuned to the **data** target dataset using cross validation. The reader should note that σ and are not found using a target dataset, but instead using cross validation and grid search to minimize the number of negative edges within clusters and the number of disconnected components in the cluster.