The distance or similarity metric plays an important role in many natural language processing (NLP) tasks. Previous studies have demonstrated the effectiveness of a number of metrics such as the Jaccard coefficient, especially in synonym acquisition. While the existing metrics perform quite well, to further improve performance, we propose the use of a supervised machine learning algorithm that fine-tunes them. Given the known instances of similar or dissimilar words, we estimated the parameters of the Mahalanobis distance. We compared a number of metrics in our experiments, and the results show that the proposed metric has a higher mean average precision than other metrics.