Disagreements, oppositions and negative opinions are indispensable parts of online political debates. In social media, people express their beliefs and attitudes not only on issues but also about each other through both their conversations and platform-specific interactions such as like, share in Facebook and retweet in Twitter. While there are explicit "like" features in these platforms, there is no explicit "dislike" feature. Many network analysis tasks, such as detecting communities and monitoring their dynamics (i.e. polarization patterns) require information about both positive and negative linkages. Hence, predicting negative links between users is an important task and a challenging problem. In this study, we propose an unsupervised framework to predict the negative links between users by utilizing explicit positive interactions and sentiment cues in conversations. We show the effectiveness of the proposed framework on a political Twitter dataset annotated through Amazon MTurk crowdsourcing platform. Our experimental results show that the proposed framework outperforms other well-known methods and proposed baselines. To illustrate the contribution of the predicted negative links, we compare the community detection accuracies using signed and unsigned user networks. Experimental results using predicted negative links show superiority on three political datasets where the camps are known a priori. We also present qualitative evaluations related to the polarization patterns (i.e. rivalries and coalitions) between the detected communities which is only possible in the presence of negative links.