The World Wide Web includes semantic relations of numerous types that exist among different entities. Extracting the relations that exist between two entities is an important step in various Web-related tasks such as information retrieval (IR), information extraction, and social network extraction. A supervised relation extraction system that is trained to extract a particular relation type (source relation) might not accurately extract a new type of a relation (target relation) for which it has not been trained. However, it is costly to create training data manually for every new relation type that one might want to extract. We propose a method to adapt an existing relation extraction system to extract new relation types with minimum supervision. Our proposed method comprises two stages: learning a lower dimensional projection between different relations, and learning a relational classifier for the target relation type with instance sampling. First, to represent a semantic relation that exists between two entities, we extract lexical and syntactic patterns from contexts in which those two entities co-occur. Then, we construct a bipartite graph between relation-specific (RS) and relation-independent (RI) patterns. Spectral clustering is performed on the bipartite graph to compute a lower dimensional projection. Second, we train a classifier for the target relation type using a small number of labeled instances. To account for the lack of target relation training instances, we present a one-sided under sampling method. We evaluate the proposed method using a data set that contains 2,000 instances for 20 different relation types. Our experimental results show that the proposed method achieves a statistically significant macroaverage F-score of 62.77. Moreover, the proposed method outperforms numerous baselines and a previously proposed weakly supervised relation extraction method.