Unstructured environments impose several challenges when robots are required to perform different tasks and adapt to unseen situations. In this context, a relevant problem arises: how can robots learn to perform various tasks and adapt to different conditions? A potential solution is to endow robots with learning capabilities. In this line, imitation learning emerges as an intuitive way to teach robots different motor skills. This learning approach typically mimics human demonstrations by extracting invariant motion patterns and subsequently applies these patterns to new situations. In this paper, we propose a novel kernel treatment of imitation learning, which endows the robot with imitative and adaptive capabilities. In particular, due to the kernel treatment, the proposed approach is capable of learning human skills associated with high-dimensional inputs. Furthermore, we study a new concept of correlation-adaptive imitation learning, which allows for the adaptation of correlations exhibited in high-dimensional demonstrated skills. Several toy examples and a collaborative task with a real robot are provided to verify the effectiveness of our approach.