In live and studio recordings unexpected sound events often lead to interferences in the signal. For non-stationary interferences, sound source separation techniques can be used to reduce the interference level in the recording. In this context, we present a novel approach combining the strengths of two algorithmic families: NMF and KAM. The recent KAM approach applies robust statistics on frames selected by a source-specific kernel to perform source separation. Based on semi-supervised NMF, we extend this approach in two ways. First, we locate the interference in the recording based on detected NMF activity. Second, we improve the kernel-based frame selection by incorporating an NMF-based estimate of the clean music signal. Further, we introduce a temporal context in the kernel, taking some musical structure into account. Our experiments show improved separation quality for our proposed method over a state-of-the-art approach for interference reduction.