We identify and formulate a novel problem: cross-channel anomaly detection from multiple data channels. Cross channel anomalies are common amongst the individual channel anomalies, and are often portent of significant events. Using spectral approaches, we propose a two-stage detection method: anomaly detection at a single-channel level, followed by the detection of cross-channel anomalies from the amalgamation of single channel anomalies. Our mathematical analysis shows that our method is likely to reduce the false alarm rate. We demonstrate our method in two applications: document understanding with multiple text corpora, and detection of repeated anomalies in video surveillance. The experimental results consistently demonstrate the superior performance of our method compared with related state-of-art methods, including the one-class SVM and principal component pursuit. In addition, our framework can be deployed in a decentralized manner, lending itself for large scale data stream analysis.