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This paper addresses a major challenge in data mining applications where the full information about the underlying processes, such as sensor networks or large online database, cannot be practically obtained due to physical limitations such as low bandwidth or memory, storage, or computing power. Motivated by the recent theory on direct information sampling called compressed sensing (CS), we propose a framework for detecting anomalies from these largescale data mining applications where the full information is not practically possible to obtain. Exploiting the fact that the intrinsic dimension of the data in these applications are typically small relative to the raw dimension and the fact that compressed sensing is capable of capturing most information with few measurements, our work show that spectral methods that used for volume anomaly detection can be directly applied to the CS data with guarantee on performance. Our theoretical contributions are supported by extensive experimental results on large datasets which show satisfactory performance. Keywords-stream data processing, anomaly detection, spectral methods, residual analysis, compressed sensing