Methods for efficiently estimating the Shannon entropy of data streams have important applications in learning, data mining, and network anomaly detections (e.g., the DDoS attacks). For nonnegative data streams, the method of Compressed Counting (CC) based on maximally-skewed stable random projections can provide accurate estimates of the Shannon entropy using small storage. However, CC is no longer applicable when entries of data streams can be below zero, which is a common scenario when comparing two streams. In this paper, we propose an algorithm for entropy estimation in general data streams which allow negative entries. In our method, the Shannon entropy is approximated by the finite difference of two correlated frequency moments estimated from correlated samples of symmetric stable random variables. Our experiments confirm that this method is able to substantially better approximate the Shannon entropy compared to the prior state-of-the-art.