Information security is the key success factor to provide safe cloud computing services. Despite its usefulness and cost-effectiveness, public cloud computing service is hard to accept because there are many security concerns such as data leakage, unauthorized access from outside the system and abnormal activities from inside the system. To detect these abnormal activities, intrusion detection system (IDS) require a learning process that can cause system performance degradation. However, providing high performance computing environment to the subscribers is very important, so a lightweight anomaly detection method is highly desired. In this paper, we propose a lightweight IDS with self-similarity measures to resolve these problems. Normally, a regular and periodic self-similarity can be observed in a cloud system's internal activities such as system calls and process status. On the other hand, outliers occur when an anomalous attack happens, and then the system's self-similarity cannot be maintained. So monitoring a system's self-similarity can be used to detect the system's anomalies. We developed a new measure based on cosine similarity and found the optimal time interval for estimating the self-similarity of a given system. As a result, we can detect abnormal activities using only a few resources.