This paper considers the real-time detection of anomalies in high-dimensional systems. The goal is to detect anomalies quickly and accurately so that the appropriate countermeasures could be taken in time, before the system possibly gets harmed. We propose a sequential and multivariate anomaly detection method that scales well to high-dimensional datasets. The proposed method follows a nonparametric, i.e., data-driven, and semi-supervised approach, i.e., trains only on nominal data. Thus, it is applicable to a wide range of applications and data types. Thanks to its multivariate nature, it can quickly and accurately detect challenging anomalies, such as changes in the correlation structure and stealth low-rate cyberattacks. Its asymptotic optimality and computational complexity are comprehensively analyzed. In conjunction with the detection method, an effective technique for localizing the anomalous data dimensions is also proposed. We further extend the proposed detection and localization methods to a supervised setup where an additional anomaly dataset is available, and combine the proposed semi-supervised and supervised algorithms to obtain an online learning algorithm under the semi-supervised framework. The practical use of proposed algorithms are demonstrated in DDoS attack mitigation, and their performances are evaluated using a real IoT-botnet dataset and simulations.
One way to describe anomalies is by saying that anomalies are not concentrated. This leads to the problem of finding level sets for the data generating density. We interpret this learning problem as a binary classification problem and compare the corresponding classification risk with the standard performance measure for the density level problem. In particular it turns out that the empirical classification risk can serve as an empirical performance measure for the anomaly detection problem. This allows us to compare different anomaly detection algorithms empirically, i.e. with the help of a test set. Furthermore, by the above interpretation we can give a strong justification for the well-known heuristic of artificially sampling "labeled" samples, provided that the sampling plan is well chosen. In particular this enables us to propose a support vector machine (SVM) for anomaly detection for which we can easily establish universal consistency. Finally, we report some experiments which compare our SVM to other commonly used methods including the standard one-class SVM. Anomaly detection is an essential component of protection mechanisms against novel attacks. We propose to use several information-theoretic measures, namely, entropy, conditional entropy, relative conditional entropy, information gain, and information cost for anomaly detection. These measures can be used to describe the characteristics of an audit data set, suggest the appropriate anomaly detection model(s) to be built, and explain the performance of the model(s). We use case studies on Unix system call data, BSM data, and network tcpdump data to illustrate the utilities of these measures. A low-rate distributed denial of service (DDoS) attack has significant ability of concealing its traffic because it is very much like normal traffic. It has the capacity to elude the current anomaly-based detection schemes. An information metric can quantify the differences of network traffic with various probability distributions. In this paper, we innovatively propose using two new information metrics such as the generalized entropy metric and the information distance metric to detect low-rate DDoS attacks by measuring the difference between legitimate traffic and attack traffic. The proposed generalized entropy metric can detect attacks several hops earlier (three hops earlier while the order α = 10 ) than the traditional Shannon metric. The proposed information distance metric outperforms (six hops earlier while the order α = 10) the popular Kullback-Leibler divergence approach as it can clearly enlarge the adjudication distance and then obtain the optimal detection sensitivity. The experimental results show that the proposed information metrics can effectively detect low-rate DDoS attacks and clearly reduce the false positive rate. Furthermore, the proposed IP traceback algorithm can find all attacks as well as attackers from their own local area networks (LANs) and discard attack traffic.