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With the availability of affordable sensors and sensor networks, sensor-based human activity recognition has attracted much attention in artificial intelligence and ubiquitous computing. In this paper, we present a novel two-phase approach for detecting abnormal activities based on wireless sensors attached to a human body. Detecting abnormal activities is a particular important task in security monitoring and healthcare applications of sensor networks, among many others. Traditional approaches to this problem suffer from a high false positive rate, particularly when the collected sensor data are biased towards normal data while the abnormal events are rare. Therefore, there is a lack of training data for many traditional data mining methods to be applied. To solve this problem, our approach first employs a one-class support vector machine (SVM) that is trained on commonly available normal activities, which filters out the activities that have a very high probability of being normal. We then derive abnormal activity models from a general normal model via a kernel nonlinear regression (KNLR) to reduce false positive rate in an unsupervised manner. We show that our approach provides a good tradeoff between abnormality detection rate and false alarm rate, and allows abnormal activity models to be automatically derived without the need to explicitly label the abnormal training data, which are scarce. We demonstrate the effectiveness of our approach using real data collected from a sensor network that is deployed in a realistic setting.