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Anomaly detection in wireless sensor networks is an important challenge for tasks such as intrusion detection and monitoring applications. This paper proposes two approaches to detecting anomalies from measurements from sensor networks. The first approach is a linear programming-based hyperellipsoidal formulation, which is called a centered hyperellipsoidal support vector machine (CESVM). While this CESVM approach has advantages in terms of its flexibility in the selection of parameters and the computational complexity, it has limited scope for distributed implementation in sensor networks. In our second approach, we propose a distributed anomaly detection algorithm for sensor networks using a one-class quarter-sphere support vector machine (QSSVM). Here a hypersphere is found that captures normal data vectors in a higher dimensional space for each sensor node. Then summary information about the hyperspheres is communicated among the nodes to arrive at a global hypersphere, which is used by the sensors to identify any anomalies in their measurements. We show that the CESVM and QSSVM formulations can both achieve high detection accuracies on a variety of real and synthetic data sets. Our evaluation of the distributed algorithm using QSSVM reveals that it detects anomalies with comparable accuracy and less communication overhead than a centralized approach.