In many applications of Internet of Things (IoT), the huge amount of data are generated by sensor nodes and processing them are complex. Offloading data classification and anomaly event detection tasks to sink nodes in sensor networks can reduce the computing complexity, lower remote communication loads, and improve the response time for the delay-sensitive IoT applications. Many existing classification and anomaly detection methods cannot be directly applied to these IoT applications, because the computing and energy resources of sensors are limited. In this paper, a new feature-based learning system for IoT applications is proposed to effectively classify data and detect anomaly event. Especially, based on the theory of distributed compression, the sparsity and relativity of the data are exploited to obtain the classification features, which can reduce the computation overhead and energy consumption. Further, an RBF-BP hybrid neural network is employed to detect the anomaly event based on the classification results, by which the training time of neural network can be significantly reduced and the accuracy can be improved for users' decisions.