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The problem of anomaly detection on time series is to predict whether a newly observed time series novel or normal, to a set of training time series. It is very useful in many monitoring applications such as video surveillance and signal recognition. Based on some existing outlier detection algorithms, we propose an instance-based anomaly detection algorithm. We also propose a local instance summarization approach to reduce the number of distance computation of time series, so that abnormal time series can be efficiently detected. Experiments show that the proposed algorithm achieves much better accuracy than the basic outlier detection algorithms. It is also very efficient for anomaly detection of time series.