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Local anomaly detection refers to detecting small anomalies or outliers that exist in some subsegments of events or behaviors. Such local anomalies are easily overlooked by most of the existing approaches since they are designed for detecting global or large anomalies. In this paper, an accurate and flexible three-phase framework TRASMIL is proposed for local anomaly detection based on TRAjectory Segmentation and Multi-Instance Learning. Firstly, every motion trajectory is segmented into independent sub-trajectories, and a metric with Diversity and Granularity is proposed to measure the quality of segmentation. Secondly, the segmented sub-trajectories are modeled by a sequence learning model. Finally, multi-instance learning is applied to detect abnormal trajectories and sub-trajectories which are viewed as bags and instances, respectively. We validate the TRASMIL framework in terms of 16 different algorithms built on the three-phase framework. Substantial experiments show that algorithms based on the TRASMIL framework outperform existing methods in effectively detecting the trajectories with local anomalies in terms of the whole trajectory. In particular, the MDL-C algorithm (the combination of HDP-HMM with MDL segmentation and Citation kNN) achieves the highest accuracy and recall rates. We further show that TRASMIL is generic enough to adopt other algorithms for identifying local anomalies.