Integrated sensing and communication (ISAC), which enables the joint radar sensing and data communications, shows its great potential in many intelligent applications. In this paper, we investigate the unmanned aerial vehicle (UAV) aided ISAC with mobile edge computing (MEC), where the ISAC device deployed on the UAV senses multiple targets with the sensing scheduling and offloads the radar sensing data to the edge-server to train a machine learning model for target recognition. The radar estimation information rate is utilized to measure the radar sensing performance. We aim to minimize a system-wise cost that includes both the UAV’s energy consumption and the data collecting time, while satisfying the requirements on both the model training error and the radar sensing performance. We formulate a joint optimization problem of the sensing scheduling, the number of time-slots, the sensing power, the communication power, and the UAV trajectory. Despite the strict non-convexity of the formulated problem, we propose an efficient algorithm for solving it. Our algorithm jointly leverages the vertical decomposition that exploits the layered structure of the formulated problem and the horizontal decomposition that utilizes the block coordinate descent (BCD) method. Numerical results are presented to validate the effectiveness of our proposed algorithms and show the performance gain of our proposed scheme.