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Facing globalized competition, there have been increasing requirements for safety and efficiency in smart factories, where the industrial Internet of Things can enable the monitoring of equipment's status and the detecting of faults before they go critical. Regarding cloud computing, data-driven methods running at clouds are adopted to train the model with a large amount of raw data at the beginning, then end machines upload their real-time readings to the cloud center for processing. However, this incurs considerable computational costs and may sometimes bear a severe delay. In this article, we consider a hierarchical structure where edge-PLCs are employed to gather sensed data locally and reduce communication costs. Since a single fault may be related to multiple influencing features, we want to first minimize the number of features that need to determine a fault, then try to find out the minimal set of edge-PLCs …