Recently, recycled field-programmable gate arrays (FPGAs) pose a significant hardware security problem due to the proliferation of the semiconductor supply chain. Ring oscillator (RO) based frequency analyzing technique is one of the popular methods, where most studies used the known fresh FPGAs (KFFs) in machine learning-based detection, which is not a realistic approach. In this paper, we present a novel recycled FPGA detection method by examining the symmetry information of the RO frequency using unsupervised anomaly detection method. Due to the symmetrical array structure of the FPGA, some adjacent logic blocks on an FPGA have comparable RO frequencies, hence our method simply analyzes the RO frequencies of those blocks to determine how similar they are. The proposed approach efficiently categorizes recycled FPGAs by utilizing direct density ratio estimation through outliers detection. Experiments using Xilinx Artix-7 FPGAs demonstrate that the proposed method accurately classifies recycled FPGAs from 10 fresh FPGAs by x fewer computations compared with the conventional method.