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The broad network (BN) based on random feature extraction has fast computational nature. However, it usually suffers from redundant features due to its randomization in dealing with massive samples, which brings the risk of overfitting. To overcome this problem, a self-organizing BN (SO-BN) is proposed in this article. First, several groups of polynomial-based fuzzy rules (P-FRs) are embedded into BN instead of the original feature nodes. Then, P-FR with the form of approximated bell functions has the capability to cope with the uncertainties of feature extraction. Second, a frequency domain parameter calculation algorithm is presented to update the parameters of P-FRs in SO-BN. Different from traditional randomization, P-FRs are shaped with frequency-domain analysis for achieving the representative features of samples. Third, an efficient self-organizing mechanism is built to adjust the structure of the enhancement layer dynamically. Then, the enhancement layer can be expanded and pruned rapidly to reduce the redundant feature as well as improve the performance of SO-BN. Finally, the proposed SO-BN is tested on two benchmark datasets and three real-world engineering applications, especially the prediction of sunspot numbers, electrical output and total phosphorus concentration. The results indicate that SO-BN can achieve superior prediction performance than other models. [ABSTRACT FROM AUTHOR]