Federated learning (FL) enables multiple clients to collaboratively train deep learning models while considering sensitive local datasets' privacy. However, adversaries can manipulate datasets and upload models by injecting triggers for federated backdoor attacks (FBA). Existing defense strategies against FBA consider specific and limited attacker models, and a sufficient amount of noise to be injected only mitigates rather than eliminates FBA. To address these deficiencies, we introduce a Flexible Federated Backdoor Defense Framework (Fedward) to ensure the elimination of adversarial backdoors. We decompose FBA into various attacks, and design amplified magnitude sparsification (AmGrad) and adaptive OPTICS clustering (AutoOPTICS) to address each attack. Meanwhile, Fedward uses the adaptive clipping method by regarding the number of samples in the benign group as constraints on the boundary. This ensures that Fedward can maintain the performance for the Non-IID scenario. We conduct experimental evaluations over three benchmark datasets and thoroughly compare them to state-of-the-art studies. The results demonstrate the promising defense performance from Fedward, moderately improved by 33% $\sim$ 75 in clustering defense methods, and 96.98%, 90.74%, and 89.8% for Non-IID to the utmost extent for the average FBA success rate over MNIST, FMNIST, and CIFAR10, respectively.

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