With the growing concerns on datasecurity and user privacy, a decentralized mechanism is implemented for federated data mining (FDM), which can bridge data silos and collaborate diverse devices in ubiquitous IoT (Internet of Things) systems and services to extract global and shareable knowledge, i.e., encoded in deep neural networks (DDNs). Moreover, compared with FDM in synchronous mode, asynchronous FDM (AFDM) is more suitable to accommodate devices with diversified computing resources and distinguishable working statuses. However, as AFDM is still in its infancy, how to harness heterogeneous resources and biased knowledge of learning participants within the asynchronous context remains to be addressed. Such that, this paper proposes an adaptive and integrated mechanism, named AiFed, in which, a layer-wise optimization of AFDM is implemented based on the integration of two dedicated strategies, i.e., an adaptive local model uploading strategy (ALMU), and an adaptive global model aggregation strategy (AGMA). As shown by the evaluation results, AiFed can outperform five state-of-the-art methods to reduce communication costs by about 61.76% and 56.88%, improve learning accuracy by about 1.66% and 3.05%, and accelerate learning speed by about 22.16% and 37.81% under IID (independent and identically distributed) and Non-IID settings of four standard datasets, respectively.