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Partial domain adaptation (PDA) attracts appealing attention as it deals with a realistic and challenging problem when the source domain label space substitutes the target domain. Most conventional domain adaptation (DA) efforts concentrate on learning domain-invariant features to mitigate the distribution disparity across domains. However, it is crucial to alleviate the negative influence caused by the irrelevant source domain categories explicitly for PDA. In this work, we propose an Adaptively-Accumulated Knowledge Transfer framework (A$^2$KT) to align the relevant categories across two domains for effective domain adaptation. Specifically, an adaptively-accumulated mechanism is explored to gradually filter out the most confident target samples and their corresponding source categories, promoting positive transfer with more knowledge across two domains. Moreover, a dual distinct classifier architecture consisting of a prototype classifier and a multilayer perceptron classifier is built to capture intrinsic data distribution knowledge across domains from various perspectives. By maximizing the inter-class center-wise discrepancy and minimizing the intra-class sample-wise compactness, the proposed model is able to obtain more domain-invariant and task-specific discriminative representations of the shared categories data. Comprehensive experiments on several partial domain adaptation benchmarks demonstrate the effectiveness of our proposed model, compared with the state-of-the-art PDA methods.