With the increasing complexity and intelligence of industrial systems, the collaborative operation of multiple devices and working conditions makes it difficult for traditional single-task analysis methods to cope with cross-domain collaborative diagnostic tasks. Therefore, a novel multitask analysis method called low-rank multidomain support matrix machine (LMSMM) is proposed. In LMSMM, a low-rank constraint matrix is constructed to mine shared feature representations between multiple tasks and achieve knowledge transfer between tasks. Meanwhile, a domain-adaptive weighting factor is designed to address model bias caused by data imbalance through differentiated penalty strategies, which can effectively solve different data imbalance problems in different tasks. Experiments on multiple benchmark datasets have shown that LMSMM not only effectively achieves multitask classification, but also exhibits higher classification accuracy in heterogeneous imbalance rate.
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