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Positive-unlabeled (PU) learning aims to train a classifier using the data containing only labeled-positive instances and unlabeled instances. However, existing PU learning methods are generally hard to achieve satisfactory performance on trifurcate data, where the positive instances distribute on both sides of the negative instances. To address this issue, firstly we propose a PU classifier with asymmetric loss (PUAL), by introducing a structure of asymmetric loss on positive instances into the objective function of the global and local learning classifier. Then we develop a kernel-based algorithm to enable PUAL to obtain non-linear decision boundary. We show that, through experiments on both simulated and real-world datasets, PUAL can achieve satisfactory classification on trifurcate data.