To deal with ambiguities in partial label learning (PLL), the existing PLL methods implement disambiguations, by either identifying the ground-truth label or averaging the candidate labels. However, these methods can be easily misled by the false-positive labels in the candidate label set. We find that these ambiguities often originate from the noise caused by highly correlated or overlapping candidate labels, which leads to the difficulty in identifying the ground-truth label on the first attempt. To give the trained models more tolerance, we first propose the top-k partial loss and convex top-k partial hinge loss. Based on the losses, we present a novel top-k partial label machine (TPLM) for partial label classification. An efficient optimization algorithm is proposed based on accelerated proximal stochastic dual coordinate ascent (Prox-SDCA) and linear programming (LP). Moreover, we present a theoretical analysis of the generalization error for TPLM. Comprehensive experiments on both controlled UCI datasets and real-world partial label datasets demonstrate that the proposed method is superior to the state-of-the-art approaches.