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Entity linking (EL) is the process of linking entity mentions appearing in text with their corresponding entities in a knowledge base. EL features of entities (e.g., prior probability, relatedness score, and entity embedding) are usually estimated based on Wikipedia. However, for newly emerging entities (EEs) which have just been discovered in news, they may still not be included in Wikipedia yet. As a consequence, it is unable to obtain required EL features for those EEs from Wikipedia and EL models will always fail to link ambiguous mentions with those EEs correctly as the absence of their EL features. To deal with this problem, in this paper we focus on a new task of learning EL features for emerging entities in a general way. We propose a novel approach called STAMO to learn high-quality EL features for EEs automatically, which needs just a small number of labeled documents for each EE collected from the Web, as it could further leverage the knowledge hidden in the unlabeled data. STAMO is mainly based on self-training, which makes it flexibly integrated with any EL feature or EL model, but also makes it easily suffer from the error reinforcement problem caused by the mislabeled data. Instead of some common self-training strategies that try to throw the mislabeled data away explicitly, we regard self-training as a multiple optimization process with respect to the EL features of EEs, and propose both intra-slot and inter-slot optimizations to alleviate the error reinforcement problem implicitly. We construct two EL datasets involving selected EEs to evaluate the quality of obtained EL features for EEs, and the experimental results show that our approach significantly outperforms other baseline methods of learning EL features.