Humans can learn word-object associations from ambiguous data using cross-situational learning and have been shown to be more efficient when actively choosing the learning sample order. Implementing such a capacity in robots has been performed using several models, among which are the latent-topic learning models based on Non-Negative Matrix Factorization and Latent Dirichlet Allocation. We compare these approaches on the same data in a batch and in an incremental learning scenario to analyze their strength and weaknesses and furthermore show that they can be the basis for efficient active learning strategies. The proposed modeling deals with both the referential ambiguity and the noisy linguistic descriptions and is grounding meanings of object's modal features (color and shape) and not only the object identity. The resulting active learning strategy is briefly discussed in comparison with active cross-situational learning of object names performed by humans.