In this paper, we compare the state-of-the-art algorithms for text-independent speaker identification under adverse far-field recording conditions with extremely short training and testing utterances. The algorithms include both the generative and discriminative methods. For the generative methods, three variants of the original Gaussian Mixture Model (GMM) and the Universal Background Model adapted Gaussian Mixture Model (UBM-GMM) are involved. For the discriminative methods, two kernel-based algorithms, namely, the Support Vector Machine (SVM) and the Relevance Vector Machine (RVM), are considered. The comparison mainly focuses on the speaker identification accuracy and the speed of the individual algorithms (for both training and testing) as well as the sparseness of the resulting model for the kernel-based methods. Finally, we demonstrate through experiments that multi-channel fusion of the far-field recordings yields improved performance across all the above algorithms.