We propose a new multiple instance learning (MIL) algorithm to learn image categories. Unlike existing MIL algorithms, in which the individual instances in a bag are assumed to be independent with each other, we develop concurrent tensors to explicitly model the inter-dependency between the instances to better capture image's inherent semantics. Rank-1 tensor factorization is then applied to obtain the label of each instance. Furthermore, we formulate the classification problem in the Reproducing Kernel Hilbert Space (RKHS) to extend instance label prediction to the whole feature space. Finally, a regularizer is introduced, which avoids overfitting and significantly improves learning machine's generalization capability, similar to that in SVMs. We report superior categorization performances compared with key existing approaches on both the COREL and the Caltech datasets.