This paper introduces and investigates large iterative multitier ensemble (LIME) classifiers specifically tailored for big data. These classifiers are very large, but are quite easy to generate and use. They can be so large that it makes sense to use them only for big data. They are generated automatically as a result of several iterations in applying ensemble meta classifiers. They incorporate diverse ensemble meta classifiers into several tiers simultaneously and combine them into one automatically generated iterative system so that many ensemble meta classifiers function as integral parts of other ensemble meta classifiers at higher tiers. In this paper, we carry out a comprehensive investigation of the performance of LIME classifiers for a problem concerning security of big data. Our experiments compare LIME classifiers with various base classifiers and standard ordinary ensemble meta classifiers. The results obtained demonstrate that LIME classifiers can significantly increase the accuracy of classifications. LIME classifiers performed better than the base classifiers and standard ensemble meta classifiers.