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In this paper, we focus on the problem of extreme learning machine (ELM)-based microarray data classification. Different from the traditional classification problem, the goal in this case is not just to predict the class labels for the unseen samples, but to make clear what lead to the results, i.e., the genes involving with a specific disease. This is especially significant for biologists, since they need to decipher the causes of disease. As a black-box method, ELM could not measure up to the task by itself. In this work, we propose a diversified sequence feature selection-based framework to address the problem. In this framework, (1) a sequence model, EWave, is introduced to ensure the structural ordering information among genes exploitable; (2) a concept of irreducible sequence is proposed, where the genes work as an orderly whole to keep high confidence with a specific class and any reduction in the genes decreases the confidence much. An efficient sequence mining algorithm together with some effective pruning rules is developed to mine such sequences; and (3) we study how to extract a set of diversified sequence features as the representative of all mined results. The problem is proved to be NP-hard. A greedy algorithm is presented to approximate the optimal solution. Experimental results show that the proposed approach significantly improves the efficiency and the effectiveness of ELM w.r.t some widely used feature selection techniques. [ABSTRACT FROM AUTHOR]