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Many-objective optimization problems involving a large number (more than four) of objectives have aroused extensive attention. It is known that problems with a high number of objectives cause additional difficulties in visualization of the objective space, stagnation in search process and high computational cost. In this paper, a special class of many objective problems, which can be degenerated to a lower dimensional Pareto optimal front, has been investigated. A new objective reduction strategy based on clustering algorithm is proposed, meanwhile, we adopt a new criterion to measure the relationship between pairs of objectives by employing the concept of mutual information. The paper concludes with experimental results that the proposed objective reduction method can accurately eliminate redundant objectives and efficiently obtain essential objective set from original many-objective set on a wide range of test problems.