Boosting is the general method which converts any weak learning algorithm into strong learner in order to improve the accuracy. The limitations in boosting is overfitting on the training data and filtering out the correct data in the subsequent function since boosting concentrates on regions not predicted well by other learners. So, the cluster based boosting (CBB) approach is used to address limitations in boosting. In this paper, initially X-Means algorithm is used to cluster the data and the clusters are selectively boosted based on the additional structure information provided by clusters and previous function accuracy on the member data. To apply Cluster Based Boosting to the high dimensional data, dimensionality reduction technique is performed. In this paper, we apply Global Redundancy Minimization frame work which considers the redundancy of the feature with all other features. The selected features will contribute more mutual information for prediction. This frame work can be used with any other feature selection technique. We provide experimental results on various dataset. These results demonstrate the effectiveness of Global redundancy framework and also effectiveness of Cluster Based Boosting with Global redundancy minimization framework than classifier with global redundancy minimization framework.