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This paper presents a new hybrid dimensionality reduction method to seek projection through optimization of both structural risk (supervised criterion) and data independence (unsupervised criterion). Classification accuracy is used as a metric to evaluate the performance of the method. By minimizing the structural risk, projection originated from the decision boundaries directly improves the classification performance from a supervised perspective. From an unsupervised perspective, projection can also be obtained based on maximum independence among features (or attributes) in data to indirectly achieve better classification accuracy over more intrinsic representation of the data. Orthogonality interrelates the two sets of projections such that minimum redundancy exists between the projections, leading to more effective dimensionality reduction. Experimental results show that the proposed hybrid dimensionality reduction method that satisfies both criteria simultaneously provides higher classification performance, especially for noisy data sets, in relatively lower dimensional space than various existing methods.