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Automated classification of hyperspectral images is a fast growing field with numerous applications in the areas of security and surveillance, agriculture, urban management, and environmental monitoring. Although significant progress has been achieved in various aspects of hyperspectral classification (e.g., feature extraction, feature selection, classification, and post-classification processing), the problem has not been addressed so far from a bias-variance decomposition point of view. In this work, we introduce a consistent unified framework that jointly considers all steps in the hyperspectral image classification chain from a bias-variance decomposition perspective. Additionally, we show how state-of-the-art techniques in feature extraction, ensemble-based classification, and post-classification segmentation are related to the bias-variance tradeoff and how this relation can be used to improve classification accuracy. An important outcome of our analysis is that all the steps of the classification chain should be optimized jointly as this unified optimization can guide toward a more favorable bias-variance tradeoff. Experimental results of the proposed framework in the case of four hyperspectral datasets prove the effectiveness of our approach.