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This paper presents a new framework for the development of generalized composite kernel machines for hyperspectral image classification. We construct a new family of generalized composite kernels which exhibit great flexibility when combining the spectral and the spatial information contained in the hyperspectral data, without any weight parameters. The classifier adopted in this work is the multinomial logistic regression, and the spatial information is modeled from extended multiattribute profiles. In order to illustrate the good performance of the proposed framework, support vector machines are also used for evaluation purposes. Our experimental results with real hyperspectral images collected by the National Aeronautics and Space Administration Jet Propulsion Laboratory's Airborne Visible/Infrared Imaging Spectrometer and the Reflective Optics Spectrographic Imaging System indicate that the proposed framework leads to state-of-the-art classification performance in complex analysis scenarios.