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Detection of clouds in satellite-generated radiance images, including those from MODIS, is an important first step in many applications of these data. In this paper we apply spectral unmixing to this problem with the aim of estimating subpixel cloud fractions, as opposed to identification only of whether or not a pixel radiance contains cloud contributions. We formulate the spectral unmixing approach in terms of multiple-kernel learning (MKL). To this end we propose a MKL-based unmixing algorithm that drives a multiple-kernel description of cloud, enabling estimation of sub-pixel cloud fractions. This approach is based on supervised learning. We generate training and testing samples by using CloudSat and CALIPSO data to compute cloud fractions within individual MODIS pixels. Results of our study on limited data (1875 training and testing MODIS pixels along with their CloudSat and CALIPSO based sub-pixel cloud fractions) show that the proposed algorithm can effectively estimate sub-pixel MODIS cloud fraction and outperforms support vector machine (SVM) in terms of estimation performance.