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We present a novel approach for spectral unmixing in hyperspectral imagery called local linear spectral unmixing (LLSU). Our new proposal relies on an existing strategy for non-linear data modelling where a general non-linear model is approximated via several piecewise linear models. The algorithm is the result of hybridizing two well-known strategies for exploratory high-dimensional data analysis: cluster analysis and non-negative matrix factorization. It has been proposed to answer the limitations of global linear unmixing models which are widely used for spectral unmixing. Our strategy is to first group similar pixels from the hyperspctral image via cluster analysis and then to consider a local linear unmixing model for each cluster in order to obtain the constituent endmembers. Subsequently, the resulted local endmembers from each cluster of mixed pixels are at their turn clustered based on their spectral similarity; the final solution is given by the clusters' centroids.