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This paper describes two new intraimage prediction methods based on two data dimensionality reduction methods: nonnegative matrix factorization (NMF) and locally linear embedding. These two methods aim at approximating a block to be predicted in the image as a linear combination of k-nearest neighbors determined on the known pixels in a causal neighborhood of the input block. Variable k can be seen as a parameter controlling some sort of sparsity constraints of the approximation vector. The impact of this parameter as well as of the nonnegativity and sum-to-one constraints for the addressed prediction problem has been analyzed. The prediction and RD performances of these two new image prediction methods have then been evaluated in a complete image coding-and-decoding algorithm. Simulation results show gains up to 2 dB in terms of the PSNR of the reconstructed signal after coding and decoding of the prediction residue when compared with H.264/AVC intraprediction modes, up to 3 dB when compared with template matching, and up to 1 dB when compared with a sparse prediction method.