Code used in the manuscript of Jeremy E.Cohen. Please reference properly if used. - 4 toolboxes are attached, and have been slightly modified to output time and error in a fair manner. Modified code lines are denoted by '% MOD' - In the file 'Manuscript' : - file 'Tools' contains various functions used through the manuscript (Randomized HOSVD, Multiplication by multilinear operator, permutation ambiguity correction using Munkres, Khatri-rao, vectorization) - file 'Compressed' contains various implemented algorithms (ALS,ANLS,PROCO-ALS,Dykstra-ALS,Primal-dual based ALS, ADMM-ALS and Compressed ADMM-ALS) and experiments are run in 'Run_decomp', 'Chemo_simu' and 'Run_decomp2', the latter being codes for comparisons with state-of-the-art algorithms in simple scenarios. 'Chemo_simu2' is not used material. - file 'Dictionary ALS' contains the two algorithms presented in the manuscript plus a side function, a test file on synthethic data and a test file on real data provided in 'snow_subsample_GR' and 'endmembers'. - file 'Fusion' contains fluorescence and NMR coupled data and some algorithms described in the manuscript. File 'EvrimDataTestsv2' contains code for the results presented in chapter 4, while 'EvrimDataTestsvTlab' is unpublished comparison with Tensorlab. Since the codes are not yet well presented, do not hesitate to contact me. If many are interested in the codes I can make a cleaner version of it.