Here , instead of sharing a low - dimensional structure , each data vector can now reside in a separate low - dimensional subspace . Therefore , together the data matrix admits a union - of - subspace model . As a result of this additional flexibility , DL finds applications in a wide range of signal processing and machine learning tasks , such as denoising , image inpainting ( Mairal et al . , 2009 ) , clustering and classification ( Ramirez et al . , 2010;Rambhatla and Haupt , 2013;Rambhatla et al . , 2016;2017;2019b;a ) , and analysis of deep learning primitives ( Ranzato et al . , 2008;Gregor and LeCun , 2010 ) ; see also Elad ( 2010 ) , and references therein .