Application of the NMF and PCA methods (introduced in Sect. 3.2) to the M filaments of the Berschel G210 field. Top left: 2D histogram of the relative orientation angle (in absolute value) between M filaments and the magnetic field, , as a function of H₂ column density, . Top right: profiles of the two principal components derived with NMF as functions of . Bottom: relative weights of the two principal components as functions of . Contour lines of the residual of the reconstruction with the two principal components are overplotted on the 2D histogram.