1. A method for generating a transformed Interim Connection Space for spectral data, the method comprising: accessing a first Interim Connection Space for spectral data in a full spectral space; accessing a first map, which characterizes a linear transformation from the full spectral space to a first color space; determining a second map, which characterizes a linear transformation from the first Interim Connection Space to the first color space; decomposing the first Interim Connection Space into orthogonal subspaces, the orthogonal subspaces including a first subspace that is a null space of the second map and a second subspace that is an orthogonal complement of the null space in the first Interim Connection Space; and generating the transformed Interim Connection Space based on the first subspace and the second subspace.