Generation of a transformed Interim Connection Space for spectral data is provided. A first Interim Connection Space for spectral data in a full spectral space is accessed. A first map, which characterizes a linear transformation from the full spectral space to a first color space, is accessed. A second map, which characterizes a linear transformation from the first Interim Connection Space to the first color space, is determined. The first Interim Connection Space is decomposed 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. The transformed Interim Connection Space is generated based on the first subspace and the second subspace.