Abstract: Based on the invariability of the sought-for chemical subspace to the linear transformation, a novel approach, called chemical subspace invariant to linear transformation method, is developed for estimation of chemical rank of two way data matrices. The idea of this approach is that the chemically meaningful subspace is the most stable one with respect to the linear transformation of the two-way data along one order. Two quantitative indexes, projection residual as well as included angle of subspace, are also proposed to measure the difference of two subspaces. The results of two NIRdata show that this method provides a very promising tool for chemical rank estimation of two-way data matrices.

Key words: Subspace difference, Estimation of rank, Near-IR, Chemometrics