Estimation of rank by chemical subspace invariant to linear transformationmethod

Based on the invariability of the sought-for chemical subspace to the linea r transformation, a novel approach, called chemical subspace invariant to l inear transformation method, is developed for estimation of chemical rank o f two-way data matrices. The idea of this approach is that the chemically m eaningful subspace is the most stable one with respect to the linear transf ormation of the two-way data along one order. Two quantitative indexes, pro jection residual as well as included angle of subspace, are also proposed t o measure the difference of two subspaces. The results of two NIR data show that this method provides a very promising tool for chemical rank estimati on of two-way data matrices.