The collinear expansion technique is generalized to thefactorization of unintegrated parton distributions and other higher twistparton correlations from the corresponding collinear hard parts thatinvolve multiple parton final state interaction. Such a generalizedfactorization provides a consistent approach to the calculation ofinclusive and semi-inclusive cross sections of deep-inelasticlepton-nucleon scattering. As an example, the azimuthal asymmetry iscalculated to the order of 1/Q in semi-inclusive deeply inelasticlepton-nucleon scattering with transversely polarized target. Anon-vanishing single-spin asymmetry in the triggered inclusive processis predicted to be 1/Q suppressed with a part of the coefficient relatedto a moment of the Sivers function.