Recent developments in the unsupervised domain adaptation (UDA) enable the unsupervised machine learning (ML) prediction for target data, thus this will accelerate real world applications with ML models such as image recognition tasks in self-driving. Researchers have reported the UDA techniques are not working well under large co-variate shift problems where e.g. supervised source data consists of handwritten digits data in monotone color and unsupervised target data colored digits data from the street view. Thus there is a need for a method to resolve co-variate shift and transfer source labelling rules under this dynamics. We perform two stages domain invariant representation learning to bridge the gap between source and target with semantic intermediate data (unsupervised). The proposed method can learn domain invariant features simultaneously between source and intermediate also intermediate and target. Finally this achieves good domain invariant representation between source and target plus task discriminability owing to source labels. This induction for the gradient descent search greatly eases learning convergence in terms of classification performance for target data even when large co-variate shift. We also derive a theorem for measuring the gap between trained models and unsupervised target labelling rules, which is necessary for the free parameters optimization. Finally we demonstrate that proposing method is superiority to previous UDA methods using 4 representative ML classification datasets including 38 UDA tasks. Our experiment will be a basis for challenging UDA problems with large co-variate shift.