Deep learning in compression is indeed a high-dimensional regression problem that try to exploit large amount of training data with a good trade-off of the Degree-of-Freedom (DoF) in prediction model. In particular for the High Efficiency Video Coding intra prediction problem, how to best predict pixels from surrounding context is the key efficiency challenge. In this work, we developed an alternative hierarchical piece-wise linear projection based on Canonical Correlation Analysis (CCA) method that allows for much larger DoF in the modeling in intra-prediction. Besides, we try to predict the transform coefficients in transform domain instead of the pixel values in spatial domain to reduce the DoF and obtain more general CCA model. Simulation results yield interesting coding gains, and the proposed framework has a lot of flexibility in designing the prediction architecture and rate-distortion trade-offs.