Data representation has received much attention in the fields of machine learning and pattern recognition. It is becoming an indispensable tool for many learning tasks. It can be useful for all learning paradigms: unsupervised, semi-supervised, and supervised. In this paper, we present a graph-based, deep and flexible data representation method using feature propagation as an internal filtering step. The presented framework ensures several desired features such as a graph-based regularization, a flexible projection model, a graph-based feature aggregation, and a deep learning architecture. The model can be learned layer by layer. In each layer, the nonlinear data representation and the unknown linear model are jointly estimated with a closed form solution. We evaluate the proposed method on semi-supervised classification tasks using six public image datasets. These experiments demonstrate the effectiveness of the presented scheme, which compares favorably to many competing semi-supervised approaches.