Representation learning, which transfers real world data such as graphs, images and texts, into representations that can be effectively processed by machine learning algorithms, has became a new focus in machine learning community. Traditional machine learning algorithms usually focus on modeling hand-crafted feature representations manually extracted from the raw data and performance of the model highly depends on the quality of the data representation. However, feature engineering is laborious, hardly accurate, and less generalizable. Thus the weakness of many current learning algorithms is not how well they can model the data, but how good their input data representation are.

In this thesis, we adopt learning algorithms both on representing and modeling the graph data in two different applications. In the first work, We first developed representation on nodes, and later apply a well-known VG kernel on this representation. In the second work, we show the power of representation captured by applying jointly optimization on the nodes representations and the model. The results of both work show significant improvement over traditional machine learning methods.