In recent years, many research works propose to embed the network structured data into a low-dimensional feature space, where each node is represented as a feature vector. However, due to the detachment of embedding process with external tasks, the learned embedding results by most existing embedding models can be ineffective for application tasks with specific objectives, e.g., community detection or information diffusion. In this paper, we propose study the application oriented heterogeneous social network embedding problem. Significantly different from the existing works, besides the network structure preservation, the problem should also incorporate the objectives of external applications in the objective function. To resolve the problem, in this paper, we propose a novel network embedding framework, namely the "appLicAtion orienTed neTwork Embedding" (Latte) model. In Latte, the heterogeneous network structure can be applied to compute the node "diffusive proximity" scores, which capture both local and global network structures. Based on these computed scores, Latte learns the network representation feature vectors by extending the autoencoder model model to the heterogeneous network scenario, which can also effectively unite the objectives of network embedding and external application tasks. Extensive experiments have been done on real-world heterogeneous social network datasets, and the experimental results have demonstrated the outstanding performance of Latte in learning the representation vectors for specific application tasks.