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Representation learning is a fundamental building block for analyzing entities in a database. While the existing embedding learning methods are effective in various data mining problems, their applicability is often limited because these methods have pre-determined assumptions on the type of semantics captured by the learned embeddings, and the assumptions may not well align with specific downstream tasks. In this work, we propose an embedding learning framework that 1) uses an input format that is agnostic to input data type, 2) is flexible in terms of the relationships that can be embedded into the learned representations, and 3) provides an intuitive pathway to incorporate domain knowledge into the embedding learning process. Our proposed framework utilizes a set of entity-relation-matrices as the input, which quantifies the affinities among different entities in the database. Moreover, a sampling mechanism is carefully designed to establish a direct connection between the input and the information captured by the output embeddings. To complete the representation learning toolbox, we also outline a simple yet effective post-processing technique to properly visualize the learned embeddings. Our empirical results demonstrate that the proposed framework, in conjunction with a set of relevant entity-relation-matrices, outperforms the existing state-of-the-art approaches in various data mining tasks.