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Hypergraphs generalize graphs by allowing each edge, known as a hyperedge, to connect multiple vertices. Recently, hypergraph theory has gained attention for its ability to represent complex relationships in fields like social networks, collaboration networks, and brain networks. In this project, we propose a novel increasing dimensional embedding approach that jointly considers sparsity and node heterogeneity, including both degree heterogeneity and node heterogeneity in the latent dependencies among hyperedges of different orders. We have developed an efficient estimation procedure using penalized loss functions, and the resulting embeddings are applied to downstream tasks such as linkage prediction in a drug-drug interaction dataset.