High-order feature interactions can capture intuitively understandable structures in data of interest. The high-order parametric embedding (HOPE) is an efficient algorithm to determine high-order features, generating data embeddings suitable for visualization. Compared to deep embedding models with complicated architectures, HOPE is considerably more effective in learning high-order feature mappings, and it can also synthesize a small number of exemplars to represent the entire dataset in a low-dimensional way. To compute this efficiently, we have developed novel techniques based on tensor factorization.

Our approach is applicable to a wide variety of problems where interpretation of the trained models is important.