Twin Kernel Embedding with back constraints

Twin Kernel Embedding (TKE) is a novel approach for visualization of non-vectorial objects. It preserves the similarity structure in high-dimensional or structured input data and reproduces it in a low dimensional latent space by matching the similarity relations represented by two kernel gram matrices, one kernel for the input data and the other for embedded data. However, there is no explicit mapping from the input data to their corresponding low dimensional embeddings. We obtain this mapping by including the back constraints on the data in TKE in this paper. This procedure still emphasizes the locality preserving. Further, the smooth mapping also solves the problem of so-called out-of-sample problem which is absent in the original TKE. Experimental evaluation on different real world data sets verifies the usefulness of this method.