  In this paper, we propose a Tensor Train Neighborhood Preserving Embedding
(TTNPE) to embed multi-dimensional tensor data into low dimensional tensor
subspace. Novel approaches to solve the optimization problem in TTNPE are
proposed. For this embedding, we evaluate novel trade-off gain among
classification, computation, and dimensionality reduction (storage) for
supervised learning. It is shown that compared to the state-of-the-arts tensor
embedding methods, TTNPE achieves superior trade-off in classification,
computation, and dimensionality reduction in MNIST handwritten digits and
Weizmann face datasets.
