| 研究実績の概要 |
We proposed a robust tensor decomposition approach for tensor completion by defining a new tubal nuclear norm on tensors. The tubal nuclear norm has orientation invariant property which is the key contribution to improve the robustness and performance for tensor completion task.
We developed a deep multimodal learning model based on multilinear tensor fusion of latent layers. The proposed tensor fusion framework is able to capture high-order interactions for inter-modal and intra-modal features, which has more expressive power. In addition, we apply tensor network to represent weight parameters, which thus reduce the computation complexity dramatically. The proposed method can improve the performance while not increasing model and computation complexity.
We studied the theory analysis of matrix completion under linear transformations. This work provides rigorous theory support for many "non-local" based low-rank completion methods. In addition, the proposed framework is able to improve matrix completion performance by low-rankness under the multiple transformations. Experiments results show its advantages in image in-painting task.
We have developed several tensor completion algorithms based on tensor ring model. By defining tensor ring based nuclear norm, we can solve low-rank tensor approximation by nuclear norm optimizations. For large-scale data, we have developed an efficient randomized tensor ring decomposition algorithm, which is fast and scalable to very large tensors.
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