Abstract
Recent approaches to the tensor completion problem have often overlooked the nonnegative structure of the data. We consider the problem of learning a nonnegative low-rank tensor, and using duality theory, we propose a novel factorization of such tensors. The factorization decouples the nonnegative constraints from the low-rank constraints. The resulting problem is an optimization problem on manifolds, and we propose a variant of Riemannian conjugate gradients to solve it. We test the proposed algorithm across various tasks such as colour image inpainting, video completion, and hyperspectral image completion. Experimental results show that the proposed method outperforms many state-of-the-art tensor completion algorithms.
Abstract (translated)
最近的Tensor completion问题的解决方案常常忽略了数据的非负结构。我们考虑学习非负低秩 Tensor 的问题，并使用双极理论提出了一种新的 Tensor Factorization。该Factorization将非负约束与低秩约束分离。结果是一个多态优化问题，我们提出了黎曼反交换梯度的一种变体来解决这个问题。我们测试了该算法在各种任务，如彩色图像修复、视频填充和高光谱图像填充。实验结果表明，该方法在许多最先进的 Tensor completion 算法中表现优异。
URL
https://arxiv.org/abs/2305.07976
