论文标题
通过交替的投影和素描的低级别非负张量近似
Low-rank nonnegative tensor approximation via alternating projections and sketching
论文作者
论文摘要
我们展示了如何在Tucker和Tensor火车格式中构建非负张量的非负低级别近似值。我们分别使用STHOSVD和TTSVD算法分别使用非负轨道和一组低级别张量之间的交替投影，并使用随机草图进一步加速交替的投影。关于合成数据和高光谱图像的数值实验表明，负元素的衰减，并且所得近似的误差接近使用STHOSVD和TTSVD获得的初始误差。在计算复杂性和负元素的衰减方面，提出的塔克病例的方法优于先前的方法。据我们所知，张量火车案例以前尚未研究过。
We show how to construct nonnegative low-rank approximations of nonnegative tensors in Tucker and tensor train formats. We use alternating projections between the nonnegative orthant and the set of low-rank tensors, using STHOSVD and TTSVD algorithms, respectively, and further accelerate the alternating projections using randomized sketching. The numerical experiments on both synthetic data and hyperspectral images show the decay of the negative elements and that the error of the resulting approximation is close to the initial error obtained with STHOSVD and TTSVD. The proposed method for the Tucker case is superior to the previous ones in terms of computational complexity and decay of negative elements. The tensor train case, to the best of our knowledge, has not been studied before.
