With the advancements in computing technology and web-based applications, data are increasingly generated in multi-dimensional form. These data are usually sparse due to the presence of a large number of users and fewer user interactions. To deal with this, the Nonnegative Tensor Factorization (NTF) based methods have been widely used. However existing factorization algorithms are not suitable to process in all three conditions of size, density, and rank of the tensor. Consequently, their applicability becomes limited. In this article, we propose a novel fast and efficient NTF algorithm using the element selection approach. We calculate the element importance using Lipschitz continuity and propose a saturation point-based element selection method that chooses a set of elements column-wise for updating to solve the optimization problem. Empirical analysis reveals that the proposed algorithm is scalable in terms of tensor size, density, and rank in comparison to the relevant state-of-the-art algorithms.

中文翻译：

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通过饱和坐标下降的高效非负张量分解

随着计算技术和基于 Web 的应用程序的进步，数据越来越多地以多维形式生成。由于存在大量用户和较少的用户交互，这些数据通常是稀疏的。为了解决这个问题，基于非负张量分解 (NTF) 的方法已被广泛使用。然而，现有的分解算法并不适合在张量的大小、密度和秩这三个条件下进行处理。因此，它们的适用性变得有限。在本文中，我们提出了一种使用元素选择方法的新型快速高效的 NTF 算法。我们使用 Lipschitz 连续性计算元素重要性，并提出了一种基于饱和点的元素选择方法，该方法按列选择一组元素进行更新以解决优化问题。