In this article, we study algorithms for nonnegative matrix factorization (NMF) in various applications involving streaming data. Utilizing the continual nature of the data, we develop a fast two-stage algorithm for highly efficient and accurate NMF. In the first stage, an alternating non-negative least squares (ANLS) framework is used, in combination with active set method with warm-start strategy for the solution of subproblems. In the second stage, an interior point method is adopted to accelerate the local convergence. The convergence of the proposed algorithm is proved. The new algorithm is compared with some existing algorithms in benchmark tests using both real-world data and synthetic data. The results demonstrate the advantage of our algorithm in finding high-precision solutions.

翻译：在本篇文章中,我们在涉及流数据的各种应用中研究非负矩阵因子化(NMF)的算法(NMF) 。利用数据的持续性质,我们为高效和准确的NMF开发了一个快速的两阶段算法。在第一阶段,我们使用一个交替的非负最小方(ANLS)框架,结合积极设定的方法和解决子问题的热启动战略。在第二阶段,采用一个内部点方法加速本地趋同。拟议的算法的趋同得到了证明。新的算法与使用真实世界数据和合成数据的基准测试中的某些现有算法进行了比较。结果显示了我们的算法在寻找高精度解决方案方面的优势。