MPI-FAUN: 一种基于MPI的交替更新非负矩阵分解框架
MPI-FAUN: An MPI-Based Framework for Alternating-Updating Nonnegative Matrix Factorization
AI总结：
本文提出MPI-FAUN框架，用于高效解决大规模非负矩阵分解问题，通过交替求解非负最小二乘子问题，实现并行计算，支持多种算法并能处理大规模密集和稀疏数据集。
摘要：
非负矩阵分解（NMF）是确定给定输入矩阵A的两个非负低秩因子W和H，使得A≈WH的问题。NMF在文本挖掘、视频分析和社交网络社区检测等领域有广泛应用。尽管在数据挖掘领域很受欢迎，但缺乏高效的并行算法来处理大数据集。本文的主要贡献是提出一种新的高性能并行计算框架，适用于广泛类别的NMF算法，通过迭代求解W和H的交替非负最小二乘（NLS）子问题。该框架在内存中维护数据和因子矩阵（分布于处理器上），使用MPI进行处理器间通信，并在密集情况下证明在温和假设下可最小化通信成本。该框架灵活，能够利用多种NMF和NLS算法，包括乘法更新、分层交替最小二乘和块主元翻转。我们的实现允许我们在数百万到数十亿规模的密集和稀疏数据矩阵上基准测试和比较不同算法。我们展示了算法的可扩展性，并将其与基线实现进行比较，显示出显著的性能提升。用于实验的代码和数据集可在网络上获取。
英文摘要：
Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors $W$ and $H$, for the given input matrix $A$, such that $A \approx W H$. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient parallel algorithms to solve the problem for big data sets. The main contribution of this work is a new, high-performance parallel computational framework for a broad class of NMF algorithms that iteratively solves alternating non-negative least squares (NLS) subproblems for $W$ and $H$. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). The framework is flexible and able to leverage a variety of NMF and NLS algorithms, including Multiplicative Update, Hierarchical Alternating Least Squares, and Block Principal Pivoting. Our implementation allows us to benchmark and compare different algorithms on massive dense and sparse data matrices of size that spans for few hundreds of millions to billions. We demonstrate the scalability of our algorithm and compare it with baseline implementations, showing significant performance improvements. The code and the datasets used for conducting the experiments are available online.
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