In this work, we propose NetMF+, a fast, memory-efficient, scalable, and effective network embedding algorithm developed for a single machine with CPU only. NetMF+ is based on the theoretically grounded embedding method NetMF and leverages the theories from randomized matrix factorization to learn embedding efficiently. We firstly propose a fast randomized eigen-decomposition algorithm for the modified Laplacian matrix. Then, sparse-sign randomized single-pass singular value decomposition (SVD) is utilized to avoid constructing dense matrix and generate promising embedding. To enhance the performance of embedding, we apply spectral propagation in NetMF+. Finally, A high-performance parallel graph processing stack GBBS is used to achieve memory-efficiency. Experiment results show that NetMF+ can learn a powerful embedding from a network with more than 10^11 edges within 1.5 hours at lower memory cost than state-of-the-art methods. The result on ClueWeb with 0.9 billion vertices and 75 billion edges shows that NetMF+ saves more than half of the memory and runtime than the state-of-the-art and has better performance. The source code of NetMF+ will be publicly available after the anonymous peer review.

翻译：在这项工作中,我们提议NetMF+, 这是一种为一台仅使用CPU的机器开发的快速、记忆效率、可缩放和有效的网络嵌入算法。 NetMF+ 以基于理论的嵌入方法 NetMF 为基础, 并运用随机矩阵因子化的理论来高效嵌入。 我们首先为修改的 Laplacian 矩阵建议了一个快速随机化的igen分解算法。 然后, 使用稀释的随机化单向单向单向单向分解算法( SVD ) 来避免构建稠密的矩阵并产生有希望的嵌入。 为了提高嵌入性, 我们在 NetMF+ 中应用光谱传播。 最后, 一个高性平行图形处理堆GBBS 用于实现记忆效率。 实验结果表明, NetMF+ 可以在1.5小时内从一个存储速度超过10°11的网络中学习一个强大的快速嵌入, 其记忆成本比最新方法要低的网络。 然后, 使用 ClueWeb 的结果是 90亿 的螺旋和750亿边缘的边缘。 显示, NetMF+ 节省了一半以上的记忆和运行的代码, 将比可公开的运行运行的代码。