无向高维稀疏网络的深度潜在因子模型  

Deep Latent Factor Model for Undirected High-dimensional Sparse Networks

作　　者：吴金荣 胡建华[1] 宋燕[2] 沈春根 WU Jin-rong;HU Jian-hua;SONG Yan;SHEN Chun-gen(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China;Department of Control Science and Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学理学院,上海200093 [2]上海理工大学光电信息与计算机工程学院,上海200093

出　　处：《小型微型计算机系统》2023年第7期1375-1381,共7页Journal of Chinese Computer Systems

基　　金：国家自然科学基金项目(62073223)资助。

摘　　要：无向、高维、稀疏网络是工业中经常遇到的问题,通常用高维、对称、稀疏矩阵来描述.潜在因子模型是从高维稀疏矩阵的少量已知信息中提取有用知识的一种经典方法.随着深度学习广泛应用于机器学习,以矩阵分解形式的深度潜在因子模型被提出.然而,目前多层次的矩阵分解模型其本质是线性模型,并难以满足矩阵非负性和对称性的要求.本文提出了非线性的深度非负、对称潜在因子模型(DNSLF)用于高维对称稀疏数据补全;在多层潜在因子之间搭建非线性映射的传递函数,严格保证了目标矩阵的非负性和对称性;为了更高效的求解模型,设计了一个步长自适应的迭代优化算法.通过与一些较新的潜在因子模型的对比实验结果表明,新提出的方法在高维对称稀疏矩阵补全时有显著的优越性.Undirected,high-dimensional,sparse networks,which are frequently encountered problems in industry,are usually described by high-dimensional,symmetric,sparse matrices.Latent factor models are classical methods to extract useful knowledge from a small amount of known information in high-dimensional sparse matrices.As deep learning is widely used in machine learning,deep latent factor models in the form of matrix decomposition have been proposed.However,the current multi-level matrix decomposition models are linear in nature.What is more,it is difficult to meet the requirements for symmetry and non-negativity of matrices.In this paper,a nonlinear deep nonnegative symmetric latent factor model(DNSLF)is proposed to complete high-dimensional symmetric sparse matrices;The transfer function,which is of nonlinear mapping between multi-layer latent factors,has been introduced to strictly guarantee the non-negativity and symmetry of the target matrix;An iterative optimization algorithm with adaptive step size is designed in order to solve the model more efficiently.Compared with some state-of-the-art latent factor models,the results have shown that the newly proposed method has significant superiority in the completion of high-dimensional symmetric sparse matrix.

关 键 词：高维稀疏矩阵 潜在因子 非线性 非负性 对称性 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]