{"title":"基于 ReLU 的非线性矩阵分解的动量加速算法","authors":"Qingsong Wang;Chunfeng Cui;Deren Han","doi":"10.1109/LSP.2024.3475910","DOIUrl":null,"url":null,"abstract":"Recently, there has been a growing interest in the exploration of Nonlinear Matrix Decomposition (NMD) due to its close ties with neural networks. NMD aims to find a low-rank matrix from a sparse nonnegative matrix with a per-element nonlinear function. A typical choice is the Rectified Linear Unit (ReLU) activation function. To address over-fitting in the existing ReLU-based NMD model (ReLU-NMD), we propose a Tikhonov regularized ReLU-NMD model, referred to as ReLU-NMD-T. Subsequently, we introduce a momentum accelerated algorithm for handling the ReLU-NMD-T model. A distinctive feature, setting our work apart from most existing studies, is the incorporation of both positive and negative momentum parameters in our algorithm. Our numerical experiments on real-world datasets show the effectiveness of the proposed model and algorithm.","PeriodicalId":13154,"journal":{"name":"IEEE Signal Processing Letters","volume":null,"pages":null},"PeriodicalIF":3.2000,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Momentum Accelerated Algorithm for ReLU-Based Nonlinear Matrix Decomposition\",\"authors\":\"Qingsong Wang;Chunfeng Cui;Deren Han\",\"doi\":\"10.1109/LSP.2024.3475910\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Recently, there has been a growing interest in the exploration of Nonlinear Matrix Decomposition (NMD) due to its close ties with neural networks. NMD aims to find a low-rank matrix from a sparse nonnegative matrix with a per-element nonlinear function. A typical choice is the Rectified Linear Unit (ReLU) activation function. To address over-fitting in the existing ReLU-based NMD model (ReLU-NMD), we propose a Tikhonov regularized ReLU-NMD model, referred to as ReLU-NMD-T. Subsequently, we introduce a momentum accelerated algorithm for handling the ReLU-NMD-T model. A distinctive feature, setting our work apart from most existing studies, is the incorporation of both positive and negative momentum parameters in our algorithm. Our numerical experiments on real-world datasets show the effectiveness of the proposed model and algorithm.\",\"PeriodicalId\":13154,\"journal\":{\"name\":\"IEEE Signal Processing Letters\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.2000,\"publicationDate\":\"2024-10-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Signal Processing Letters\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/10706860/\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Signal Processing Letters","FirstCategoryId":"5","ListUrlMain":"https://ieeexplore.ieee.org/document/10706860/","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
A Momentum Accelerated Algorithm for ReLU-Based Nonlinear Matrix Decomposition
Recently, there has been a growing interest in the exploration of Nonlinear Matrix Decomposition (NMD) due to its close ties with neural networks. NMD aims to find a low-rank matrix from a sparse nonnegative matrix with a per-element nonlinear function. A typical choice is the Rectified Linear Unit (ReLU) activation function. To address over-fitting in the existing ReLU-based NMD model (ReLU-NMD), we propose a Tikhonov regularized ReLU-NMD model, referred to as ReLU-NMD-T. Subsequently, we introduce a momentum accelerated algorithm for handling the ReLU-NMD-T model. A distinctive feature, setting our work apart from most existing studies, is the incorporation of both positive and negative momentum parameters in our algorithm. Our numerical experiments on real-world datasets show the effectiveness of the proposed model and algorithm.
期刊介绍:
The IEEE Signal Processing Letters is a monthly, archival publication designed to provide rapid dissemination of original, cutting-edge ideas and timely, significant contributions in signal, image, speech, language and audio processing. Papers published in the Letters can be presented within one year of their appearance in signal processing conferences such as ICASSP, GlobalSIP and ICIP, and also in several workshop organized by the Signal Processing Society.