Approximate decoupling of multivariate polynomials using weighted tensor decomposition

Hollander Gabriel; Dreesen Philippe; Ishteva Mariya; Schoukens Johan

摘要

Summary >Many scientific and engineering disciplines use multivariate polynomials. Decomposing a multivariate polynomial vector function into a sandwiched structure of univariate polynomials surrounded by linear transformations can provide useful insight into the function while reducing the number of parameters. Such a decoupled representation can be realized with techniques based on tensor decomposition methods, but these techniques have only been studied in the exact case. Generalizing the existing techniques to the noisy case is an important next step for the decoupling problem. For this extension, we have considered a weight factor during the tensor decomposition process, leading to an alternating weighted least squares scheme. In addition, we applied the proposed weighted decoupling algorithm in the area of system identification, and we observed smaller model errors with the weighted decoupling algorithm than those with the unweighted decoupling algorithm. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract Type =“Main”XML：Lang =“en”XML：ID =“NLA2135-ABS-0001”> <标题类型=“main”>摘要</ title> >许多科学和工程学科使用多变量多项式。将多变量多项式向量函数分解成夹在由线性变换包围的单变量多项式的夹心结构中，可以在减少参数的数量的同时提供对功能的有用洞察力。这种解耦表示可以通过基于张量分解方法的技术实现，但是仅在精确的情况下已经研究了这些技术。将现有技术概括为嘈杂案例是解耦问题的重要下一步。对于这种扩展，我们已经考虑了张量分解过程中的权重因因子，导致交替加权最小二乘方案。此外，我们在系统识别领域应用了所提出的加权解耦算法，并且我们观察到比具有未加权解耦算法的解耦算法的较小模型误差。</ p> </ abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-26104/'>《Numerical linear algebra with applications》</a> <b style="margin: 0 2px;">|</b><span>2018年第2期</span><b style="margin: 0 2px;">|</b><span>共20页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Hollander Gabriel&option=202" target="_blank" rel="nofollow">Hollander Gabriel;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Dreesen Philippe&option=202" target="_blank" rel="nofollow">Dreesen Philippe;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Ishteva Mariya&option=202" target="_blank" rel="nofollow">Ishteva Mariya;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Schoukens Johan&option=202" target="_blank" rel="nofollow">Schoukens Johan;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Department VUB‐ELECVrije Universiteit Brussel (VUB)Brussels B‐1050 Belgium;</p> <p>Department VUB‐ELECVrije Universiteit Brussel (VUB)Brussels B‐1050 Belgium;</p> <p>Department VUB‐ELECVrije Universiteit Brussel (VUB)Brussels B‐1050 Belgium;</p> <p>Department VUB‐ELECVrije Universiteit Brussel (VUB)Brussels B‐1050 Belgium;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/4602.html" title="代数方程论、线性代数">代数方程论、线性代数;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=multilinear algebra&option=203" rel="nofollow">multilinear algebra;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=multivariate polynomial&option=203" rel="nofollow">multivariate polynomial;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=tensor decomposition&option=203" rel="nofollow">tensor decomposition;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=weighted least squares approximation&option=203" rel="nofollow">weighted least squares approximation;</a> </p> <div class="translation"> 机译：多线性代数;多变量多项式;张量分解;加权最小二乘近似; 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