Hankel矩阵及其逆矩阵的快速三角分解算法的改进

本文改进了求Hankel矩阵及其逆矩阵三角分解的Chun-Kailath快速算法,减少了该算法的计算量,提高了精度。     

对称Loewner型矩阵三角分解的快速算法

给出了对称Loewner型矩阵三角分解的快速算法，所需计算量为O（n^2)。一般矩阵三角分解的计算量为O（n^3)。     

范德蒙类矩阵之逆阵的一种三角分解

给出了范德蒙类矩阵之逆矩阵的一种三角分解算法，所需计算量为O(n^2).     

求Hankel型线性方程组的一种算法

本文给出了矩阵为Hankel矩阵的充要条件,由此定义了一种新的矩阵-Hankel型矩阵,说明了Hankel矩阵是Hankel型矩阵的特殊情况.为了降低Hankel型线性方程组的计算量和减小这类算法的误差,利用Hankel型矩阵的位移性质,给出了求Hankel型线性方程组的一种算法.矩阵为Hankel矩阵时,该算法与Gohberg-Kailath-Koltracht算法相比计算量相当,但改进了精度;矩阵为一般Hankel型矩阵时,该算法与Cholesky分解算法相比计算量大为减少,极大改进了精度.     

g-r循环矩阵求逆的快速算法

利用FFT,给出g-r循环矩阵求逆的快速算法,计算复杂性为O(n log2 n) (g 2)n。     

基于Hankel矩阵与奇异值分解（SVD）的滤波方法以及在飞机颤振试验数据预处理中的应用

将Hankle矩阵与SVD分解相结合对受噪声污染的飞机颤振试验数据进行滤波,以提高颤振模态参数识别的精度,首先对由测量数据构造的Hankle矩阵进行SVD分解,再根据对噪声统计特性的掌握程度,采用两种不同的方法,即基于噪声统计特性的方法和基于奇异值变化曲线突变点的方法,将由含噪的测量数据所构成的Hankel矩阵分成两个互不相关的空间--真实信号空间和噪声空间,最后在真实信号空间中,利用平均的方法重构经过滤波的数据.通过数值仿真和应用于实际的飞机颤振试验数据,对Hankel矩阵取不同维数时对空间划分和滤波效果的影响进行了分析和研究,并验证了该方法是有效和可行的.     

非负矩阵分解的分布式算法

提出一种解决大规模非负矩阵分解的分布式算法.非负矩阵分解一直是矩阵分解领域中的热点问题之一,已有一些相关的算法.但是,对于大规模的非负矩阵,至今尚无高效的方法.本文采用近来解决大数据的分布式思想和并行式计算方法,并将它们与传统的矩阵分解算法相结合,提出一种基于并行式计算的分布式网络算法,以此实现大规模的非负矩阵分解问题.实验结果表明,所提出的算法较一般的分布式算法与集中式矩阵分解的算法更加有效和快速.     

基于低秩Hankel矩阵逼近的模态参数识别方法

针对测量结构输出响应信号所受噪声干扰问题,提出利用低秩Hankel矩阵逼近方法对响应信号降噪。该方法利用结构脉冲响应信号构建Hankel矩阵,对其进行奇异值分解后计算奇异值相对变化率确定模型阶次,通过迭代低秩逼近方法获得降噪信号后进行模态参数识别。用数值算例研究矩阵维数对降噪效果、计算效率影响,并用悬臂梁模型实验验证该方法的有效性。     

求鳞状因子循环矩阵的逆阵及广义逆阵的快速算法

利用多项式快速算法，给出了求鳞状因子循环矩阵的逆阵、自反g-逆、群逆及Moore-Penrose逆的快速算法。该算法避免了一般快速算法中，要计算大量的三角函数等可能带来误差及影响效率的问题。该算法仅用到鳞状因子循环矩阵的第一行元素及对角阵D中的常数d1，d2，…，dn进行计算，在计算机上实现时只有舍入误差。特别地，在有理数域上用计算机求得的结果是精确的。     

非负矩阵分解及其应用探讨

介绍非负矩阵分解(non-negative matrix factorization,NMF)的基本算法思想及其实现过程,并对其在一些重要领域内的应用现状进行概括归纳,最后提出NMF方法在图像处理方面存在的问题及其改进的趋势。     

An Entity-Association-Based Matrix Factorization Recommendation Algorithm

Collaborative filtering is the most popular approach when building recommender systems, but the large scale and sparse data of the user-item matrix seriously affect the recommendation results. Recent research shows the user’s social relations information can improve the quality of recommendation. However, most of the current social recommendation algorithms only consider the user's direct social relations, while ignoring potential users’ interest preference and group clustering information. Moreover, project attribute is also important in item rating. We propose a recommendation algorithm which using matrix factorization technology to fuse user information and project information together. We first detect the community structure using overlapping community discovery algorithm, and mine the clustering information of user interest preference by a fuzzy clustering algorithm based on the project category information. On the other hand, we use project-category attribution matrix and user-project score matrix to get project comprehensive similarity and compute project feature matrix based on Entity Relation Decomposition. Fusing the user clustering information and project information together, we get Entity-Association-based Matrix Factorization (EAMF) model which can be used to predict user ratings. The proposed algorithm is compared with other algorithms on the Yelp dataset. Experimental studies show that the proposed algorithm leads to a substantial increase in recommendation accuracy on Yelp data set.     

Recommendation Algorithm Based on Probabilistic Matrix Factorization with Adaboost

A current problem in diet recommendation systems is the matching of food preferences with nutritional requirements, taking into account individual characteristics,such as body weight with individual health conditions, such as diabetes. Current dietary recommendations employ association rules, content-based collaborative filtering, and constraint-based methods, which have several limitations. These limitations are due to the existence of a special user group and an imbalance of non-simple attributes. Making use of traditional dietary recommendation algorithm researches, we combine the Adaboost classifier with probabilistic matrix factorization. We present a personalized dietrecommendation algorithm by taking advantage of probabilistic matrix factorization via Adaboost. A probabilistic matrix factorization method extracts the implicit factorsbetween individual food preferences and nutritional characteristics. From this, we can make use of those features with strong influence while discarding those with little influence. After incorporating these changes into our approach, we evaluated our algorithm’s performance. Our results show that our method performed better than others at matching preferred foods with dietary requirements, benefiting user health as a result. The algorithm fully considers the constraint relationship between users’ attributes and nutritional characteristics of foods. Considering many complex factors in our algorithm, the recommended food result set meets both health standards and users’ dietary preferences. A comparison of our algorithm with others demonstrated that our method offers high accuracy and interpretability.     

广义Vandermonde矩阵的显式LU分解

利用对称函数给出了广义Vandermonde矩阵的显示LU分解和带宽为1的分解,从而可将广义Vandermonde矩阵表示为n个带宽为1的下三角矩阵和n个带宽为1的上三角矩阵的乘积。     

友循环矩阵求逆和广义逆的Euclid算法

利用多项式的Euclid算法给出了任意域上非奇异的友循环矩阵求逆矩阵的一个新算法,该算法同时推广到用于求任意域上奇异友循环矩阵的群逆和Moore-Penrose逆,最后给出了应用该算法的数值例子。     

Loewner方程组极小范数最小二乘解的快速算法

本文给出了求以m×n阶Loewner矩阵为系数阵的线性方程组极小范数最小二乘解的快速算法。     

图像特征点集匹配的稳健非线性投影NMF方法

包含相同目标的图像由于可能存在结构差异而导致特征匹配困难、不精确,针对该问题提出了一种新的匹配方法.首先,提出一种稳健的非线性投影非负矩阵分解方法(RNPNMF),利用RNPNMF得到特征点集的共同投影空间;然后,计算特征点集在共同投影空间的投影,利用特征点集在共同投影空间上的投影实现点集的精确匹配.最后,为验证本文方法的有效性,分别对光学图像和SAR图像进行了实验,实验结果表明:和现有方法相比,本文所提方法能更精确有效的实现特征点集的匹配,同时,应用于图像配准也得到了很好的结果.