Hierarchical Singular Value Decomposition of Tensors

Hierarchical Singular Value Decomposition of Tensors

Multilinear Singular Value Decomposition for Structured Tensors

The Higher-Order SVD (HOSVD) is a generalization of the Singular Value Decomposition (SVD) to higher-order tensors (i.e. arrays with more than two indices) and plays an important role in various domains. Unfortunately, this decomposition is computationally demanding. Indeed, the HOSVD of a third-order tensor involves the computation of the SVD of three matrices, which are referred to as "modes"...

Graph Clustering by Hierarchical Singular Value Decomposition with Selectable Range for Number of Clusters Members

Graphs have so many applications in real world problems. When we deal with huge volume of data, analyzing data is difficult or sometimes impossible. In big data problems, clustering data is a useful tool for data analysis. Singular value decomposition(SVD) is one of the best algorithms for clustering graph but we do not have any choice to select the number of clusters and the number of members ...

پیشنهاد روش جدیدی برای محاسبه polynomial singular value decomposition ) psvd )

در این پایان نامه به معرفی روشهای مختلف محاسبه psvd می پردازیم. بخشی از این روشها به بررسی روشهای مختلف محاسبه psvd در مقالات مطالعه شده می پردازد که می توان به محاسبهpsvd با استفاده از الگوریتمهای pqrd و pevd و sbr2 و محاسبه psvd براساس تکنیک kogbetliantz و روش پارامتریک برای محاسبه psvd اشاره نمود. بخش بعدی نیز به بررسی روشهای مستقیم پیشنهادی محاسبه psvd برای ماتریسهای 2×2و2× n و n×2 و 3× n و...

Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD)

The singular value decomposition (SVD) is a generalization of the eigen-decomposition which can be used to analyze rectangular matrices (the eigen-decomposition is definedonly for squaredmatrices). By analogy with the eigen-decomposition, which decomposes a matrix into two simple matrices, the main idea of the SVD is to decompose a rectangular matrix into three simple matrices: Two orthogonal m...