The problem of estimating the principal eigenvector related to the largest eigenvalue of a given (left) stochastic matrix A has many applications in ranking search results, multi-agent consensus, networked control and data mining. The well-known power method is a typical tool, but it modifies ...
youdao The results showed why the right principal eigenvector of a judgement matrix can be regarded as the priority vector. Consistency test to a judgement matrix is also discussed. 指出了用判断矩阵的右特征向量作为排序向量的理由,并且还讨论了判断矩阵的一致性检验问题。 youdao 更多双语例句 应用...
\begin{equation*} \overrightarrow{vector_{output}} = A\times\overrightarrow{vector_{input}} \\\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space= \begin{bmatrix} 2 & 1\\ 0 & 2 \end{bmatrix}\times \begin{bmatrix} 1 ...
In this paper it is shown that the principal eigenvector is a necessary representation of the priorities derived from a positive reciprocal pairwise comparison judgment matrix A=( a ij) when A is a small perturbation of a consistent matrix. When providing numerical judgments, an individual attempt...
([119]). Let A=(aij)n×n be a nonnegative, irreducible matrix. Let si=∑j=1naij be the ith rowsum of A, and let △=maxisi and δ=minisi be the maximum and the minimum rowsums of A. If λ1 and x are the spectral radius and the principal eigenvector of A, then (2.15)x...
An eigenvector of a matrix is a non-zero vector such that when the matrix multiplies the vector, the output is a scaled version of the same vector. The scaling factor is the eigenvalue. In PCA, eigenvectors point in the direction of the largest variance, and their corresponding eigenvalues...
Fast eigenvector centrality mapping of voxel-wise connectivity in functional magnetic resonance imaging: implementation, validation, and interpretation 3. The dominant eigenvector of the original matrix A¢ (*) and of the covariance matrix of the simulated data X (,), both computed in MatLab, ....
the simplest of the true eigenvector-based multivariate analyses. Often, its operation can be thought of as revealing the internal structure of the data in a way which best explains the variance in the data. If a multivariate dataset is visualised as a set of coordinates in a ...
This paper describes an efficient algorithm for finding the principal eigenvalue and a corresponding positive eigenvector of a positive matrix. It is based on the use of a merit function for the problem. A separately quasi-convex function defined on the positive unit simplex cross the positive nu...
计算data points的covariance matrix。 做eigen decomposition,找到eigen values 和 vectors。 选取top eigenvector构建一个transformation matrix。 用这个transformation matrix把原有data points transform成low-dimension data。 具体可以参考以下python 代码: import numpy as np INPUT = [[7, 4, 3], [4, 1, 8]...