在《深度学习》\textsuperscript{\cite{dl}}一书中,为说明Linear ALgebra在深度学习中的作用,chapter2的最后一节引入了PCA的思想,并且为方便起见,提前给定了解码器的映射,即 f(c)=Dc ,其中D∈Rn×l , 那么相应的编码器的映射需要依照解码器给出,在教材中利用 L2 范数对解码后的向量与原向量间距离最小给出...
向量v \in R^n在标准基e_1、e_2 ... e_n下的坐标为x = \left[ \begin{array}{} x_1&x...
Eigenvalues and Eigenvectors: Foundational concepts in linear algebra, eigenvalues and eigenvectors are essential components of PCA, serving as the basis for deriving principal components. Multivariate Analysis: An overarching framework that includes PCA, multivariate analysis encompasses various statistical metho...
We know that v is a covariance matrix, so it is symmetric, and then linear algebra tells us that the eigenvectors must be orthogonal to one another. Again because v is a covariance matrix, it is a positive matrix, in the sense that This tells us that the eigenvalues of v must all be...
Principal component analysis (PCA) is the first somewhat advanced technique discussed in this book. While everything else thus far has been simple statistics, PCA will combine statistics and linear algebra to produce a preprocessing step that can help to reduce dimensionality, which can be the enem...
If you are familiar with the language of linear algebra, you could also say that principal component analysis is finding the eigenvectors of the covariance matrix to identify the directions of maximum variance in the data. One important thing to note about PCA is that it is an unsupervised ...
SVD is based on a theorem from linear algebra which says that a rectangular matrix M can be split down into the product of three new matrices: An orthogonal matrix U; A diagonal matrix S; The transpose of an orthogonal matrix V. Usually the theorem is written as follows: Mmn=UmmSmn...
SVD is based on a theorem from linear algebra which says that a rectangular matrix M can be split down into the product of three new matrices: An orthogonal matrix U; A diagonal matrix S; The transpose of an orthogonal matrix V. Usually the theorem is written as follows: Mmn=UmmSm...
PCA Banknotesimport numpy as np # linear algebra iNotebookInputOutputLogsComments (1)Logs check_circle Successfully ran in 14.1s Accelerator None Environment Latest Container Image Output 0 B Something went wrong loading notebook logs. If the issue persists, it's likely a problem on our side.Re...
Eigenvectors and eigenvalues are the linear algebra concepts that we need to compute from the covariance matrix in order to determine the principal components of the data. What you first need to know about eigenvectors and eigenvalues is that they always come in pairs, so that every eigenvector ...