PCA,SVD

2024-10-19 18:42:48

PCA的数学原理

https://www.zhihu.com/question/34143886/answer/196294308

奇异值分解的揭秘（二）：降维与奇异向量的意义

奇异值分解的揭秘（一）：矩阵的奇异值分解过程

浅谈张量分解（三）：如何对稀疏矩阵进行奇异值分解？

如何直观地理解「协方差矩阵」？

PCA(主成分分析)

奇异值分解（SVD）

奇异值的物理意义是什么？

https://www.zhihu.com/question/22237507/answer/53804902

https://zhuanlan.zhihu.com/p/21580949

http://colah.github.io/posts/2014-10-Visualizing-MNIST/

https://www.matongxue.com/madocs/491.html

https://arxiv.org/pdf/1404.1100.pdf

https://stats.stackexchange.com/questions/134282/relationship-between-svd-and-pca-how-to-use-svd-to-perform-pca

http://www.ams.org/publicoutreach/feature-column/fcarc-svd

What is the intuitive relationship between SVD and PCA -- a very popular and very similar thread on math.SE.
Why PCA of data by means of SVD of the data? -- a discussion of what are the benefits of performing PCA via SVD [short answer: numerical stability].
PCA and Correspondence analysis in their relation to Biplot -- PCA in the context of some congeneric techniques, all based on SVD.
Is there any advantage of SVD over PCA? -- a question asking if there any benefits in using SVD instead of PCA [short answer: ill-posed question].
Making sense of principal component analysis, eigenvectors & eigenvalues -- my answer giving a non-technical explanation of PCA. To draw attention, I reproduce one figure here:

http://ufldl.stanford.edu/tutorial/unsupervised/PCAWhitening/

https://zh.wikipedia.org/wiki/%E5%8D%8F%E6%96%B9%E5%B7%AE%E7%9F%A9%E9%98%B5

http://www.visiondummy.com/2014/04/geometric-interpretation-covariance-matrix/

http://www.visiondummy.com/2014/05/feature-extraction-using-pca/

http://www.visiondummy.com/2014/03/divide-variance-n-1/

http://www.visiondummy.com/2014/03/eigenvalues-eigenvectors/

http://www.visiondummy.com/2014/03/eigenvalues-eigenvectors/

http://www.visiondummy.com/2014/04/geometric-interpretation-covariance-matrix/

http://pinkyjie.com/2010/08/31/covariance/

https://en.wikipedia.org/wiki/Variance

https://deeplearning4j.org/eigenvector#a-beginners-guide-to-eigenvectors-pca-covariance-and-entropy

https://stats.stackexchange.com/questions/2691/making-sense-of-principal-component-analysis-eigenvectors-eigenvalues/140579#140579

https://math.stackexchange.com/questions/24456/matrix-multiplication-interpreting-and-understanding-the-process/24469#24469

https://stats.stackexchange.com/questions/217995/what-is-an-intuitive-explanation-for-how-pca-turns-from-a-geometric-problem-wit

https://stats.stackexchange.com/questions/130721/what-norm-of-the-reconstruction-error-is-minimized-by-the-low-rank-approximation?noredirect=1&lq=1

https://stats.stackexchange.com/questions/32174/pca-objective-function-what-is-the-connection-between-maximizing-variance-and-m/136072#136072

http://blog.csdn.net/watkinsong/article/details/8234766

http://blog.csdn.net/watkinsong/article/details/38536463

https://stats.stackexchange.com/questions/10251/what-is-the-objective-function-of-pca/10256#10256

主成分分析推导

https://www.cnblogs.com/Merodach/p/9033734.html

关于PCA的形象理解

https://zhuanlan.zhihu.com/p/29993872

http://www.cnblogs.com/LeftNotEasy/archive/2011/01/19/svd-and-applications.html

PCA （主成分分析）详解（写给初学者）结合matlab

https://my.oschina.net/gujianhan/blog/225241

如何理解矩阵特征值？

https://www.zhihu.com/question/21874816/answer/181864044

行列式的本质是什么？

相似矩阵是什么？

机器学习中的数学(5)-强大的矩阵奇异值分解(SVD)及其应用

主成份分析(PCA)最详细和全面的诠释

https://mp.weixin.qq.com/s?__biz=MzI2MzAxMTA1Ng==&mid=2649499654&idx=2&sn=23f750ea4c67ac366e60067d8eb448ec&chksm=f25ae799c52d6e8fb2caf0c43e0b47cb4b0df55b1c627186baefad97b3a6deee190400d992de&mpshare=1&scene=2&srcid=0927Ddf4Tr7vrTgZCKdUVyF2&from=timeline&isappinstalled=0#wechat_redirect

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