03_Multivariate_Analysis_of_Omic
The principal componentN = number of observations K = number of variables A = number of principal components ws = scaling weights t1, t2,..., tA scores (forming matrix T) p1, p2,..., pA loadings (forming matrix P)t1 t2KXNp’1 p’2MKS Confidential3
Data pre-...
The principal componentN = number of observations K = number of variables A = number of principal components ws = scaling weights t1, t2,..., tA scores (forming matrix T) p1, p2,..., pA loadings (forming matrix P)t1 t2KXNp’1 p’2MKS Confidential3
Data pre-processing - CenteringInvestigate changes relative to the mean of the data Mean center data– Calculate the mean of each variable (column) and subtract it from each value.meanMean Center DataX_ xMKS Confidential4
Unit Variance (UV) Scaling1/SDIf variables are measured in different units, data are scaled to give each variable equal chance to influence the model Divide each variable by its standard deviation – Variance of scaled variables = 1 If variables are measured on the same scale data are generally centredXUV = x−x sdws meanUV scalingCtrMKS Confidential5
PCA - Geometric Interpretationx3t1 t2PC1xiKxiXN PC2x2x1Projections are calculated for ALL observations. The PCA model is the projections on the plane. Each projection is defined by t1 and t2.MKS Confidential 12
PCA - Geometric Interpretationt1 t2PC1PC2These projections form the score plot. Now only t1 and t2 values are used.MKS Confidential13
PCA - Geometric Interpretationx3t1PC1cos(α3)KXNp’1α3 α2 α1cos(α1) cos(α2)x2x1The direction of PC1 (and all PCs) are given by the cosine of the angles. These values are correlation coefficients and indicate how the variables “load” into PC1.MKS Confidential14
Summaryt1 t2KXNws mean p’1 p’2T and P are new matrices which summarize the original X matrixX = 1* x ¯´ + T*P´ + Eleft overEWhat’s left over is the residual (or error) matrix– This contains the unexplained variationMKS Confidential15
PCA Example - HealthIncreased risk for Heart ProblemsObservations, Scores plotVariables, Loadings plotMKS Confidential 17
本文档为【03_Multivariate_Analysis_of_Omic】，请使用软件OFFICE或WPS软件打开。作品中的文字与图均可以修改和编辑，
图片更改请在作品中右键图片并更换，文字修改请直接点击文字进行修改，也可以新增和删除文档中的内容。
该文档来自用户分享，如有侵权行为请发邮件ishare@vip.sina.com联系网站客服，我们会及时删除。
[版权声明] 本站所有资料为用户分享产生，若发现您的权利被侵害，请联系客服邮件isharekefu@iask.cn，我们尽快处理。
本作品所展示的图片、画像、字体、音乐的版权可能需版权方额外授权，请谨慎使用。
网站提供的党政主题相关内容(国旗、国徽、党徽..)目的在于配合国家政策宣传，仅限个人学习分享使用，禁止用于任何广告和商用目的。
浙公网安备 33021202002483