简单总结R语言PCA相关函数 这里是数据集

yearX1X2X319511-2.7-4.31952-5.3-5.9-3.51953-2-3.4-0.81954-5.7-4.7-1.11955-0.9-3.8-3.11956-5.7-5.3-5.91957-2.1-5-1.619580.6-4.3-0.21959-1.7-5.721960-3.6-3.61.319613-3.1-0.819620.1-3.9-1.11963-2.6-3-5.21964-1.4-4.9-1.71965-3.9-5.7-2.51966-4.7-4.8-3.31967-6-5.6-4.91968-1.7-6.4-5.11969-3.4-5.6-2.91970-3.1-4.2-21971-3.8-4.9-3.91972-2-4.1-2.41973-1.7-4.2-21974-3.6-3.3-21975-2.7-3.70.11976-2.4-7.6-2.2

princomp

这个函数是R中的标准PCA函数，可用cor，也可用cov协方差阵来做PCA

> pca <- princomp(temprature) > summary(pca,loadings = T) Importance of components: Comp.1 Comp.2 Comp.3 Standard deviation 2.3927483 1.6766875 1.0093123 #标准差，特征值的平方根 Proportion of Variance 0.5991735 0.2942137 0.1066129 #方差比 Cumulative Proportion 0.5991735 0.8933871 1.0000000 #方差累积 #载荷阵，特征向量，(有些缺失值一直不知道为什么，回头在填坑) Loadings: Comp.1 Comp.2 Comp.3 X1 0.800 -0.532 0.278 X2 0.238 -0.145 -0.960 X3 0.551 0.834

相关数据

#输出每组的得分，也可用predict(pca) > pca$scores Comp.1 Comp.2 Comp.3 1951 2.1396991 -3.83416758 -0.86081047 1952 -3.2170709 0.65036989 0.46732300 1953 1.5047115 0.78326549 -0.98770616 1954 -1.9282363 2.69070902 -0.77199999 1955 1.0208400 -1.66238671 -0.32088258 1956 -4.7179457 -1.22586764 -0.24479186 1957 0.6034101 0.40169317 0.51297983 1958 3.7008125 0.03107027 0.60645276 1959 2.7423145 3.29340498 1.33340102 1960 1.3359150 3.41533524 -1.21947452 1961 5.5741402 -1.92082051 0.11577404 1962 2.8996923 -0.51171559 0.07392112 1963 -1.3065888 -2.62572541 -1.58383704 1964 1.1317614 -0.06871931 0.61074000 1965 -1.4985797 0.71048716 0.67510633 1966 -2.3656444 0.33808233 -0.42011674 1967 -4.4776216 -0.18852359 -0.02993928 1968 -1.3395824 -2.52711224 1.93314844 1969 -1.2956017 0.09625872 0.71413634 1970 -0.2267435 0.48388739 -0.53777663 1971 -2.0006306 -0.62674492 -0.07971504 1972 0.4560127 -0.44959984 -0.33175339 1973 0.8927389 -0.26104978 -0.14812577 1974 -0.4127266 0.61914798 -1.54132776 1975 1.3700344 1.95003688 -0.88520432 1976 -0.5851104 0.43868459 2.92047869 #载荷阵 > pca$loadings Loadings: Comp.1 Comp.2 Comp.3 X1 0.800 -0.532 0.278 X2 0.238 -0.145 -0.960 X3 0.551 0.834 > screeplot(pca,type = "lines")#碎石图

biplot(pca)#绘制主成分方向图

椭圆图还不会画，等以后填坑

注意

若要用相关系数矩阵，指定参数 cor=true若要求完整载荷矩阵(权重矩阵)可以用cor，或者cov先求协差阵或相关阵，然后用eigen求特征值和特征向量(不过一般不需要用完整特征向量数据)

principal

应用平行法则挑选主成分

> fa.parallel(temprature,n.iter = 100,fa="pc",main="screen plot with parallel analysis") Parallel analysis suggests that the number of factors = NA and the number of components = 1

他会画出图，应用平行法则挑选主成分变量

主成分principal

参数 - data: 相关矩阵或者数据框 - rotate: 指定旋转方法 - scores: 是否计算得分 - nfactor: 主成分个数

> pca <- principal(temprature,rotate = "none",nfactors = 2,scores = T) > pca Principal Components Analysis Call: principal(r = temprature, nfactors = 2, rotate = "none", scores = T) Standardized loadings (pattern matrix) based upon correlation matrix PC1 PC2 h2 u2 com X1 0.82 -0.11 0.69 0.313 1.0 X2 0.74 -0.51 0.81 0.193 1.8 X3 0.63 0.75 0.95 0.045 1.9 PC1 PC2 SS loadings 1.62 0.83 Proportion Var 0.54 0.28 Cumulative Var 0.54 0.82 Proportion Explained 0.66 0.34 Cumulative Proportion 0.66 1.00 Mean item complexity = 1.6 Test of the hypothesis that 2 components are sufficient. The root mean square of the residuals (RMSR) is 0.17 with the empirical chi square 4.31 with prob < NA Fit based upon off diagonal values = 0.73

得分和权重

> pca$weights PC1 PC2 X1 0.5067548 -0.1384156 X2 0.4575790 -0.6118978 X3 0.3885133 0.9012161 > pca$scores PC1 PC2 1951 1.15613102 -2.14274863 1952 -1.40397385 0.29619057 1953 0.87645580 0.02225637 1954 -0.55355307 0.79852707 1955 0.52133957 -0.89617467 1956 -1.73868595 -1.09440483 1957 0.07029356 0.49584374 1958 1.25079371 0.60192968 1959 0.60373762 2.49012260 1960 0.84116086 1.19371677 1961 2.16014463 -0.45293824 1962 1.11189864 0.01144684 1963 0.02078349 -2.17040460 1964 0.25282918 0.35309338 1965 -0.80115014 0.56219311 1966 -0.79512763 -0.22411286 1967 -1.72761805 -0.45915894 1968 -1.07610798 -0.40767704 1969 -0.72471773 0.29431309 1970 0.06988130 -0.04170145 1971 -0.74303145 -0.50504203 1972 0.28630899 -0.34781995 1973 0.39653695 -0.13092458 1974 0.30440309 -0.47945781 1975 0.77438081 0.63703597 1976 -1.13311339 1.59589645