R软件 主成分分析.docx

R软件 主成分分析.docx

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R软件主成分分析

1.盐泉水化学分析资料的主成分分析和因子分析：

今有20个盐泉，盐泉的水化学特征系数值见下表.试对盐泉的水化学分析资料作主成分分析和因子分析.

X1

X2

X3

X4

X5

X6

X7

1

11.835

0.48

14.36

25.21

25.21

0.81

0.98

2

45.596

0.526

13.85

24.04

26.01

0.91

0.96

3

3.525

0.086

24.40

49.3

11.3

6.82

0.85

4

3.681

0.37

13.57

25.12

26.0

0.82

1.01

5

48.287

0.386

14.5

25.9

23.32

2.18

0.93

6

17.956

0.28

9.75

17.05

37.2

0.464

0.98

7

7.37

0.506

13.6

34.28

10.69

8.8

0.56

8

4.223

0.34

3.8

7.1

88.2

1.11

0.97

9

6.442

0.19

4.7

9.1

73.2

0.74

1.03

10

16.234

0.39

3.1

5.4

121.5

0.42

1.0

11

10.585

0.42

2.4

4.7

135.6

0.87

0.98

12

23.535

0.23

2.6

4.6

151.8

0.31

1.02

13

5.398

0.12

2.8

6.2

111.2

1.14

1.07

14

283.149

0.148

1.763

2.968

215.86

0.14

0.98

15

316.604

0.317

1.453

2.432

263.41

0.249

0.98

16

307.31

0.173

1.627

2.729

235.7

0.214

0.99

17

322.515

0.312

1.382

2.32

282.21

0.024

1.00

18

254.58

0.297

0.899

1.476

410.3

0.239

0.93

19

304.092

0.283

0.789

1.357

438.36

0.193

1.01

20

202.446

0.042

0.741

1.266

309.77

0.29

0.99

其中x1:

矿化度（g/L）;x2:

Br•103/Cl;x3:

K•103/Σ盐;x4:

K•103/Cl;x5:

Na/K;x6:

Mg•102/Cl;x7:

εNa/εCl.

1.数据准备

导入数据保存在对象saltwell中

>saltwell<-read.table（"c:

/saltwell.txt",header=T）

>saltwell

X1X2X3X4X5X6X7

111.8350.48014.36025.21025.210.8100.98

245.5960.52613.85024.04026.010.9100.96

33.5250.08624.40049.30011.306.8200.85

43.6810.37013.57025.12026.000.8201.01

548.2870.38614.50025.90023.322.1800.93

617.9560.2809.75017.05037.200.4640.98

77.3700.50613.60034.28010.698.8000.56

84.2230.3403.8007.10088.201.1100.97

96.4420.1904.7009.10073.200.7401.03

1016.2340.3903.1005.400121.500.4201.00

1110.5850.4202.4004.700135.600.8700.98

1223.5350.2302.6004.600151.800.3101.02

135.3980.1202.8006.200111.201.1401.07

14283.1490.1481.7632.968215.860.1400.98

15316.6040.3171.4532.432263.410.2490.98

16307.3100.1731.6272.729235.700.2140.99

17322.5150.3121.3822.320282.210.0241.00

18254.5800.2970.8991.476410.300.2390.93

19304.0920.2830.7891.357438.360.1931.01

20202.4460.0420.7411.266309.770.2900.99

>

2.数据分析

1标准误、方差贡献率和累积贡献率

>arrests.pr<-prcomp（saltwell,scale=TRUE）

>summary（arrests.pr，loadings=TRUE）

Importanceofcomponents:

PC1PC2PC3PC4PC5PC6PC7

Standarddeviation2.06081.11750.95920.661530.338410.177280.02614

ProportionofVariance0.60670.17840.13140.062520.016360.004490.00010

CumulativeProportion0.60670.78510.91650.979050.995410.999901.00000

>

2每个变量的标准误和变换矩阵

>prcomp（saltwell,scale=TRUE）

Standarddeviations:

[1]2.06081091.11746860.95919800.66153460.33841220.17727720.0261419

Rotation:

PC1PC2PC3PC4PC5PC6

X10.34688530.504503850.04884241-0.55817600.5239549-0.191489310

X2-0.2002213-0.120290250.93023876-0.1733966-0.0967612-0.201658411

X3-0.4414777-0.05850625-0.18016824-0.5534399-0.15360550.186904467

X4-0.45860100.04257557-0.18275574-0.4025103-0.14823750.009825109

X50.40560060.417668390.04962230-0.1398811-0.79545970.079036986

X6-0.40063530.44480041-0.138996850.2887128-0.1012846-0.709580413

X70.3306722-0.59453862-0.21125225-0.2951966-0.1659059-0.614723279

PC7

X1-0.001864597

X2-0.001522652

X30.635916793

X4-0.755239886

X5-0.003042766

X60.158763393

X7-0.001295549

3查看对象arests.pr中的内容

>>str（arrests.pr）

Listof5

$sdev:

num[1:

7]2.0611.1170.9590.6620.338...

$rotation:

num[1:

7,1:

7]0.347-0.2-0.441-0.4590.406...

..-attr（*,"dimnames"）=Listof2

....$:

chr[1:

7]"X1""X2""X3""X4"...

....$:

chr[1:

7]"PC1""PC2""PC3""PC4"...

$center:

Namednum[1:

7]109.7680.2956.60412.627149.842...

..-attr（*,"names"）=chr[1:

7]"X1""X2""X3""X4"...

$scale:

Namednum[1:

7]134.1890.1386.78113.572134.642...

..-attr（*,"names"）=chr[1:

7]"X1""X2""X3""X4"...

$x:

num[1:

20,1:

7]-1.67-1.66-4.1-1.39-1.88...

..-attr（*,"dimnames"）=Listof2

....$:

NULL

....$:

chr[1:

7]"PC1""PC2""PC3""PC4"...

-attr（*,"class"）=chr"prcomp"

>

4利用主成分的标准误计算出主成分的累积方差比例

>cumsum（arrests.pr$sdev^2）/7

[1]0.60670600.78509680.91653410.97905240.99541280.99990241.0000000

>

5各个化学成分占主成分的得分

>arrests.pr$x

PC1PC2PC3PC4PC5

[1,]-1.67419700-1.15390757.812973e-01-0.82154434-0.09559387

[2,]-1.65924015-0.93029891.166840e+00-0.874901520.05107312

[3,]-4.098385481.0111567-2.567612e+00-0.68730247-0.31976517

[4,]-1.38589039-1.24908033.749759e-05-0.66715185-0.08448647

[5,]-1.88022254-0.38899371.671917e-01-0.571127580.13190861

[6,]-0.69655135-0.9728592-3.030663e-01-0.034241970.20614983

[7,]-4.753206462.74264371.213314e+001.168467300.18776151

[8,]-0.08633651-0.71588223.871693e-010.785116490.04007332

[9,]0.22003394-1.0391225-7.757745e-010.630159110.12089601

[10,]0.29149770-0.91519367.624748e-010.57357593-0.12752807

[11,]0.20307566-0.71352461.008511e+000.73605261-0.21843357

[12,]0.77537521-0.7882670-3.089778e-010.70624777-0.17305749

[13,]0.71166897-1.0074449-1.248452e+000.86096256-0.06535513

[14,]1.770617670.6549572-6.064948e-01-0.128936570.62744865

[15,]1.775069430.80349935.680314e-01-0.474313490.36704946

[16,]1.892374560.7433814-4.402613e-01-0.282171090.57360330

[17,]1.965394110.73093015.200281e-01-0.588025960.26351255

[18,]1.997721491.32828585.946532e-01-0.13000624-0.62597984

[19,]2.503422741.14914743.741488e-01-0.56734140-0.71010526

[20,]2.127778380.7105729-1.293059e+000.36648272-0.14917150

PC6PC7

[1,]0.07084792-0.007513416

[2,]0.028143710.015953231

[3,]-0.152160160.016299237

[4,]0.04143780-0.074960637

[5,]0.029513800.063346130

[6,]0.33477919-0.007866628

[7,]0.01788053-0.024497758

[8,]-0.015429830.031130241

[9,]-0.02170366-0.020193011

[10,]-0.069563050.010431127

[11,]-0.138202810.014603566

[12,]0.072751440.001164613

[13,]-0.31007297-0.009840824

[14,]0.12358561-0.001945118

[15,]-0.185193610.002965969

[16,]-0.021469220.002545690

[17,]-0.22556715-0.013751662

[18,]0.300591020.001904014

[19,]-0.19369360-0.007138842

[20,]0.313525040.007364079

>

5.数据分析结果图形表示

>screeplot（arrests.pr,main="saltwell"）

>biplot（arrests.pr）

按第一主成分排序的结果：

>data.frame（sort（arrests.pr$x[,1]））

sort.arrests.pr.x...1..

1-4.75320646

2-4.09838548

3-1.88022254

4-1.67419700

5-1.65924015

6-1.38589039

7-0.69655135

8-0.08633651

90.20307566

100.22003394

110.29149770

120.71166897

130.77537521

141.77061767

151.77506943

161.89237456

171.96539411

181.99772149

192.12777838

202.50342274

>

主因子分析

计算数据的相关系数矩阵

saltwell.cor<-cor（saltwell）

>saltwell.cor

X1X2X3X4X5X6X7

X11.0000000-0.2911815-0.5704925-0.56763260.8488512-0.38857440.1689518

X2-0.29118151.00000000.27250120.2592747-0.34623270.1386043-0.3445447

X3-0.57049250.27250121.00000000.9868546-0.75087730.6694637-0.4707286

X4-0.56763260.25927470.98685461.0000000-0.73793670.7778797-0.5854959

X50.8488512-0.3462327-0.7508773-0.73793671.0000000-0.47468580.2815300

X6-0.38857440.13860430.66946370.7778797-0.47468581.0000000-0.8875089

X70.1689518-0.3445447-0.4707286-0.58549590.2815300-0.88750891.0000000

计算特征值和特征向量及因子的贡献率和累积贡献率

>saltwell.eigen<-eigen（saltwell.cor）

>saltwell.eigen

$values

[1]4.24694166751.24873605500.92006075820.43762806380.11452284400.03142721240.0006833991

$vectors

[,1][,2][,3][,4][,5][,6][,7]

[1,]0.3468853-0.504503850.04884241-0.55817600.5239549-0.191489310-0.001864597

[2,]-0.20022130.120290250.93023876-0.1733966-0.0967612-0.201658411-0.001522652

[3,]-0.44147770.05850625-0.18016824-0.5534399-0.15360550.1869044670.635916793

[4,]-0.4586010-0.04257557-0.18275574-0.4025103-0.14823750.009825109-0.755239886

[5,]0.4056006-0.417668390.04962230-0.1398811-0.79545970.079036986-0.003042766

[6,]-0.4006353-0.44480041-0.138996850.2887128-0.1012846-0.7095804130.158763393

[7,]0.33067220.59453862-0.21125225-0.2951966-0.1659059-0.614723279-0.001295549

根据主成分分析结果确定公共因子个数.

>saltwell.pr<-princomp（saltwell,cor=T）

>

>summary（saltwell.pr）

Importanceofcomponents:

Comp.1Comp.2Comp.3Comp.4Comp.5Comp.6Comp.7

Standarddeviation2.0608111.11746860.95919800.661534630.338412240.1772772192.614190e-02

ProportionofVariance0.6067060.17839090.13143730.062518290.016360410.0044896029.762844e-05

CumulativeProportion0.6067060.78509680.91653410.979052360.995412770.9999023721.000000e+00

>

均值

>saltwell.pr$center

X1X2X3X4X5X6X7

109.768150.294806.6042012.62740149.842001.337150.96100

标准误

>saltwell.pr$scale

X1X2X3X4X5X6X7

130.79077540.13488726.609676913.2284214131.23287272.23307450.1016317

>

下面用特征值的平方根乘以相应的特征向量得到因子载荷矩阵.并且只显示前2个因子的结果：

>t（sqrt（saltwell.eigen$values）*t（saltwell.eigen$vectors））[,1:

2]

[,1][,2]

[1,]0.7148649-0.56376721

[2,]-0.41261820.13442058

[3,]-0.90980210.06537890

[4,]-0.9450901-0.04757686

[5,]0.8358661-0.46673130

[6,]-0.8256336-0.49705049

[7,]0.68145290.66437824

>

用R语言自带的函数factanal（）进行分析

>saltwell.fa<-factanal（saltwell,factors=2）

>

>print（saltwell.fa,cutoff=0.001）

Call:

factanal（x=saltwell,factors=2）

Uniquenesses:

X1X2X3X4X5X6X7

0.6680.9230.0050.0050.4280.0050.179

Loadings:

Factor1Factor2

X1-0.543-0.193

X20.2730.045

X30.9400.338

X40.8750.481

X5-0.725-0.213

X60.3820.922

X7-0.181-0.888

Factor1Factor2

SSloadings2.7232.067

ProportionVar0.3890.295

CumulativeVar0.3890.684

Testofthehypothesisthat2factorsaresufficient.

Thechisquarestatisticis42.91on8degreesoffreedom.

Thep-valueis9.14e-0