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1、实验四主成分分析1.根据1998年部分地区洪灾损失数据（见表1）进行主成分分析，看看哪些省受灾较轻？ 受灾最重的是哪几个省？其中x1x12分别为：受灾面积、成灾面积、绝收面积、受灾 /万人次、成灾/万人次、死亡（人）、伤病（人）、紧急转移（人）、倒塌房屋/万间、损 坏房屋/万间、死亡大牲畜/万头、直接经济损失/亿元。表一地区X1x2x3x4x5x6x7x8x9x10x11x12蒙130.4107764.8448037501471054769773705903601640_吉_109.764726.7306.1214.57311000983560623148140.0黑242.9160.693.
2、7581.0521.02316844156.4820750161_218.0皖199 6130 857 11562 01012 893262461100 426949310130 5闽6972374459754558146840219536891678100.0879赣241.6193.687.82381.01702.6237126505304.6117.9168.2507434.2鄂254.0169.044.51939.01534.7353891200247.4869241.2270357.0湘2130141 339 9217801652 4854224400350 8939224 5839
3、422 8黑79354828.213785992831538000811107763661149川128.275416.91757.91044.358114806370212431131747渝65.349467904.0668.230421715391_171271_45555滇399161_35462 75281662357610414815231_陕408262486500475021530691279924618430解：由于矩阵中主对角元素相差太大，故用相关系数矩阵，首先输入数据A=130.4107.764.8448.0375.014710547697.737.059.036.016
4、4.0;109.764.726.7306.1214.5731100098.356.062.314.8140.0;242.9160.693.7581.0521.02316844156.482.075.016.1218.0;199.6130.857.11562.01012.893262461100.426.949.31.0130.5;69.723.74.4597.5455.81468402195.368.9167.8100.087.9;241.6193.687.82381.01702.6237126505304.6117.9168.250.7434.2;254.0169.044.51939.015
5、34.7353891200247.486.9241.227.0357.0;213.0141.339.92178.01652.4854224400350.893.9224.583.9422.8;79.354.828.21378.5992.83153800081.110.776.36.6114.9;128.275.416.91757.91044.35811480637.021.243.113.174.7;65.349.46.7904.0668.23042171539.117.127.14.555.5;39.916.13.5462.752.81662357.610.414.81.523.1;40.8
6、26.24.8650.0475.0215306912.79.924.61.843.0;R=corrcoef（A）得到相关系数矩阵为:R =1.00000.97740.83120.62700.69680.15530.69250.73910.77600.62180.22950.8448；0.97741.00000.88300.63990.71190.13810.62190.72110.75850.57330.19040.8671；0.83120.88301.00000.31710.3910-0.19470.38370.51450.62190.28450.08490.6583；0.62700.639
7、90.31711.00000.97530.66550.30280.63270.46810.60840.24440.7100；0.69680.71190.39100.97531.00000.64020.40200.73150.57100.71100.32070.7989；0.15530.1381-0.19470.66550.64021.0000-0.00490.38320.13360.43530.34040.3832；0.69250.62190.38370.30280.4020-0.00491.00000.46190.50360.58420.00660.5593；0.7391 0.7211 0.
8、51450.63270.73150.38320.46191.00000.92520.92590.75060.9298；0.77600.75850.62190.46810.57100.13360.50360.92521.00000.82150.65840.8865；0.62180.57330.28450.60840.71100.43530.58420.92590.82151.00000.73990.8275；0.22950.19040.08490.24440.32070.34040.00660.75060.65840.73991.00000.4965；0.8448 0.8671 0.65830.
9、71000.79890.38320.55930.92980.88650.82750.49651.0000；表明12个指标之间都没有明显的线性相关性。A1=zscore(A);消除量纲V,D=eig(corrcoef(A1)%计算特征值和特征向量W=sum(D)/sum(sum(D)计算贝献率F=A1*V计算主成分得分Y=F(:,10:12)*W(:,10:12)计算综合评价值得分Y1,L1=sort(Y,descend) ；% L1给出受灾最严重的序号Y2,L2=sort(L1)%给出各省受灾综合排名结果见表：V = 0.5463-0.0135-0.04440.2781-0.3102-0.41
10、320.35300.1965-0.0140-0.11550.26660.3275-0.2179-0.63790.2048-0.49270.0694-0.03940.09850.1328-0.1388-0.14940.28350.3243-0.23110.3160-0.17980.25330.27440.39750.16770.1769-0.4376-0.01350.45760.2376-0.23790.0990-0.5687-0.1462-0.1271-0.17950.1080-0.4465-0.1074-0.4340-0.22660.27950.17200.21980.66760.06680
11、.22970.13180.0774-0.3694-0.0476-0.3512-0.19410.3100-0.14120.0241-0.01560.11560.1396-0.0528-0.04350.7190-0.0017-0.3261-0.54510.1458-0.23900.33290.0126-0.17560.00030.04970.11880.11670.8031-0.05970.27110.2209-0.4115-0.07990.22140.3314-0.65830.1396-0.1458-0.0443-0.03900.2395-0.11340.3431-0.16270.11910.03270.10250.3950-0.6264-0.4149-0.0643-0.05340.33280.06620.32430.1771-0.4685-0.27320.35000.34960.31230.1080-0.16270.31440.2312-0.20290.31730.04680.24730.0161-0.4203-0.00370.00350.50320.0536-0.15690.5662-0.3479
