聚類分析課件

聚類分析

(clusteranalysis)17聚類分析主要內(nèi)容聚類分析的基本思想聚類分析的統(tǒng)計(jì)量聚類分析的方法系統(tǒng)聚類法動(dòng)態(tài)聚類法聚類分析的正確應(yīng)用17聚類分析聚類分析的基本思想分類問題根據(jù)骨骼的特征將人類從猿到人分為幾個(gè)不同的階段根據(jù)耳朵特征，將正常耳朵劃分為幾個(gè)類別根據(jù)醫(yī)院的醫(yī)療水平，工作效率等指標(biāo)，將醫(yī)院分為幾個(gè)等級(jí)將身體體型的指標(biāo)分類，制定服裝標(biāo)準(zhǔn)17聚類分析聚類分析的基本思想物以類聚：相似或相近的樣本或指標(biāo)歸類

10名學(xué)生的某門功課成績(jī)12121617181925262627身高體重17聚類分析聚類分析的基本思想樣品號(hào)x1x2…xp123…nn個(gè)樣品的p個(gè)指標(biāo)樣品聚類(Q)變量（指標(biāo)）聚類(R)距離最近的原則相似系數(shù)最大的原則17聚類分析聚類分析的統(tǒng)計(jì)量距離：用于樣品聚類歐氏距離馬氏距離相似系數(shù)：用于變量聚類相關(guān)系數(shù)列聯(lián)系數(shù)17聚類分析聚類分析的統(tǒng)計(jì)量歐氏距離(Euclideandistance)缺陷：受量綱影響；沒有考慮變量間的變異；沒有考慮變量間的相關(guān)。17聚類分析聚類分析的統(tǒng)計(jì)量馬氏距離(Mahalanobisdistance)HottelingT2統(tǒng)計(jì)量方差協(xié)方差矩陣17聚類分析聚類分析的統(tǒng)計(jì)量相關(guān)系數(shù)：用于定量變量17聚類分析聚類分析的統(tǒng)計(jì)量列聯(lián)系數(shù)：用于定性變量17聚類分析聚類分析的方法系統(tǒng)聚類法(systematicclustermethod)

：用于樣品聚類(小樣本)、變量聚類動(dòng)態(tài)聚類法用于樣品聚類(大樣本)條件系統(tǒng)聚類法用于有序樣品聚類17聚類分析

系統(tǒng)聚類法基本步驟構(gòu)造n個(gè)類，每個(gè)類包含且只包含一個(gè)樣品。計(jì)算n個(gè)樣品兩兩間的距離，構(gòu)成距離矩陣，記作D0。合并距離最近的兩類為一新類。計(jì)算新類與當(dāng)前各類的距離。若類的個(gè)數(shù)等于1，轉(zhuǎn)到步驟(5)，否則回到步驟(3)。畫聚類圖。決定類的個(gè)數(shù)，及各類包含的樣品數(shù)，并對(duì)類作出解釋。17聚類分析類間距離最短距離法(singlelingage)最長(zhǎng)距離法(completelingage)中間距離法(medianmethod)可變距離法(flexiblemedian)重心法(centroid)類平均法(average)可變類平均法(flexibleaverage)Ward最小方差法(Ward’sminimumvariance)17聚類分析類間距離S1S3S2S4S5最短距離17聚類分析類間距離最長(zhǎng)距離S1S3S4S517聚類分析類間距離S1S3S2S4S5重心間距離17聚類分析類間距離S1S3S2S4S5類平均距離17聚類分析類間距離Ward最小方差法（僅用于樣品聚類）類內(nèi)變異小，類間變異大17聚類分析例16個(gè)不同民族的標(biāo)化死亡率與出生時(shí)的期望壽命

民族原始數(shù)據(jù)標(biāo)準(zhǔn)化數(shù)據(jù)標(biāo)化死亡率(‰)出生時(shí)期望壽命(歲)標(biāo)化死亡率(‰)出生時(shí)期望壽命(歲)滿族

5.8070.59-1.59

1.44朝鮮族

7.4467.14-0.62

0.73蒙古族

8.1165.48-0.22

0.38維吾爾族10.2158.88

1.03-0.99藏族

9.5159.24

0.61-0.91哈薩克族

9.8160.47

0.79-0.66均數(shù)8.480063.6333

0.00

0.00標(biāo)準(zhǔn)差1.68664.8167

1.00

1.0017聚類分析各民族之間的歐氏距離(標(biāo)準(zhǔn)化資料)D0

滿族朝鮮族蒙古族維吾爾族藏族哈薩克族G1={S1}G2={S2}G3={S3}G4={S4}G5={S5}G6={S6}滿族G1={S1}0朝鮮族G2={S2}1.2080蒙古族G3={S3}1.7320.5260維吾爾族G4={S4}3.5702.3741.8510藏族G5={S5}3.2242.0481.5390.4220哈薩克族G6={S6}3.1731.9731.4480.4060.311017聚類分析

最短距離法

D1

G1={S1}G2={S2}G3={S3}G4={S4}G7={S5,S6}G1={S1}0G2={S2}1.2080G3={S3}1.7320.5260G4={S4}3.5702.3741.8510G7={S5,S6}3.1731.9731.4480.406017聚類分析D2G1={S1}G2={S2}G3={S3}G8={S4,S5,S6}G1={S1}0G2={S2}1.2080G3={S3}1.7320.5260G8={S4,S5,S6}3.1731.9731.448017聚類分析D3G1={S1}G9={S2,S3}G8={S4,S5,S6}G1={S1}0G9={S2,S3}1.2080G8={S4,S5,S6}3.1731.448017聚類分析D4G10={S1,S2,S3}G8={S4,S5,S6}G10={S1,S2,S3}0G8={S4,S5,S6}1.448017聚類分析例1資料的譜系聚類圖(最短距離法)

藏族哈薩克族維吾爾族朝鮮族蒙古族滿族Dendrograms(clustertrees)0.3110.4060.5261.2081.44817聚類分析各民族之間的歐氏距離(標(biāo)準(zhǔn)化資料)D0

滿族朝鮮族蒙古族維吾爾族藏族哈薩克族G1={S1}G2={S2}G3={S3}G4={S4}G5={S5}G6={S6}滿族G1={S1}0朝鮮族G2={S2}1.2080蒙古族G3={S3}1.7320.5260維吾爾族G4={S4}3.5702.3741.8510藏族G5={S5}3.2242.0481.5390.4220哈薩克族G6={S6}3.1731.9731.4480.4060.311017聚類分析最長(zhǎng)距離法

D1

G1={S1}G2={S2}G3={S3}G4={S4}G7={S5,S6}G1={S1}0G2={S2}1.2080G3={S3}1.7320.5260G4={S4}3.5702.3741.8510G7={S5,S6}3.2242.0481.5390.422017聚類分析D2G1={S1}G2={S2}G3={S3}G8={S4,S5,S6}G1={S1}0G2={S2}1.2080G3={S3}1.7320.5260G8={S4,S5,S6}3.5702.3741.851017聚類分析D3G1={S1}G9={S2,S3}G8={S4,S5,S6}G1={S1}0G9={S2,S3}1.7320G8={S4,S5,S6}3.5702.374017聚類分析D4G10={S1,S2,S3}G8={S4,S5,S6}G10={S1,S2,S3}0G8={S4,S5,S6}3.570017聚類分析例1資料的譜系聚類圖(最長(zhǎng)距離法)

藏族哈薩克族維吾爾族朝鮮族蒙古族滿族Dendrograms(clustertrees)0.3110.4220.5261.7323.57017聚類分析8種系統(tǒng)聚類法所得聚類圖17聚類分析指標(biāo)的聚類上體長(zhǎng)手臂長(zhǎng)胸圍頸圍總肩寬前胸寬后背寬前腰節(jié)高后腰節(jié)高總體高身高下體長(zhǎng)腰圍臀圍上體長(zhǎng)1.000手臂長(zhǎng)0.3701.000胸圍0.2420.2351.000頸圍0.2800.1960.5901.000總肩寬0.3600.3270.4760.4351.000前胸寬0.2810.2650.4830.4700.4521.000后背寬0.2450.2670.5400.4780.5340.6631.000前腰節(jié)高0.4480.3490.4520.4040.4310.3220.2661.000后腰節(jié)高0.4860.3710.3650.3570.4290.2830.2870.8201.000總體高0.6480.6680.2160.3160.4290.2830.2630.5270.5471.000身高0.6790.6880.2430.3130.4300.3020.2940.5200.5580.9571.000下體長(zhǎng)0.4860.6420.1740.2430.3750.2900.2550.4030.4170.8570.8521.000腰圍0.1330.1540.7320.4770.3390.3920.4460.2660.2410.0540.0990.0551.000臀圍0.3760.2540.6760.5810.4410.4470.4400.4240.3720.3630.3760.3210.6271.00017聚類分析定義距離dij＝1－|rij|17聚類分析ClustertreeAverageLinkageClusterAnalysisNameofObservationorCluster

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|..XXXXXXX..........|..XXXXXXX..........|..XXXXXXX..........|..............0+..............17聚類分析3454名成年女子14個(gè)部位的譜系聚類圖(類平均法)

上體長(zhǎng)y1手臂長(zhǎng)y2下體長(zhǎng)y12總體高y10身高y11前腰節(jié)高y8后腰節(jié)高y9胸圍y3腰圍y13臀圍y14頸圍y4前胸寬y6后背寬y7總肩寬y5

距離00.10.20.30.40.50.60.7

相關(guān)系數(shù)10.90.80.70.60.50.40.317聚類分析系統(tǒng)聚類法的優(yōu)缺點(diǎn)優(yōu)點(diǎn)事先不用指定分類的類別數(shù)缺點(diǎn)樣品量多時(shí)，計(jì)算耗時(shí)分類一旦確定，就不再變動(dòng)17聚類分析SAS程序Procstandardmean=0std=1out=temp;Vary1-y6;Procclusterdata=tempmethod=singlestdnosqu