1. Cluster/Group Analysis

Cluster Analysis allows data to be grouped using two types of methods: Hierarchical or K-means.

For the hierarchical method, you can choose the distance parameters (Euclidean, Manhattan or Gower) and the method (ward, single, complete, average, median or centroid). There are options to standardize the data, display the data in a dendrogram and display groups.

For the K-means method there is only the possibility of defining the number of groups and standardizing the data.

Example 1:

A financial analyst would like to segment the companies analyzed according to the factors that impact their financial health. The consumer goods manufacturer, after mapping the market structure and determining the factors that differentiate the products, would like to segment them. We will apply Cluster Analysis using the hierarchical complete linkage method using Euclidean distance to compare groups.

The mapped factors are shown in the table below.

COMPANY LC GA ROA SIT
AQUATEC 0.1159 0.2673 -0.2101 INSOLV
BANCO_CREFISUL 1.0317 0.1721 0.0196 INSOLV
CASA ANGLO MAPPIN 2.1758 0.0456 0.0179 INSOLV
CETENCO 1.0213 0.5076 0.0178 INSOLV
CNV CIA VEST 1.9036 1.1809 -0.0283 INSOLV
COPAS 0.9484 1.3017 -0.0434 INSOLV
INBRAC 0.6121 0.4972 -0.3229 INSOLV
MENDES JR 204 0.0667 0.0561 INSOLV
MONTREAL 0.0045 0 -4.1594 INSOLV
PEIXE 0.2049 0 -0.7039 INSOLV
BRASINCA 0.1775 0.8322 -0.3944 INSOLV
CIBRAN 0.4855 0.1843 -0.0048 INSOLV
FERRO LIGAS 0.6955 0.3195 -0.4052 INSOLV
INDS VER ISHIBRA S 0.0683 0.3828 -0.0293 INSOLV
LOJAS HERING 0.6238 0.1983 -0.1372 INSOLV
PARA DE MINAS 0.2326 1014 -0.4158 INSOLV
TECTOY 0.9442 0.9431 -0.5884 INSOLV
AIR LIQUIDE 3.5053 0.6109 -0.0464 SOLV
ANTARCTICA 0.6613 0.3192 0.0379 SOLV
ARACRUZ 1.5707 0.1427 1 SOLV
ARNO 2.9656 2.0212 0.2423 SOLV
ATLAS 0.9515 1.1676 0.1214 SOLV
BARDELLA 2.0071 0.2559 0.0276 SOLV
BOMPRECO 0.6804 1.6503 -0.2219 SOLV
BRAHMA 0.7031 0.5195 0.0797 SOLV
BRASILIT 1105 0.1958 0.2984 SOLV
CACIQUE 1.1209 748 0.0464 SOLV
CONFAB TUBOS 2266 0.3392 98 SOLV
DURATEX 2.4744 0.4178 0.0647 SOLV
EBERLE 0.4188 1.1136 -0.1495 SOLV
EMBRACO 1.7798 0.7221 0.0558 SOLV
ENGEMIX 1.2954 1.2006 0.0345 SOLV
ERICSSON 1.6473 629 0.1568 SOLV
FICAP 2.3485 1.4813 0.1218 SOLV
GERDAU 1.2619 0.3317 0.0381 SOLV
LPC DANONE 1.4377 2.3197 0.1207 SOLV
MAGNESITA 1.7495 0.7416 0.0576 SOLV
MILLENNIUM 0.9254 0.4134 -0.0289 SOLV
MONARK 1.9217 0.8222 0.1926 SOLV
MULTIBRA S 1.7066 1.2666 0.2244 SOLV
NADIR FIGUEIREDO 1.5415 826 0.0058 SOLV
NITROCARBONO 0.7424 0.9485 0.0401 SOLV
PETTENATI 1.4648 0.6864 0.2433 SOLV
PIRELLI PNEUS 1.3069 1452 0.1059 SOLV
PRONOR PETROQ 758 499 0.0472 SOLV
REFINARIA IPIRANGA 2.5089 0.6693 0.1258 SOLV
SANTA MARINA 2.3696 0.7963 0.1109 SOLV
SP ALPARGATAS 1.7617 1092 -0.1962 SOLV
YAKULT 2673 1234 0.37 SOLV

We will upload the data to the system.

Configuring as shown in the figure below to perform the analysis of clustering.

Then click Calculate to get the results. You can also generate the analyses and download them in Word format.

The results are:

hierarchical Clustering

Group 1 Group 2 Group 3 Group 4 Group 5
AQUATEC CASA ANGLO (MAPPIN) MONTREAL AIR LIQUIDE ANTARCTICA
BANCO_CREFISUL CNV CIA VEST ARNO ARACRUZ
CETENCO CONFAB TUBOS ATLAS
COPAS DURATEX BARDELLA
INBRAC FICAP BOMPREÇO
MENDES JR. REFINARIA IPIRANGA BRAHMA
PEIXE SANTA MARINA BRASILIT
BRASINCA YAKULT CACIQUE
CIBRAN EBERLE
FERRO LIGAS EMBRACO
INDS.VER.ISHIBRA´S ENGEMIX
LOJAS HERING ERICSSON
PARA DEMINAS GERDAU
TECTOY LPC(DANONE)
MAGNESITA
MILLENNIUM
MONARK
MULTIBRA´S
NADIR
FIGUEIREDO
NITROCARBONO
PETTENATI
PIRELLI PNEUS
PRONOR PETROQ.
SP ALPARGATAS

Group

Labels Residual Order Groups
AQUATEC 1 1
BANCO_CREFISUL 2 1
CASA ANGLO (MAPPIN) 3 2
CETENCO 4 1
CNV CIA VEST 5 2
COPAS 6 1
INBRAC 7 1
MENDES JR. 8 1
MONTREAL 9 3
PEIXE 10 1
BRASINCA 11 1
CIBRAN 12 1
FERRO LIGAS 13 1
INDS.VER.ISHIBRA´S 14 1
LOJAS HERING 15 1
PARA DEMINAS 16 1
TECTOY 17 1
AIR LIQUIDE 18 4
ANTARCTICA 19 5
ARACRUZ 20 5
ARNO 21 4
ATLAS 22 5
BARDELLA 23 5
BOMPREÇO 24 5
BRAHMA 25 5
BRASILIT 26 5
CACIQUE 27 5
CONFAB TUBOS 28 4
DURATEX 29 4
EBERLE 30 5
EMBRACO 31 5
ENGEMIX 32 5
ERICSSON 33 5
FICAP 34 4
GERDAU 35 5
LPC(DANONE) 36 5
MAGNESITA 37 5
MILLENNIUM 38 5
MONARK 39 5
MULTIBRA´S 40 5
NADIR FIGUEIREDO 41 5
NITROCARBONO 42 5
PETTENATI 43 5
PIRELLI PNEUS 44 5
PRONOR PETROQ. 45 5
REFINARIA IPIRANGA 46 4
SANTA MARINA 47 4
SP ALPARGATAS 48 5
YAKULT 49 4

Example 2:

Consider the monthly income (in minimum wages) and age of six individuals in a given location. We will apply Cluster Analysis using the hierarchical method of linking means using Euclidean distance to compare the groups.

Individual Rent Age
A 9.6 28
B 8.4 31
C 2.4 42
D 18.2 38
E 3.9 25
F 6.4 41

Configuring as shown in the figure below to perform the analysis of clustering.

Then click Calculate to get the results. You can also generate the analyses and download them in Word format.

The results are:

Hierarchical Clustering

Group 1 Group 2
A D
B
C
E
F

Group

Labels Residual Order Group
A 1 1
B 2 1
C 3 1
D 4 2
E 5 1
F 6 1

Example 3:

The data represents, according to the UN database (2002), the life expectancy, education, income (GDP) and political stability and security indices of 21 countries. The higher the index value, the better the quality of the country. We will apply Cluster Analysis using the hierarchical method using Euclidean distance with Ward’s method to compare the groups.

Let us upload the data into the system.

Countries Life expectancy Education PIB Political stability
United Kingdom 0.88 0.99 0.91 1.1
Australia 0.9 0.99 0.93 1.26
Canada 0.9 0.98 0.94 1.24
United States 0.87 0.98 0.97 1.18
Japan 0.93 0.93 0.93 1.2
France 0.89 0.97 0.92 1.04
Singapore 0.88 0.87 0.91 1.41
Argentina 0.81 0.92 0.8 0.55
Uruguay 0.82 0.92 0.75 1.05
Cuba 0.85 0.9 0.64 0.07
Colombia 0.77 0.85 0.69 -1.36
Brazil 0.71 0.83 0.72 0.47
Paraguay 0.75 0.83 0.63 -0.87
Egypt 0.7 0.62 0.6 0.21
Nigeria 0.44 0.58 0.37 -1.36
Senegal 0.47 0.37 0.45 -0.68
Sierra Leone 0.23 0.33 0.27 -1.26
Angola 0.34 0.36 0.51 -1.98
Ethiopia 0.31 0.35 0.32 -0.55
Mozambique 0.24 0.37 0.36 0.2
China 0.76 0.8 0.61 0.39

Configuring as shown in the figure below to perform the analysis of clustering.

Then click Calculate to get the results. You can also generate the analyses and download them in Word format.

The results are:são:

Hierarchical Clustering

Group 1 Group 2 Group 3
United Kingdom Argentina Colombia
Australia Cuba Paraguay
Canada Brazil Nigeria
United States Egypt Senegal
Japan China Sierra Leone
France Angola
Singapore Ethiopia
Uruguay Mozambique

Group

Labels Residual Order Groups
1 United Kingdom 1 1
2 Australia 2 1
3 Canada 3 1
4 United States 4 1
5 Japan 5 1
6 France 6 1
7 Singapore 7 1
8 Argentina 8 2
9 Uruguay 9 1
10 Cuba 10 2
11 Colombia 11 3
12 Brazil 12 2
13 Paraguay 13 3
14 Egypt 14 2
15 Nigeria 15 3
16 Senegal 16 3
17 Sierra Leone 17 3
18 Angola 18 3
19 Ethiopia 19 3
20 Mozambique 20 3
21 China 21 2

Example 4:

It is common to use stratified random sampling when collecting survey data. The table below shows data from a survey of 120 households in a given region, measuring five variables: the location of the household, the level of education of the head of the household, the number of people living in the household, the monthly household income in minimum wages and the monthly household income per capita. We will use cluster analysis to help define these strata, employing the hierarchical method using the Manhattan distance with Ward’s method for group comparison.

Residence Local Instruction Nro of Residents Monthly Income Per capita income
1 1 3 4 10.3 2.575
2 1 3 4 15.4 3.850
3 1 2 4 9.6 2.400
4 1 2 5 5.5 1.100
5 1 3 4 9 2.250
6 1 1 1 2.4 2.400
7 1 3 2 4.1 2.050
8 1 3 3 8.4 2.800
9 1 3 6 10.3 1.717
10 1 2 4 4.6 1.150
11 1 2 6 18.6 3.100
12 1 1 4 7.1 1.775
13 1 2 4 12.9 3.225
14 1 2 6 8.4 1.400
15 1 3 3 19.3 6.433
16 1 2 5 10.4 2.080
17 1 3 3 8.9 2.967
18 1 3 4 12.9 3.225
19 1 3 4 5.1 1.275
20 1 3 4 12.2 3.050
21 1 3 5 5.8 1.160
22 1 3 5 12.9 2.580
23 1 3 5 7.7 1.540
24 1 2 4 1.1 0.275
25 1 2 8 7.5 0.938
26 1 3 4 5.8 1.450
27 1 1 5 7.2 1.440
28 1 3 3 8.6 2.867
29 1 2 4 5.1 1.275
30 1 3 5 2.6 0.520
31 1 3 5 7.7 1.540
32 1 2 2 2.4 1.200
33 1 3 5 4.8 0.960
34 1 1 2 2.1 1.050
35 1 1 6 4 0.667
36 1 1 8 12.5 1.563
37 1 3 3 6.8 2.267
38 1 3 5 3.9 0.780
39 1 3 5 9 1.800
40 1 3 3 10.9 3.633
41 2 2 5 5.4 1.080
42 2 1 3 6.4 2.133
43 2 1 6 4.4 0.733
44 2 1 5 2.5 0.500
45 2 1 6 5.5 0.917
46 2 1 8 4.8 0.600
47 2 3 4 14 3.500
48 2 2 4 8.5 2.125
49 2 1 5 7.7 1.540
50 2 2 3 5.8 1.933
51 2 3 5 5 1.000
52 2 1 3 4.8 1.600
53 2 2 2 2.8 1.400
54 2 2 4 4.2 1.050
55 2 3 3 10.2 3.400
56 2 2 4 7.4 1.850
57 2 2 5 5 1.000
58 2 3 2 6.4 3.200
59 2 3 4 5.7 1.425
60 2 2 4 10.8 2.700
61 2 3 1 2.3 2.300
62 2 1 7 6.1 0.871
63 2 1 3 5.5 1.833
64 2 1 7 3.5 0.500
65 2 3 3 9 3.000
66 2 3 6 5.8 0.967
67 2 1 6 4.2 0.700
68 2 3 3 6.8 2.267
69 2 2 5 4.8 0.960
70 2 3 5 6 1.200
71 2 2 7 9 1.286
72 2 1 4 5.3 1.325
73 2 3 4 3.1 0.775
74 2 3 1 6.4 6.400
75 2 1 3 3.9 1.300
76 2 2 3 6.4 2.133
77 2 3 4 2.7 0.675
78 2 2 4 2.4 0.600
79 2 2 4 3.6 0.900
80 2 3 5 6.4 1.280
81 2 3 2 11.3 5.650
82 2 1 5 3.8 0.760
83 2 2 3 4.1 1.367
84 3 1 5 1.8 0.360
85 3 3 5 7.1 1.420
86 3 1 3 13.9 4.633
87 3 2 6 4 0.667
88 3 1 6 2.9 0.483
89 3 2 9 3.9 0.433
90 3 1 4 2.2 0.550
91 3 2 3 5.8 1.933
92 3 2 5 2.8 0.560
93 3 2 5 4.5 0.900
94 3 2 4 5.8 1.450
95 3 3 8 3.9 0.488
96 3 2 7 2.8 0.400
97 3 1 3 1.3 0.433
98 3 3 5 3.9 0.780
99 3 3 5 5 1.000
100 3 1 5 0.1 0.020
101 3 2 3 4.6 1.533
102 3 2 4 2.6 0.650
103 3 1 6 2.3 0.383
104 3 2 5 4.9 0.980
105 3 1 5 2.3 0.460
106 3 1 3 3.9 1.300
107 3 1 4 2.1 0.525
108 3 1 4 2.7 0.675
109 3 2 5 11.1 2.220
110 3 1 6 6.4 1.067
111 3 3 7 25.7 3.671
112 3 1 4 0.9 0.225
113 3 3 5 3.9 0.780
114 3 1 5 5.1 1.020
115 3 2 6 4.2 0.700
116 3 1 6 4.4 0.733
117 3 1 7 7.9 1.129
118 3 1 4 4.2 1.050
119 3 1 4 3.5 0.875
120 3 2 6 11.4 1.900

We will upload the data to the system.

Configuring as shown in the figure below to perform the analysis of clustering.

Then click Calculate to get the results. You can also generate the analyses and download them in Word format.

Hierarchical Clustering

Group 1 Group 2 Group 3 Group 4 Group 5 Group 6
1 2 4 6 24 35
3 11 10 7 44 43
5 13 19 32 73 45
8 15 21 34 77 46
9 18 26 37 78 62
12 20 29 42 82 64
14 22 30 50 84 67
16 47 33 52 88 87
17 86 38 53 90 89
23 111 41 58 92 95
25 51 61 97 96
27 54 63 100 110
28 57 68 102 115
31 59 72 103 116
36 66 75 105 117
39 69 76 107
40 70 83 108
48 79 91 112
49 80 94 118
55 85 101 119
56 93 106
60 98
65 99
71 104
74 113
81 114
109
120

Group

Labels Residual Order Groups
1 1 1
2 2 2
3 3 1
4 4 3
5 5 1
6 6 4
7 7 4
8 8 1
9 9 1
10 10 3
11 11 2
12 12 1
13 13 2
14 14 1
15 15 2
16 16 1
17 17 1
18 18 2
19 19 3
20 20 2
21 21 3
22 22 2
23 23 1
24 24 5
25 25 1
26 26 3
27 27 1
28 28 1
29 29 3
30 30 3
31 31 1
32 32 4
33 33 3
34 34 4
35 35 6
36 36 1
37 37 4
38 38 3
39 39 1
40 40 1
41 41 3
42 42 4
43 43 6
44 44 5
45 45 6
46 46 6
47 47 2
48 48 1
49 49 1
50 50 4
51 51 3
52 52 4
53 53 4
54 54 3
55 55 1
56 56 1
57 57 3
58 58 4
59 59 3
60 60 1
61 61 4
62 62 6
63 63 4
64 64 6
65 65 1
66 66 3
67 67 6
68 68 4
69 69 3
70 70 3
71 71 1
72 72 4
73 73 5
74 74 1
75 75 4
76 76 4
77 77 5
78 78 5
79 79 3
80 80 3
81 81 1
82 82 5
83 83 4
84 84 5
85 85 3
86 86 2
87 87 6
88 88 5
89 89 6
90 90 5
91 91 4
92 92 5
93 93 3
94 94 4
95 95 6
96 96 6
97 97 5
98 98 3
99 99 3
100 100 5
101 101 4
102 102 5
103 103 5
104 104 3
105 105 5
106 106 4
107 107 5
108 108 5
109 109 1
110 110 6
111 111 2
112 112 5
113 113 3
114 114 3
115 115 6
116 116 6
117 117 6
118 118 5
119 119 5
120 120 1

Example 5:

A brewery wants to study its customers' tastes in relation to certain brands of beer. The table below shows the results of a study of the perceptions and preferences of 32 students about 10 different brands of beer. Each student rated the 10 beer brands on a 10-point scale: Anchor Steam, Bass Ale, Beck's, Corona, Gordo-Biersch, Guinness, Heineken, Pete's Wicked Ale, Sam Adams, Sierra and Nevada. We will apply Cluster Analysis using the K-means method to compare the groups.

Observation Anchor Steam Bass Ale Beck's Corona Gordo-Biersch Guinness Heineken Pete's Wicked Ale Sam Adams Sierra Nevada
P1 5 9 7 1 7 6 6 5 9 5
P2 7 5 6 8 8 4 8 8 7 7
P3 7 7 5 6 6 1 8 4 7 5
P4 7 7 5 2 5 8 4 6 8 9
P5 9 7 3 1 6 8 2 7 6 8
P6 7 6 4 3 7 6 6 5 4 9
P7 5 5 5 6 6 4 7 5 5 6
P8 5 3 1 5 5 5 3 5 5 9
P9 9 3 2 6 4 6 1 5 3 6
P10 2 6 6 5 6 4 8 4 4 3
P11 7 7 7 5 7 8 6 7 7 8
P12 8 3 3 9 9 2 1 9 7 8
P13 6 5 3 7 6 5 8 6 7 5
P14 5 6 3 8 6 7 6 7 6 7
P15 4 7 2 8 5 9 8 3 8 8
P16 3 3 4 5 6 5 9 7 5 5
P17 2 5 5 7 6 6 8 1 7 4
P18 9 3 7 4 2 4 6 3 8 6
P19 5 3 4 7 7 7 6 6 6 6
P20 2 4 4 8 5 5 5 4 6 6
P21 5 7 6 7 5 8 8 7 5 7
P22 8 9 6 7 7 8 6 8 8 8
P23 5 6 6 7 5 3 7 3 4 3
P24 5 5 6 7 7 4 6 3 7 6
P25 5 5 7 8 7 6 7 5 4 7
P26 3 5 4 7 3 1 2 6 6 5
P27 4 3 6 8 6 1 8 2 7 7
P28 3 8 4 8 6 2 8 4 6 1
P29 3 5 1 5 5 3 4 6 7 5
P30 3 8 5 8 7 5 5 3 7 8
P31 8 8 5 7 9 9 7 7 6 8
P32 7 6 2 2 6 6 2 7 5 5

We will upload the data to the system.

Configuring as shown in the figure below to perform the analysis of clustering.

Then click Calculate to get the results. You can also generate the analyses and download them in Word format.

The results are:

K - Mean Clustering

Group 1 Group 2
P1 P3
P2 P7
P4 P10
P5 P13
P6 P16
P8 P17
P9 P18
P11 P20
P12 P23
P14 P24
P15 P25
P19 P26
P21 P27
P22 P28
P31 P29
P32 P30

Note that the K-means method grouped the customers into 2 groups. We can put together a table with the average scores each group gave to the beer brands.

In Group 1, beers that were \“dark\” and had a \“stronger\” flavor had a higher mean. a higher mean; in Group 2, “light” colored beers had the highest mean. A possible conclusion from this segmentation is as follows:

Customers classified in Group 1 have a greater preference for dark dark beers with a more intense taste, while those classified in Group Group 2 have a greater preference for \“light\” colored beers.