COMMunication
RESearch.NET

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|	| BOS  | NY  | DC  | MIA  | CHI  | SEA  | SF  | LA  | DEN  |
| BOS  | 0  | 206  | 429  | 1504  | 963  | 2976  | 3095  | 2979  | 1949  |
| NY  | 206  | 0  | 233  | 1308  | 802  | 2815  | 2934  | 2786  | 1771  |
| DC  | 429  | 233  | 0  | 1075  | 671  | 2684  | 2799  | 2631  | 1616  |
| MIA  | 1504  | 1308  | 1075  | 0  | 1329  | 3273  | 3053  | 2687  | 2037  |
| CHI  | 963  | 802  | 671  | 1329  | 0  | 2013  | 2142  | 2054  | 996  |
| SEA  | 2976  | 2815  | 2684  | 3273  | 2013  | 0  | 808  | 1131  | 1307  |
| SF  | 3095  | 2934  | 2799  | 3053  | 2142  | 808  | 0  | 379  | 1235  |
| LA  | 2979  | 2786  | 2631  | 2687  | 2054  | 1131  | 379  | 0  | 1059  |
| DEN  | 1949  | 1771  | 1616  | 2037  | 996  | 1307  | 1235  | 1059  | 0  |

  - Start by assigning each item to its own cluster, so that if you have N items, you now have N clusters, each containing just one item. Let the distances (similarities) between the clusters equal the distances (similarities) between the items they contain.
  - Find the closest (most similar) pair of clusters and merge them into a single cluster, so that now you have one less cluster.
  - Compute distances (similarities) between the new cluster and each of the old clusters.
  - Repeat steps 2 and 3 until all items are clustered into a single cluster of size N.

Step 3 can be done in different ways, which is what distinguishes single-link from complete-link and average-link clustering.

  * **single-link clustering** (also called the connectedness or minimum method) = the shortest distance from any member of one cluster to any member of the other cluster. 
  * **complete-link clustering** (also called the diameter or maximum method) = the longest distance from any member of one cluster to any member of the other cluster.
  * **average-link clustering** = the average distance from any member of one cluster to any member of the other cluster.

|	| BOS  | NY  | DC  | MIA  | CHI  | SEA  | SF  | LA  | DEN  |
| BOS  | 0  | **206**  | 429  | 1504  | 963  | 2976  | 3095  | 2979  | 1949  |
| NY  | 206  | 0  | 233  | 1308  | 802  | 2815  | 2934  | 2786  | 1771  |
| DC  | 429  | 233  | 0  | 1075  | 671  | 2684  | 2799  | 2631  | 1616  |
| MIA  | 1504  | 1308  | 1075  | 0  | 1329  | 3273  | 3053  | 2687  | 2037  |
| CHI  | 963  | 802  | 671  | 1329  | 0  | 2013  | 2142  | 2054  | 996  |
| SEA  | 2976  | 2815  | 2684  | 3273  | 2013  | 0  | 808  | 1131  | 1307  |
| SF  | 3095  | 2934  | 2799  | 3053  | 2142  | 808  | 0  | 379  | 1235  |
| LA  | 2979  | 2786  | 2631  | 2687  | 2054  | 1131  | 379  | 0  | 1059  |
| DEN  | 1949  | 1771  | 1616  | 2037  | 996  | 1307  | 1235  | 1059  | 0  |

  - 가장 가까운 거리의 도시: BOS 와 NY, 206
  - 두 도시를 합하여 BOS/NY로 하고 다시 이를 포함한 도시들 간의 거리를 구함
  - single link 방법을 사용한다면 BOS/NY와 DC간의 거리는 223이 됨 (가장 가까운 거리를 클러스터와의 거리로 환산하는 방법이 single link method). 마찬가지로 DEN까지의 거리는 1771이 됨

|   | BOS/NY  | DC  | MIA  | CHI  | SEA  | SF  | LA  | DEN  |
| BOS/NY  | 0  | 223  | 1308  | 802  | 2815  | 2934  | 2786  | 1771  |
| DC  | 223  | 0  | 1075  | 671  | 2684  | 2799  | 2631  | 1616  |
| MIA  | 1308  | 1075  | 0  | 1329  | 3273  | 3053  | 2687  | 2037  |
| CHI  | 802  | 671  | 1329  | 0  | 2013  | 2142  | 2054  | 996  |
| SEA  | 2815  | 2684  | 3273  | 2013  | 0  | 808  | 1131  | 1307  |
| SF  | 2934  | 2799  | 3053  | 2142  | 808  | 0  | 379  | 1235  |
| LA  | 2786  | 2631  | 2687  | 2054  | 1131  | 379  | 0  | 1059  |
| DEN  | 1771  | 1616  | 2037  | 996  | 1307  | 1235  | 1059  | 0  |

  - BOS/NY와 가장 가까운 거리의 도시는 DC이고 거리는 223
  - BOS/NY/DC 로 클러스터링하고 이와 다른 도시들, 그리고 각 도시들 간의 거리를 다시 계산

|   | BOS/NY/DC  | MIA  | CHI  | SEA  | SF  | LA  | DEN  |
| BOS/NY/DC  | 0  | 1075  | 671  | 2684  | 2799  | 2631  | 1616  |
| MIA  | 1075  | 0  | 1329  | 3273  | 3053  | 2687  | 2037  |
| CHI  | 671  | 1329  | 0  | 2013  | 2142  | 2054  | 996  |
| SEA  | 2684  | 3273  | 2013  | 0  | 808  | 1131  | 1307  |
| SF  | 2799  | 3053  | 2142  | 808  | 0  | 379  | 1235  |
| LA  | 2631  | 2687  | 2054  | 1131  | 379  | 0  | 1059  |
| DEN  | 1616  | 2037  | 996  | 1307  | 1235  | 1059  | 0  |

  - 위에서 가장 가까운 도시들 간의 거리는 379이고 이는 SF와 LA 간의 거리
  - SF/LA로 합치고 다시 계산하여 매트릭스를 구함 

|   | BOS/NY/DC  | MIA  | CHI  | SEA  | SF/LA  | DEN  |
| BOS/NY/DC  | 0  | 1075  | 671  | 2684  | 2631  | 1616  |
| MIA  | 1075  | 0  | 1329  | 3273  | 2687  | 2037  |
| CHI  | 671  | 1329  | 0  | 2013  | 2054  | 996  |
| SEA  | 2684  | 3273  | 2013  | 0  | 808  | 1307  |
| SF/LA  | 2631  | 2687  | 2054  | 808  | 0  | 1059  |
| DEN  | 1616  | 2037  | 996  | 1307  | 1059  | 0  |

  - 이제 CHI가 BOS/NY/DC/CHI와 가장 가까움 (671)
  - BOS/NY/DC/CHI로 병합

|   | BOS/NY/ \\ DC/CHI  | MIA  | SEA  | SF/LA  | DEN  |
| BOS/NY/ \\ DC/CHI  | 0  | 1075  | 2013  | 2054  | 996  |
| MIA  | 1075  | 0  | 3273  | 2687  | 2037  |
| SEA  | 2013  | 3273  | 0  | 808  | 1307  |
| SF/LA  | 2054  | 2687  | 808  | 0  | 1059  |
| DEN  | 996  | 2037  | 1307  | 1059  | 0  |

  - 같은 방법으로 SEA을 SF/LA에 병합 (SF/LA/SEA)
 
|   | BOS/NY/ \\ DC/CHI  | MIA  | SF/LA \\ /SEA  | DEN  |
| BOS/NY/ \\ DC/CHI  | 0  | 1075  | 2013  | 996  |
| MIA  | 1075  | 0  | 2687  | 2037  |
| SF/LA/ \\ SEA  | 2054  | 2687  | 0  | 1059  |
| DEN  | 996  | 2037  | 1059  | 0  |


|   | BOS/NY/DC/ \\ CHI/DEN  | MIA  | SF/LA/SEA  |
| BOS/NY/DC/ \\ CHI/DEN  | 0  | 1075  | 1059  |
| MIA  | 1075  | 0  | 2687  |
| SF/LA/SEA  | 1059  | 2687  | 0  |


|   | BOS/NY/DC/CHI/ \\ DEN/SF/LA/SEA  | MIA  |
| BOS/NY/DC/CHI/ \\ DEN/SF/LA/SEA  | 0  | 1075  |
| MIA  | 1075  | 0  |

{{:hiclus1.gif}}
<code>JOHNSON'S HIERARCHICAL CLUSTERING
--------------------------------------------------------------------------------

Method:                                 SINGLE_LINK (minimum distance)
Type of Data:                           Dissimilarities
Input dataset:                          cities (D:\Users\Hyo\Documents\UCINET data\Cities\cities)

HIERARCHICAL CLUSTERING

        M S     B     C D
        I E S L O N D H E
        A A F A S Y C I N

Level   4 6 7 8 1 2 3 5 9
-----   - - - - - - - - -
  206   . . . . XXX . . .
  233   . . . . XXXXX . .
  379   . . XXX XXXXX . .
  671   . . XXX XXXXXXX .
  808   . XXXXX XXXXXXX .
  996   . XXXXX XXXXXXXXX
 1059   . XXXXXXXXXXXXXXX
 1075   XXXXXXXXXXXXXXXXX



Measures of cluster adequacy

                  1      2      3      4      5      6      7
             ------ ------ ------ ------ ------ ------ ------
  1     Eta  -0.284 -0.480 -0.554 -0.657 -0.711 -0.687 -0.151
  2       Q  -0.133 -0.163 -0.188 -0.203 -0.240 -0.214 -0.033
  3 Q-prime  -0.152 -0.190 -0.226 -0.254 -0.320 -0.322 -0.065
  4     E-I   0.994  0.973  0.961  0.884  0.824  0.625 -0.490


Size of each cluster, expressed as a proportion of the total population clustered

             1     2     3     4     5     6     7     8
         ----- ----- ----- ----- ----- ----- ----- -----
  1 CL1  0.222 0.333 0.333 0.111 0.111 0.111 0.111 1.000
  2 CL2  0.111 0.111 0.111 0.444 0.444 0.333 0.889      
  3 CL3  0.111 0.111 0.111 0.111 0.333 0.556            
  4 CL4  0.111 0.111 0.111 0.222 0.111                  
  5 CL5  0.111 0.111 0.222 0.111                        
  6 CL6  0.111 0.111 0.111                              
  7 CL7  0.111 0.111                                    
  8 CL8  0.111                                          

Actor-by-Partition indicator matrix saved as dataset Part

----------------------------------------
Running time:  00:00:01
Output generated:  21 11 16 09:10:06
UCINET 6.614 Copyright (c) 1992-2016 Analytic Technologies

</code>

{{hiclus2.gif}}
{{hiclus4.gif}}

====== E.g. 1 ======
<code csv cities2.csv>0	206	429	1504	963	2976	3095	2979	1949
206	0	233	1308	802	2815	2934	2786	1771
429	233	0	1075	671	2684	2799	2631	1616
1504	1308	1075	0	1329	3273	3053	2687	2037
963	802	671	1329	0	2013	2142	2054	996
2976	2815	2684	3273	2013	0	808	1131	1307
3095	2934	2799	3053	2142	808	0	379	1235
2979	2786	2631	2687	2054	1131	379	0	1059
1949	1771	1616	2037	996	1307	1235	1059	0

</code>

# Prepare Data
setwd("d:/rdata")
mydata <- read.csv("cities.csv")
mydata <- na.omit(mydata) # listwise deletion of missing
mydata <- scale(mydata) # standardize variables