1. 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.
2. Find the closest (most similar) pair of clusters and merge them into a single cluster, so that now you have one less cluster.
3. Compute distances (similarities) between the new cluster and each of the old clusters.
4. 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.

1. 가장 가까운 거리의 도시: BOS 와 NY, 206
2. 두 도시를 합하여 BOS/NY로 하고 다시 이를 포함한 도시들 간의 거리를 구함
3. 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

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

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

1. 이제 CHI가 BOS/NY/DC/CHI와 가장 가까움 (671)
2. BOS/NY/DC/CHI로 병합

1. 같은 방법으로 SEA을 SF/LA에 병합 (SF/LA/SEA)

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

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