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I want to cluster a graph using the FCM algorithm, I used the adjacency matrix of the graph as the data, and the "Euclidean" distance as metric. The problem is that the adjacency matrix is full of zero's (depends actually on the degree of the node) and my network is a kinda huge more than 2000 node. For the results I get many small size clusters and some big size clusters, that some time contain about 50% of the population and it is not right.

I think my problem is from the data representation. is there any conditions that must be satisfied apart from the FCM algorithm conditions.

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Different types of measures that form the matrix may be used to identify the cell values, where the measure controls how the clusters are formed. Some examples of values that can be used as measures include minimum distance from one node to the other, the degree of connectivity of each node and the amount of nodes needed to pass by to reach the other node.

I consider that minimum distance from one node to the other should be the best choice.

You can also try using the minkowsky distance which is the standard distance used in fcm, for calculating this distance you need a parameter which is the degree of fuzzyness of the distance, wwhen this parameter is 1 this distance is equal to the euclidian distan.

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  • $\begingroup$ Thank you, a nice point, the problem with minimum distance in my case is that it is I have thousands of nodes. $\endgroup$
    – sirus
    Commented Dec 10, 2010 at 7:55
  • $\begingroup$ I want to give you +1 but I need at least 15 points of reputation:( $\endgroup$
    – sirus
    Commented Dec 10, 2010 at 7:56
  • $\begingroup$ Thanks a lot sirus anyway, I am glad you found it helpfull $\endgroup$
    – mariana soffer
    Commented Dec 10, 2010 at 17:55
  • $\begingroup$ An other question, do the data need to be positive or normalized, because the representation of no-path can be many values, like "inf" or a negative value. $\endgroup$
    – sirus
    Commented Dec 12, 2010 at 13:55

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