sergios theodoridis pattern recognition pdf

Note that the rst sum in the above is the sum of the data samples x i around the individual cluster representatives w j , and the second sum is the sum of cluster representatives w j around the global center w. Thus when the choice of the value of the threshold is transfered to the choice of a value for we are eectivly saying that we will stop clustering when we get sets that have a average dissimilatrity greater than standard deviations from the average pointwise dissimilarity. If the same expression holds for the argument of the second sum we have J fuzzy 2 , U 2. Now with these two new sum, in the rst sum since we are ignoring the cluster j it can be written as r. That the matrix second derivative is negative denite is the condition for the solution to L.

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