Dear Ganguly,
The optimal value of K is searched by means of cross validation
procedures, i.e. by testing a set of values for K (e.g. from 1 to 10); then, the
value giving the lowest classication error in cross-validation can be selected as
the optimal one.
Best regards.
Dear Ganguly,
The optimal value of K is searched by means of cross validation
procedures, i.e. by testing a set of values for K (e.g. from 1 to 10); then, the
value giving the lowest classication error in cross-validation can be selected as
the optimal one.
Best regards.
The algorithm k-means needs an initial number of clusters 'k' to start with, however, the search for a good initial 'k' value can be tedious, that is why you could search for the 'k' that leads to less average clusters' distance using an exponential search algorithm or a golden section search. The following steps could be used to find the optimal k in a much faster fashion than just doing brute-force search.
1. Initialization: the user specifies the desired initial number of clusters, k, a range of values where to search for the best k value.
2. Search: the algorithm iterates over different number of clusters, k, i.e. the parameter k that leads to less within-group distance between the elements in the cluster by means of one of the following algorithms:
2.1. Exponential Search: to perform a broadly search of possible good k values, we obtain clusters for different number of clusters k until a bracketed minimum is found or the maximal number of exponential steps is reached.
2.2. Golden Section Search: to perform a fine tuning on finding best parameter k, once a bracketed minimum is found. It uses the golden section method, see Brent's method Golden Section Search in one dimension (http://www.aip.de/groups/soe/local/numres/bookcpdf/c10-1.pdf), to determine how much to increase/decrease the value of parameter k in order to find the minimum.
Regards!
Unless you know the answer, it is difficult to say this K is better than the other K. Moreover, for a given K, the results of K-means clustering also depend on the initial assignment of objects to K-cluster. Your prior knowledge about the data might help you sort out the clustering problem.
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