So I'm planning on clustering a bunch of observation data using k-medoids. There are seven attributes for each instance and the data is numerical and discrete. I'm a little uncertain of how to evaluate the model to find the correct number of clusters. I was thinking I could run the cluster technique for an increasing number of clusters (say start at 1 and increase by one each time), measure the silhouette coefficient for each cluster model and then select the number of clusters with the highest value?
Would anybody be able to tell me if this is a good idea for evaluating the model and if not what else I could do?