How to find the number of clusters when more than one datasets are aggregated as one? Suppose 3 datasets has 3 ,7, 4 clusters in their respective dataset.
When I aggregated them as one dataset what's the safest number of cluster to choose as perimeter for kmeans or any supervised clustering?
Already tried by considering average(3,7,4) but not giving me near to good solution as the dataset can vary with dimensions, number of samples etc.

It depends on the degree of overlap between the clusters across datasets.
For example, imagine data points fall within the clusters below, which are colored according to the dataset: red for dataset 1 (3 clusters), green for dataset 2 (7 clusters), blue for dataset 3 (4 clusters). The clusters might be completely disjoint (left plot), giving the maximum of 14 clusters in the aggregated data. At the opposite extreme (middle plot), the clusters might overlap such that they merge into a single cluster in the aggregated data. Or, there might be partial overlap (right plot), yielding some intermediate number of clusters in the aggregated data.

So, assuming the initial clusters are all correctly identified, the aggregated data could contain anywhere between a single cluster and 14 clusters (the total number of initial clusters). The number can't be narrowed down beyond that without further assumptions.
