DBSCAN Clustering

Question

I used K-means to get the number of clusters for my data(Elbow Method). Then I was trying to see if for some specific hyperparameters can we get the same number of clusters for DBSCAN. I tried Brute-Force to get the parameter values and got some value for different data sets.
However, I was wondering if there is a justification for this or whether it's just a fluke?
Edit- All the datasets are 2-dimensional.

prashant0598 · Answer

First of all K-means is a partitioning algorithm where as DBSCAN is a Density clustering algorithm.
K-means tries to find cluster centers that are representative of certain regions of the data. DBSCAN doesn’t require every point be assigned to a cluster and hence doesn’t partition the data, but instead extracts the dense clusters and leaves sparse background classified as noise. It use the concept of reachability i.e. how many neighbors has a point within a radius.
If suppose by bruteforce you get same number of clusters but Rand_score will be quite different having said that if the dataset is quite trivial ( we get clusters of data point equally far from each other and equally dense) both will get same number of clusters.

DBSCAN Clustering

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