A new approach to density-based clustering and unsupervised classification is introduced for topographic maps. By virtue of our topographic map learning rule, called the kernel-based Maximum Entropy learning Rule (kMER), all neurons have an equal probability to be active (equiprobabilistic map) and, in addition, pilot density estimates are obtained that are compatible with the variable kernel density estimation method. The neurons receive their cluster labels by performing hill-climbing on the density estimates which are located at the neuron weights only. Several methods are suggested and explored for determining the cluster boundaries and the clustering performance is tested for the case where the cluster regions are used for unsupervised classification purposes. Finally, the difference is indicated between (Gaussian) kernel-based density modeling with kMER, and (Gaussian) mixture modeling with maximum likelihood learning.