How Many Clusters? An Entropic Approach to Hierarchical Cluster Analysis

Clustering large and heterogeneous data of user-profiles from social media is problematic as the problem of finding the optimal number of clusters becomes more critical than for clustering smaller and homogeneous data. We propose a new approach based on the deformed Renyi entropy for determining the optimal number of clusters in hierarchical clustering of user-profile data. Our results show that this approach allows us to estimate Renyi entropy for each level of a hierarchical model and find the entropy minimum (information maximum). Our approach also shows that solutions with the lowest and the highest number of clusters correspond to the entropy maxima (minima of information).

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