Graph construction with condition-based weights for spectral clustering of hierarchical datasets

Most of the unsupervised machine learning algorithms focus on clustering the data based on similarity metrics, while ignoring other attributes, or perhaps other type of connections between the data points. In case of hierarchical datasets, groups of points (point-sets) can be defined according to the hierarchy system. Our goal was to develop such spectral clustering approach that preserves the structure of the dataset throughout the clustering procedure. The main contribution of this paper is a set of conditions for weighted graph construction used in spectral clustering. Following the requirements – given by the set of conditions – ensures that the hierarchical formation of the dataset remains unchanged, and therefore the clustering of data points imply the clustering of point-sets as well. The proposed spectral clustering algorithm was tested on three datasets, the results were compared to baseline methods and it can be concluded the algorithm with the proposed conditions always preserves the hierarchy structure.