Nonparametric Feature Extraction from Dendrograms

We study nonparametric feature extraction from hierarchies. The commonly used Minimax distance measures correspond to building a dendrogram with single linkage criterion, with the definition of specific forms of a level function and a distance function over that. Therefore, we develop a generalized framework wherein different distance measures can be inferred from different types of dendrograms, level functions and distance functions. Via an appropriate embedding, we compute a vector-based representation of the inferred distances, in order to enable many numerical machine learning algorithms to employ such distances. Then, we study the aggregation of different dendrogram-based distances respectively in solution space and in representation space in the spirit of deep learning models. Finally, we demonstrate the effectiveness of our approach via numerical studies.