  We propose unsupervised representation learning and feature extraction from
dendrograms. The commonly used Minimax distance measures correspond to building
a dendrogram with single linkage criterion, with defining specific forms of a
level function and a distance function over that. Therefore, we extend this
method to arbitrary dendrograms. We develop a generalized framework wherein
different distance measures and representations 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, to address the model selection problem, we study
the aggregation of different dendrogram-based distances respectively in
solution space and in representation space in the spirit of deep
representations. In the first approach, for example for the clustering problem,
we build a graph with positive and negative edge weights according to the
consistency of the clustering labels of different objects among different
solutions, in the context of ensemble methods. Then, we use an efficient
variant of correlation clustering to produce the final clusters. In the second
approach, we investigate the combination of different distances and features
sequentially in the spirit of multi-layered architectures to obtain the final
features. Finally, we demonstrate the effectiveness of our approach via several
numerical studies.
