# Learning Representations from Dendrograms

## TL;DR

This paper introduces a generalized framework for unsupervised representation learning from dendrograms, extending Minimax distance measures to arbitrary dendrograms and combining multiple distances for improved clustering and feature extraction.

## Contribution

It develops a flexible method to infer and embed distances from various dendrograms, enabling advanced ensemble and multi-layered approaches for unsupervised learning.

## Key findings

- Effective in clustering tasks with improved accuracy
- Versatile framework applicable to different dendrogram types
- Demonstrated success in numerical experiments

## Abstract

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.