Learning on hierarchical trees with Random Forest

Hierarchies, as described in mathematical morphology, represent nested regions of interest and provide mechanisms to create coherent data organization. They facilitate high-level analysis and management of large amounts of data. Represented as hierarchical trees, they have formalisms intersecting with graph theory and generalizable applications. Due to the deterministic algorithms, the multiform representations, and the absence of a direct quality evaluation, it is hard to insert hierarchical information into a learning framework and benefit from the recent advances. Researchers usually tackle this problem by refining the hierarchies for a specific media and assessing their quality for a particular task. The downside of this approach is that it depends on the application, and the formulations limit the generalization to similar data. This work aims to create a learning framework that can operate with hierarchical data and is agnostic to the input and application. The idea is to transform the data into a regular representation required by most learning models while preserving the rich information in the hierarchical structure. The proposed methods use edge-weighted image graphs and hierarchical trees as input, and they evaluate different proposals on the edge detection and segmentation tasks. The learning model is the Random Forest, a fast and scalable method for working with high-dimensional data. Results demonstrate that it is possible to create a learning framework dependent only on the hierarchical data that presents a state-of-the-art performance in multiple tasks.