HARP (algorithm)

HARP is an algorithm used in the field of graph representation learning. It stands for Hierarchical Representation Learning for Hyperbolic Networks. It is designed to learn node embeddings for graph-structured data, specifically aiming to capture the hierarchical and structural properties inherent in many real-world networks.

HARP operates by first coarsening the input graph into a series of smaller, representative graphs. This coarsening process creates a hierarchy of graphs, where each level represents a more abstract view of the original graph. The algorithm then learns node embeddings at each level of the hierarchy, starting from the coarsest graph and progressively refining the embeddings as it moves towards the original graph.

The core idea behind HARP is that learning embeddings on coarser graphs allows the algorithm to capture global structural information more effectively, while learning on finer graphs allows it to capture local structural information. By combining information from different levels of the hierarchy, HARP aims to produce node embeddings that are both globally consistent and locally accurate.

The algorithm can be broadly divided into two main stages:

1. Graph Coarsening: This stage involves creating a hierarchy of graphs by repeatedly coarsening the original graph. Various graph coarsening techniques can be employed, such as random matching, edge collapsing, or spectral clustering. The goal is to reduce the size of the graph while preserving its important structural characteristics.

2. Embedding Refinement: This stage involves learning node embeddings at each level of the graph hierarchy. The process starts at the coarsest level, where node embeddings are initialized. Then, the embeddings are refined by propagating information from coarser levels to finer levels. This propagation is typically done using a neural network model, such as a graph convolutional network (GCN) or a Skip-gram model. The learned embeddings are then used to initialize the embeddings at the next finer level, and the process is repeated until the original graph is reached.

HARP's ability to capture hierarchical structure makes it suitable for applications such as link prediction, node classification, and graph visualization in domains where hierarchical relationships are significant, such as social networks, biological networks, and knowledge graphs. Compared to some other graph embedding techniques, HARP emphasizes the importance of leveraging hierarchical information for improved representation learning.