Julien's Podcast

Cleora is an unsupervised graph embedding algorithm designed to generate node representations for downstream machine learning tasks.

1. Context and Importance

Graph Structures

Graphs model real-world interactions using nodes (entities) and edges (relationships). They are widely used in various domains, such as biology, road networks, and social networks.

Node Embeddings

Node embeddings are crucial for representing node properties as numerical vectors, making them suitable for machine learning models. Traditional embedding methods often struggle to scale with large graphs.

2. How Cleora Works

• It iteratively performs normalized, weighted averaging of neighbor embeddings.
• Each embedding dimension is optimized independently.
• It does not require an explicit learning objective or sampling.

3. Key Advantages

• Simplicity: Few configurable parameters.
• Versatility: The absence of an explicit objective makes the embeddings highly flexible.
• Scalability: Efficiently handles massive graphs.
• Speed: Faster than other CPU-based methods, up to 5 times faster than PBG and over 200 times faster than DeepWalk.
• Additivity: Supports chunked graph embeddings that can be merged later.
• Inductivity: Generalizes to unseen data.

4. Hypergraph Expansion

Cleora handles hyper-edges by breaking them down into simple edges using clique expansion or star expansion techniques.

5. Embedding Process

Cleora leverages a random walk transition matrix and refines embeddings through iterative updates. The process can be viewed as an iterated L2-normalized weighted averaging of neighboring nodes’ representations.

6. Comparison with Other Methods

Cleora offers node embedding inductivity and allows for computing partial embeddings on chunked graphs, which can later be merged. By adjusting the iteration number, Cleora can be fine-tuned for different tasks, such as complementary or substitute prediction.

Compared to other graph embedding methods like PBG and GOSH, Cleora achieves competitive embedding quality while significantly improving computational speed.

7. Open-Source Availability

Cleora is released under the MIT license, making it freely available for research and practical applications.