Random walks lifting (Point Cloud to Graph)

[nkanak]

GraphRandomWalksLifting

This lifting transforms point cloud data into graph representations using random walks. The method facilitates a way to capture the underlying topological features of point cloud data, something that is essential for various applications in machine learning, including computer vision and computational geometry.

Implementation

1. Point cloud to k-NN graph:

   • The algorithm initially creates a k-nearest neighbors graph using the point cloud data. It represents each point in the cloud as a node and connects it to its k nearest neighbors based on the Euclidean distance.

2. Edge weight calculation:

   • The edges in the k-NN graph have weights calculated by the Euclidean distances between connected points. These weights correspond to the geometric proximity of the points.

3. Normalization of edge weights:

   • The edge weights are stochastically normalized to transition probabilities using a softmax function. Here we ensure that the transition probabilities from any node sum up to 1.

4. Random walks:

   • Multiple random walks are conducted from each node in the graph. During these walks, transitions between nodes are affected by the normalized edge weights. The frequency of transitions between nodes is recorded. In that way, we capture the topological relationships in the data.

5. Topological graph construction:

   • A new topological graph is constructed based on the calculated transition counts from the random walks.

Team

• Nikos Kanakaris ([email protected])
• Veljko Kovač ([email protected])
• Nesreen K Ahmed ([email protected])
• Paul Bogdan ([email protected])
• Andrei Irimia ([email protected])

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[levtelyatnikov]

Hello, @nkanak ! Thank you for your submission. As we near the end of the challenge, I am collecting participant info for the purpose of selecting and announcing winners. Please email me (or have one member of your team email me) at [email protected] so I can share access to the voting form. In your email, please include:

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