Visualization of tree-structured data through generative topographic mapping.

Area of Science:

• Machine Learning
• Data Visualization
• Computational Statistics

Background:

• Topographic maps are essential for visualizing high-dimensional data.
• Existing methods like self-organizing maps for structured data (SOMSD) have limitations in probabilistic interpretation and flexibility.
• Tree-structured data presents unique challenges for traditional mapping techniques.

Purpose of the Study:

• To develop a probabilistic generative approach for constructing topographic maps of tree-structured data.
• To offer a more interpretable and flexible alternative to existing methods.
• To enable effective cluster detection through magnification factors.

Main Methods:

• A probabilistic generative model is proposed, defining a low-dimensional manifold of local noise models (hidden Markov tree models).
• The model utilizes a smooth mapping from a low-dimensional latent space to the local model space.
• The approach is contrasted with recursive neural-based techniques, specifically SOMSD.

Main Results:

• The probabilistic model provides a natural cost function for optimization and principled model comparison.
• The method allows for transparent interpretation by inspecting underlying local noise models.
• Magnification factors are calculated, aiding in the detection of data clusters.
• The approach is validated on toy, artificial, and quadtree image datasets.

Conclusions:

• The proposed probabilistic generative approach offers significant advantages for topographic mapping of tree-structured data.
• Benefits include enhanced interpretability, principled model evaluation, and improved cluster detection capabilities.
• This method provides a flexible framework for incorporating various notions of data similarity through different local noise models.