Improved learning of Riemannian metrics for exploratory analysis

Area of Science:

• Machine Learning
• Data Science
• Information Geometry

Background:

• Metric-based learning methods can be adapted to focus on discriminative data properties.
• Unsupervised learning often models all data variation, potentially obscuring interesting patterns.

Purpose of the Study:

• To review and enhance a metric learning principle for supervised unsupervised learning.
• To introduce improved approximations for information-geometric distances.
• To demonstrate applications in prototype-based and pairwise distance-based unsupervised methods.

Main Methods:

• Leveraging an information-geometric formulation to derive metrics.
• Developing improved approximations for distance calculations.
• Applying the enhanced metrics to self-organizing maps (SOM) and multidimensional scaling (MDS).

Main Results:

• The refined metric learning principle effectively guides unsupervised methods to model salient data variations.
• Improved distance approximations lead to more focused and discriminative learning.
• Successful application demonstrated in both SOM and Sammon's mapping (a form of MDS).

Conclusions:

• The metric learning principle offers a powerful way to supervise unsupervised learning.
• Enhanced approximations improve the performance of prototype-based and distance-based algorithms.
• This approach provides a principled way to model meaningful data variations.