Horospherical Decision Boundaries for Large Margin Classification in Hyperbolic Space.

Area of Science:

• Machine Learning
• Data Science
• Geometry

Background:

• Hyperbolic spaces are increasingly used for hierarchical data representation.
• Existing classification algorithms in hyperbolic spaces often lead to non-convex optimization problems.
• Current methods utilize hyperplanes or geodesics for decision boundaries, posing optimization challenges.

Purpose of the Study:

• To propose a novel large margin classifier for hyperbolic spaces.
• To develop a classifier with a geodesically convex optimization problem.
• To achieve guaranteed global optimality in classification tasks.

Main Methods:

• Introduced horospherical decision boundaries for classification in hyperbolic spaces.
• Formulated a geodesically convex optimization problem.
• Utilized Riemannian gradient descent techniques for optimization.

Main Results:

• The proposed classifier leads to a geodesically convex optimization problem.
• The method guarantees a globally optimal solution.
• Experimental results show competitive performance against state-of-the-art (SOTA) classifiers.

Conclusions:

• The novel horospherical classifier offers a robust and globally optimal solution for hyperbolic data.
• This approach overcomes the non-convexity issues of previous methods.
• The classifier demonstrates strong performance, making it a valuable tool for hierarchical data analysis.