Ordinal regression neural networks based on concentric hyperspheres

Area of Science:

• Machine Learning
• Statistics
• Ordinal Regression

Background:

• Threshold models are standard for ordinal regression but rely on restrictive one-dimensional projections.
• These one-dimensional projections can be inadequate for complex datasets.

Purpose of the Study:

• To propose a multidimensional latent space representation for ordinal regression.
• To relax the strict projection requirement of traditional threshold models.
• To enhance the performance and flexibility of ordinal regression methods.

Main Methods:

• A neural network model is developed to implement a multidimensional latent space.
• Each dimension is constructed as a linear combination of basis functions.
• Classes are organized using concentric hyperspheres, with each class encompassing previous ones.

Main Results:

• The proposed multidimensional latent space demonstrated improved performance on two key metrics across 12 datasets.
• A three-dimensional latent space model achieved competitive results against state-of-the-art ordinal regression techniques.
• The method outperformed a nominal neural network and a proportional odds model.

Conclusions:

• The multidimensional latent space offers a more flexible and effective approach to ordinal regression.
• The concentric hypersphere arrangement provides a robust structure for ordinal data.
• This novel method shows significant promise for improving ordinal classification tasks.