GPS: A Probabilistic Distributional Similarity with Gumbel Priors for Set-to-Set Matching.

Area of Science:

• Computer Science
• Machine Learning
• Artificial Intelligence

Background:

• Set-to-set matching is crucial for identifying correspondences between unordered data.
• Traditional metrics like Chamfer Distance (CD) and Earth Mover's Distance (EMD) have limitations in accuracy, robustness, and computational cost.

Purpose of the Study:

• To propose a novel and effective set-to-set matching similarity measure.
• To address the limitations of existing metrics in accuracy and computational efficiency.

Main Methods:

• Developed a new similarity measure, GPS (Gumbel Prior Similarity), leveraging Gumbel prior distributions.
• Modeled the distribution of minimum distances from CD using Gumbel distributions, inspired by real-world applications.
• Validated the method on few-shot image classification and 3D point cloud completion tasks.

Main Results:

• GPS demonstrates significant improvements over state-of-the-art loss functions.
• The method shows enhanced accuracy and robustness in benchmark datasets.
• The approach effectively models minimum distance distributions encountered in applications like point cloud completion.

Conclusions:

• GPS offers a powerful and efficient alternative for set-to-set matching.
• The Gumbel distribution provides an effective framework for developing advanced similarity measures.
• The proposed method advances the state-of-the-art in machine learning applications involving set-to-set comparisons.