Learning Multiple Local Metrics: Global Consideration Helps.

Area of Science:

• Machine Learning
• Computer Vision
• Data Science

Background:

• Learning distance metrics is crucial for object comparison.
• Heterogeneous objects require multiple local metrics due to complex properties.
• Existing methods often build local metrics independently, potentially missing global context.

Purpose of the Study:

• To propose a novel framework, Local metrics Facilitated Transformation (Lift), that emphasizes the synergistic effect of global metrics in generating local ones.
• To theoretically analyze the relationship between global and local metrics within the Lift framework.
• To demonstrate the practical superiority and adaptability of the Lift approach.

Main Methods:

• The Lift framework adaptively constructs local transformations guided by a global metric counterpart.
• Locality anchored centers are employed to decompose multiple local views.
• A diversity regularizer is introduced to minimize redundancy among learned biases.

Main Results:

• Generalization analyses reveal the theoretical underpinnings of the global-local metric relationship in Lift.
• Empirical comparisons demonstrate the superior performance of the Lift framework in classification tasks.
• Numerical and visualization studies validate the framework's adaptability across different domains.

Conclusions:

• The Lift framework effectively integrates global and local metric learning for improved object comparison.
• The joint learning approach enhances the performance and representation of complex data.
• Lift offers a theoretically sound and empirically validated method for distance metric learning.