Adaptive local linear regression with application to printer color management.

Area of Science:

• Machine Learning
• Computer Vision
• Data Science

Background:

• Local learning methods rely on nearby data points.
• Current methods often use a fixed number of neighbors, determined globally.
• This can be suboptimal for varying data densities.

Purpose of the Study:

• To propose and evaluate adaptive neighborhood definitions for local learning.
• To reduce the need for cross-validation in selecting the number of neighbors.
• To improve estimation accuracy by adapting to local data geometry.

Main Methods:

• Introduced the concept of "enclosing neighborhoods" whose convex hull contains the test point.
• Developed three specific enclosing neighborhood definitions: natural neighbors, natural neighbors inclusive, and enclosing k-NN.
• Applied these neighborhoods to local linear regression for color management lookup table estimation.

Main Results:

• Enclosing neighborhoods were proven to yield bounded estimation variance under certain assumptions.
• Significant improvements in error metrics were observed when using enclosing neighborhoods with local linear regression.
• The adaptive approach demonstrated effectiveness in color management tasks.

Conclusions:

• Enclosing neighborhoods offer a promising adaptive strategy for local learning.
• This method enhances estimation accuracy by considering local data geometry.
• The approach shows potential for various local learning applications beyond color management.