Adaptive Local Linear Regression With Application to Printer Color Management

Abstract--Local learning methods, such as local linear regression and nearest neighbor classifiers, base estimates on nearby training samples, neighbors. Usually, the number of neighbors used in estimation is fixed to be a global "optimal" value, chosen by cross validation. This paper proposes adapting the number of neighbors used for estimation to the local geometry of the data, without need for cross validation. The term enclosing neighborhood is introduced to describe a set of neighbors whose convex hull contains the test point when possible. It is proven that enclosing neighborhoods yield bounded estimation variance under some assumptions. Three such enclosing neighborhood definitions are presented: natural neighbors, natural neighbors inclusive, and enclosing k-NN. The effectiveness of these neighborhood definitions with local linear regression is tested for estimating lookup tables for color management. Significant improvements in error metrics are shown, indicating tha...

• Type: Journal
• Year: 2008
• Where: TIP
• Authors: Maya R. Gupta, Eric K. Garcia, E. Chin
• Keywords: Local Linear Regression, Neighborhood Definition, Term Enclosing Neighborhood, TIP 2008