Learning Robust Discriminant Projections via Double Capped L_p-Norm Distance Metrics With "Min" Constraints.

Area of Science:

• Machine Learning
• Computer Vision
• Data Science

Background:

• Robust norm distance-based linear discriminant analysis (LDA) is crucial for feature extraction.
• Existing methods struggle to suppress outliers without hindering normal data discrimination.
• Outliers can disproportionately affect LDA performance, especially with higher Lp-norm values.

Purpose of the Study:

• To develop a novel robust LDA technique that accurately discriminates normal points while effectively handling outliers.
• To introduce a new metric, double capped Lp-norm distance (CLD) with min constraints (DCLDA), for measuring dispersions.
• To address the nonconvexity and nonsmoothness of the objective function through reformulation and an iterative algorithm.

Main Methods:

• Proposed a novel robust LDA model using double capped Lp-norm distance (CLD) metrics with min constraints (DCLDA).
• The DCLDA model treats normal points and outliers separately, using Lp-norm for normal points and mitigating outlier effects.
• Introduced a theoretical reformulation to address the objective function's nonconvexity and nonsmoothness, enabling an effective iterative algorithm.

Main Results:

• The proposed DCLDA model effectively discriminates normal points while minimizing the impact of outliers.
• The developed iterative algorithm, based on the reformulation, is theoretically proven to be convergent.
• Extensive experiments on real-world image classification datasets demonstrate the method's superior effectiveness.

Conclusions:

• The DCLDA method offers a robust solution for feature extraction in the presence of outliers.
• The novel metric and algorithmic approach provide a significant advancement in robust LDA techniques.
• The method shows strong performance across various image classification tasks, highlighting its practical applicability.