Regularized Label Relaxation Linear Regression.

Area of Science:

• Machine Learning
• Computer Science
• Data Science

Background:

• Linear regression (LR) and its variants are common for classification.
• Existing LR methods often lack flexibility in fitting labels due to strict binary matrices.
• This limitation can hinder accurate classification performance.

Purpose of the Study:

• To propose a novel regularized label relaxation LR method.
• To enhance the flexibility of label fitting and improve class separation.
• To develop algorithms that are efficient and easy to implement.

Main Methods:

• Introduced a nonnegative label relaxation matrix to transform strict binary labels into slack variables.
• Incorporated a class compactness graph, derived from manifold learning, as a regularization term.
• Devised two algorithms based on L1 and L2 norm loss functions with closed-form solutions.

Main Results:

• The proposed method offers greater freedom in fitting labels and maximizes margins between classes.
• The class compactness graph regularization prevents overfitting by keeping similar labeled samples close.
• Experimental results demonstrate superior classification accuracy and reduced running times compared to state-of-the-art methods.

Conclusions:

• The novel regularized label relaxation LR method effectively addresses limitations of traditional LR for classification.
• The incorporation of label relaxation and class compactness graph leads to improved performance.
• The developed algorithms are practical due to their efficient, closed-form solutions.