Scatter balance: an angle-based supervised dimensionality reduction.

Area of Science:

• Machine Learning
• Data Science
• Pattern Recognition

Background:

• Subspace selection is crucial for efficient data classification, clustering, and visualization.
• Linear Discriminant Analysis (LDA) and Maximum Margin Criterion (MMC) are established subspace selection algorithms.
• Understanding scatter effects and outlier impacts is key to improving subspace selection.

Purpose of the Study:

• To analyze the effects of scatters and outlier classes on LDA and MMC algorithms.
• To propose a novel subspace selection method, Angle Linear Discriminant Embedding (ALDE).
• To extend ALDE for high-dimensional data processing via a two-stage approach (TS-ALDE).

Main Methods:

• Intensive research and analysis of LDA and MMC algorithms, focusing on scatter boundaries.
• Development of ALDE based on angle measurement to redefine within-class and between-class scatter matrices.
• Extension of ALDE to TS-ALDE for handling high-dimensional datasets.

Main Results:

• ALDE effectively balances within-class and between-class scatters and demonstrates robustness to outlier classes.
• TS-ALDE achieves lower time complexity compared to ALDE for high-dimensional data.
• Experimental validation on synthetic, UCI, and image datasets confirms ALDE and TS-ALDE efficacy.

Conclusions:

• ALDE provides an effective approach to subspace selection, addressing limitations of existing methods.
• TS-ALDE offers a computationally efficient solution for subspace selection in high-dimensional data.
• The proposed methods enhance data processing efficiency and robustness in classification and clustering tasks.