Dimensionality Reduction for Tensor Data Based on Local Decision Margin Maximization.

Area of Science:

• Machine Learning
• Data Science
• Computer Vision

Background:

• Maximizing the margin is a key concept in classifier design.
• Preserving local discriminant information is crucial for effective dimensionality reduction.

Purpose of the Study:

• Propose a novel supervised dimensionality reduction method for tensor data.
• Develop a technique based on local decision margin maximization.
• Preserve local discriminant information in a low-dimensional space.

Main Methods:

• Decompose tensor data into overlapping local regions.
• Extract similarity and anti-similarity coefficients.
• Utilize multilinear projection to preserve coefficients in the embedding space.
• Employ an iterative scheme for optimization.

Main Results:

• Dimension-reduced local regions form convex sets with clustered intraclass points.
• Local decision margins are maximized, enhancing data separation.
• Local discriminant structure is effectively maintained in the reduced-dimensional space.
• The method demonstrated effectiveness on 6 real-world datasets.

Conclusions:

• The proposed method successfully reduces dimensionality while preserving crucial local data structures.
• Local decision margin maximization is an effective strategy for tensor data analysis.
• The iterative scheme provides an efficient solution for the optimization problem.