Persistent Laplacian-enhanced algorithm for scarcely labeled data classification

Area of Science:

• Machine Learning
• Computational Topology
• Data Science

Background:

• Supervised machine learning (ML) requires extensive labeled data, which is often costly and time-consuming to acquire.
• Semi-supervised learning (SSL) leverages both labeled and unlabeled data to mitigate data acquisition challenges.
• Graph-based SSL methods are effective but can be computationally intensive.

Purpose of the Study:

• To develop an efficient semi-supervised learning method that minimizes the requirement for labeled data.
• To integrate algebraic topology with graph-based techniques for enhanced ML performance.
• To address data scarcity issues in domains like medical analysis and natural language processing.

Main Methods:

• Proposed a novel method: persistent Laplacian-enhanced graph MBO.
• Integrated persistent spectral graph theory with the Merriman-Bence-Osher (MBO) scheme.
• Utilized filtration to generate chain complexes and simplicial complexes, constructing persistent Laplacians.

Main Results:

• The proposed method demonstrates high efficiency and requires significantly less labeled data compared to traditional ML techniques.
• The method is adaptable for both small and large datasets.
• Evaluated on classification tasks, the persistent Laplacian-enhanced graph MBO outperformed existing semi-supervised algorithms.

Conclusions:

• The persistent Laplacian-enhanced graph MBO offers a powerful and data-efficient approach to semi-supervised learning.
• This method provides a valuable alternative for applications with limited labeled data.
• The integration of algebraic topology enhances the capabilities of graph-based SSL.