Inhomogeneous graph trend filtering via a l 2,0 -norm cardinality penalty

Area of Science:

• Graph Signal Processing
• Machine Learning
• Network Analysis

Background:

• Estimating signals on graphs is crucial for analyzing complex network data.
• Existing methods struggle with signals exhibiting varying smoothness across graph nodes.

Purpose of the Study:

• To develop a novel Graph Trend Filtering (GTF) model for piecewise smooth graph signals.
• To address challenges posed by inhomogeneous smoothness in graph data.
• To provide a unified framework for graph clustering and edge cut.

Main Methods:

• Proposing a novel L1-norm penalized Graph Trend Filtering (GTF) model.
• Developing spectral decomposition and simulated annealing methods for solving the GTF model.
• Demonstrating the model's equivalence to k-means clustering and minimum graph cut.

Main Results:

• The GTF model achieves superior performance in denoising, support recovery, and semi-supervised classification compared to existing methods.
• The proposed GTF model offers more efficient computation, especially for large graph datasets.
• Experimental validation on synthetic and real-world data confirms the model's effectiveness.

Conclusions:

• The proposed GTF model provides an effective and efficient approach for analyzing piecewise smooth signals on graphs.
• The unified framework of clustering and graph cut offers new insights into graph signal processing.
• This work advances graph-based machine learning applications through improved signal estimation.