Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming

• URL: http://arxiv.org/abs/2506.01826v1
• Date: Mon, 02 Jun 2025 16:09:51 GMT
• Title: Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming
• Authors: Haruki Yokota, Hiroshi Higashi, Yuichi Tanaka, Gene Cheung,
• Abstract summary: A balanced signed graph has eigenvectors that map via a simple linear transform to ones in a corresponding positive graph.<n>We propose an efficient method to learn a balanced signed graph Laplacian directly from data.
• Score: 26.334739062500674
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph is a signed graph with no cycles containing an odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map via a simple linear transform to ones in a corresponding positive graph Laplacian, thus enabling reuse of spectral filtering tools designed for positive graphs. We propose an efficient method to learn a balanced signed graph Laplacian directly from data. Specifically, extending a previous linear programming (LP) based sparse inverse covariance estimation method called CLIME, we formulate a new LP problem for each Laplacian column $i$, where the linear constraints restrict weight signs of edges stemming from node $i$, so that nodes of same / different polarities are connected by positive / negative edges. Towards optimal model selection, we derive a suitable CLIME parameter $\rho$ based on a combination of the Hannan-Quinn information criterion and a minimum feasibility criterion. We solve the LP problem efficiently by tailoring a sparse LP method based on ADMM. We theoretically prove local solution convergence of our proposed iterative algorithm. Extensive experimental results on synthetic and real-world datasets show that our balanced graph learning method outperforms competing methods and enables reuse of spectral filters, wavelets, and graph convolutional nets (GCN) constructed for positive graphs.

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