Go to ICLR 2025 Conference homepageSolving Normalized Cut Problem with Constrained Action Space
Keywords: graph partitioning, reinforcement learning, combinatorial optimization
Abstract: We address the problem of Normalized Cut (NC) in weighted graphs where the shape of the partitions follow an apriori pattern, namely they must approximately be shaped like rings and wedges on a planar graph. Classical methods like spectral clustering and METIS do not have a provision to specify such constraints and neither do newer methods that combine GNNs and Reinforcement Learning as they are based on initialization from classical methods. The key insight that underpins our approach, Wedge and Ring Transformers (WRT), is based on representing a graph using polar coordinates and then using a multi-head transformer with a PPO objective to optimize the non-differential NC objective. To the best of our knowledge, WRT is the first method to explicitly constrain the shape of NC and opens up possibility of providing a principled approach for fine-grained shape-controlled generation of graph partitions. On the theoretical front we provide new Cheeger inequalities that connect the spectral properties of a graph with algebraic properties that capture the shape of the partitions. Comparisons with adaptations of strong baselines attest to the strength of WRT.
Primary Area: learning on graphs and other geometries & topologies
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Submission Number: 13226
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