Unsupervised Representation Learning with Adaptive Multi-Order Structural Graph Fusion

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High-dimensional unlabeled data often contain complex latent structures that are easily obscured by redundant features, noise, and unreliable neighborhood relationships. Although graph-based learning provides an effective means of preserving sample relationships, most existing methods mainly rely on first-order neighborhoods and therefore fail to fully exploit multi-order dependencies revealed by multi-hop propagation. To address this limitation, we formulate unsupervised representation learning as a graph-guided structure-preserving projection problem and propose Unsupervised Representation Learning with Adaptive Multi-order Structural Graph Fusion (URL-AMGF). The proposed method constructs multi-order graphs to characterize structural relationships at different neighborhood orders and adaptively fuses them into a unified guidance graph. This graph is then integrated into projection matrix learning, enabling graph structure optimization and low-dimensional representation learning to be jointly performed within a unified framework. By integrating local neighborhood information with multi-order structural cues, URL-AMGF learns low-dimensional representations that better reflect the structural relationships among samples. Experiments on multiple benchmark datasets show that URL-AMGF achieves generally competitive clustering performance compared with representative unsupervised dimensionality reduction and graph-based learning methods. These results indicate that adaptive multi-order graph fusion can provide effective structural guidance for structure-preserving unsupervised representation learning.