Method

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First， LAST-MGCL incorporates a local-global graph augmentation strategy， which combines two complementary techniques： a Conditional Variational Autoencoder （CVAE） for local enhancement and an SVD-based module for global enhancement. The CVAE is designed to enrich feature representations within local neighborhoods， enabling the model to better capture the intricate relationships between nodes that have limited neighborhood connectivity. This is particularly beneficial for sparse graphs， where local structure is often underrepresented. By generating richer local feature representations， the CVAE ensures that the model can more effectively process nodes with few neighbors， ultimately improving the overall quality of graph embeddings. On the other hand， the SVD-based module focuses on global structural patterns， leveraging singular value decomposition to capture the topological essence of the graph at a broader scale. This global enhancement ensures that key topological features are preserved， facilitating the model's ability to generalize across different graph types. By combining these local and global enhancement techniques， LAST-MGCL creates a multi-granularity augmentation strategy that provides diverse views of the graph， enriching the learning process and improving the expressiveness of various graph neural networks （GNNs）. Second， LAST-MGCL adopts a triple encoding network architecture， which leverages the power of multi-head attention to process both the original and augmented graph data. In this architecture， the graph data is passed through three sub-networks， each guided by a multi-head attention mechanism that enables the model to focus on different aspects of the graph's structure. The multi-head attention mechanism is designed to capture diverse， multi-scale dependencies across the graph， making it particularly effective at integrating information from various views of the graph. Through cross-network information exchange， the sub-networks collaborate， strengthening the model's ability to integrate representations from different graph perspectives. This cross-network collaboration enhances the multi-view fusion， which is critical for improving the robustness and stability of the learned graph embeddings. By ensuring that information is effectively shared between sub-networks， the model can integrate complementary information from both original and augmented graph views， thus improving the overall representation quality. Third， LAST-MGCL introduces an innovative multi-dimensional contrastive learning optimization framework to further refine the learning process. This novel framework integrates multiple contrastive learning objectives to optimize graph representation learning across various dimensions. The contrastive loss is designed to combine cross-network contrastive learning， which aligns representations between the original and augmented graphs， with cross-view contrastive learning that enhances generalization across different augmented perspectives. Additionally， neighbor contrastive learning is incorporated to maintain local semantic coherence by focusing on the relationships between neighboring nodes within the graph. These objectives work together to reinforce the structural consistency and semantic alignment of graph representations at multiple granularities， ensuring that both local and global dependencies are effectively captured. By applying this multi-dimensional contrastive framework， LAST-MGCL addresses critical challenges such as the underutilization of contrastive information in traditional methods， the reliance on negative samples， and the difficulty of aligning representations across different graph views.

Conclusion

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In node classification tasks， the LAST-MGCL model demonstrates strong performance across several benchmark datasets， achieving classification accuracies of 82.5% on Cora， 72.5% on Citeseer， and 81.6% on PubMed. These results indicate that LAST-MGCL consistently outperforms state-of-the-art contrastive learning methods， offering superior classification accuracy and robustness. Additionally， the node embeddings generated by LAST-MGCL exhibit more compact intra-cluster cohesion and clearer inter-cluster boundaries， highlighting the model's ability to effectively capture and distinguish graph structures. Ablation experiments were conducted to assess the contribution of each model component. The results revealed that removing key components significantly degraded performance. For example， removing multi-dimensional contrastive learning resulted in the most significant performance drop， with a reduction of 9.7%. These findings underscore the importance of the combined local-global graph augmentation approach， which captures both local and global graph information， and the role of multi-dimensional contrastive learning in enhancing node interactions and clustering. Furthermore， a hyperparameter sensitivity analysis was performed to optimize model performance. Finally， t-SNE visualizations comparing LAST-MGCL to the best baseline models show that LAST-MGCL excels in node clustering and maintains clear class boundaries across all datasets， further validating its superior performance in representation learning. In summary， LAST-MGCL enhances the existing graph contrastive learning framework by integrating local-global graph augmentation， multi-view representation learning， and multi-dimensional contrastive optimization. Specifically designed for unsupervised graph learning， it provides an effective solution for learning high-quality node representations from unlabeled graph data.

Purpose

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Graph representation learning has been widely applied across various domains， including social networks， bioinformatics， and recommendation systems， due to its ability to effectively capture and encode structural and relational information within graph-structured data. Among existing approaches， unsupervised graph contrastive learning （GCL） has gained significant attention as it enables high-quality node representations without relying on extensive labeled data， making it particularly suitable for real-world applications where labeled annotations are costly and scarce. However， despite its advantages， current GCL methods suffer from several inherent limitations. Most existing graph contrastive learning techniques rely on single-perspective augmentation strategies， such as randomly removing edges or nodes， which can only capture a limited range of structural variations within a graph. However， graphs often exhibit intricate， multi-level dependencies that a single augmentation approach cannot adequately represent. For instance， a graph may contain subgraphs with varying node connectivity patterns or may encode higher-order relationships that are overlooked by such simple augmentations. As a result， relying solely on one perspective reduces the richness and diversity of learned node representations， limiting the model's ability to generalize across different graph structures. Moreover， conventional contrastive learning frameworks often employ coarse-grained contrastive mechanisms， comparing entire subgraphs or large sets of nodes at a high level of abstraction. While this can work in certain contexts， it fails to capture finer-grained distinctions in local node structures and semantic attributes， leading to suboptimal node embeddings. These limitations hinder the model’s ability to learn discriminative representations， thereby affecting its effectiveness in tasks such as node classification， clustering， and link prediction.