Traditional clustering methods assume that precise pairwise distances for the input data are readily available. However, this assumption is often impractical in real-world scenarios where data points cannot be measured accurately. For instance, machine learning-based techniques for estimating distances may fail when the dataset consists of images, videos, or natural language. This paper studies clustering and graph problems in settings where direct access to pairwise distances between all pairs is expensive. We adopt oracle-based methods as defined by Galhotra et al. (2024), focusing on two types of oracles: the quadruplet oracle, a weak and inexpensive comparator that answers binary queries of the form "Is A closer to B or C closer to D?" and the distance oracle, a stronger but costlier oracle that returns exact pairwise distances. The quadruplet oracle can be implemented via crowdsourcing, trained classifiers, or other predictive models. As these sources are often unreliable, the oracle’s responses may be noisy; we consider both probabilistic and adversarial noise models. Consider a finite metric space $\Sigma=(\mathcal{V},d)$ of size $|\mathcal{V}|=n$ that supports the quadruplet and the distance oracle. When the input dataset has low intrinsic (doubling) dimension, for each of the $k$-center, $k$-median, and $k$-means clustering problem on $\mathcal{V}$, we design constant approximation algorithms that perform $\widetilde{O}(n+k^2)$ calls to the quadruplet oracle and $\widetilde{O}(1)$ calls to the distance oracle in both noise models. For general metric spaces, our algorithms achieve constant approximation while making $\widetilde{O}(nk)$ calls to the quadruplet oracle and $\widetilde{O}(1)$ calls to the distance oracle. In all cases, we improve the quadruplet oracle query complexity by a factor of $k$ and the distance oracle call complexity by a factor of $k^2$ compared to Galhotra et al. (2024). Furthermore, in low dimensional settings, if the spread of the input data is polynomially bounded, we construct a data structure performing $\widetilde{O}(n)$ queries to the quadruplet oracle and $\widetilde{O}(1)$ queries to the distance oracle, such that given any query pair of vertices $(u,v)\in \mathcal{V}\times \mathcal{V}$, it approximates the distance $d(u,v)$ without using any oracle queries. Once the data structure is constructed, we can emulate standard algorithms for various graph problems on $\Sigma$ without additional oracle queries. In summary, our results show that access to a noisy pairwise ranker for distances is to sufficient to efficiently solve a large class of problems while almost entirely bypassing exact distance computations.

Graph contrastive learning (GCL) has become the de-facto approach to conducting self-supervised learning on graphs for its superior performance. However, non-semantic graph augmentation methods prevent it from achieving better performance, and it suffers from vulnerability to graph attacks. To deal with these problems, we propose AEGCL to leverage graph AutoEncoder in Graph Contrastive Learning which directly targets graph property reconstruction to boost GCL effectiveness and robustness. Specifically, AEGCL has two distinctive characteristics, (1) a novel adaptive augmentation strategy based onmotifcentrality is proposed, which leverages semantic significant higher-order graph property; (2) the original attributed graph is decoupled into feature graph and topology graph to extract their dedicated information, and a simpleAttnFuseis proposed to combine the two augmented graphs and the two decoupled graphs. Graph autoencoder can thus be applied to the topology domain and raw attribute domain. Empirically, extensive experiments on benchmark graph datasets show that AEGCL outperforms existing baseline methods in terms of classification accuracy and robustness.

Class imbalance is the phenomenon that some classes have much fewer instances than others, which is ubiquitous in real-world graph-structured scenarios. Recent studies find that off-the-shelf Graph Neural Networks (GNNs) would under-represent minor class samples. We investigate this phenomenon and discover that the subspaces of minor classes being squeezed by those of the major ones in the latent space is the main cause of this failure. We are naturally inspired to enlarge the decision boundaries of minor classes and propose a general framework GraphSHA by Synthesizing HArder minor samples. Furthermore, to avoid the enlarged minor boundary violating the subspaces of neighbor classes, we also propose a module called SemiMixup to transmit enlarged boundary information to the interior of the minor classes while blocking information propagation from minor classes to neighbor classes. Empirically, GraphSHA shows its effectiveness in enlarging the decision boundaries of minor classes, as it outperforms various baseline methods in class-imbalanced node classification with different GNN backbone encoders over seven public benchmark datasets. Code is avilable at https://github.com/wenzhilics/GraphSHA.

Contrastive learning (CL) has become the de-facto learning paradigm in self-supervised learning on graphs, which generally follows the "augmenting-contrasting'' learning scheme. However, we observe that unlike CL in computer vision domain, CL in graph domain performs decently even without augmentation. We conduct a systematic analysis of this phenomenon and argue that homophily, i.e., the principle that "like attracts like'', plays a key role in the success of graph CL. Inspired to leverage this property explicitly, we propose HomoGCL, a model-agnostic framework to expand the positive set using neighbor nodes with neighbor-specific significances. Theoretically, HomoGCL introduces a stricter lower bound of the mutual information between raw node features and node embeddings in augmented views. Furthermore, HomoGCL can be combined with existing graph CL models in a plug-and-play way with light extra computational overhead. Extensive experiments demonstrate that HomoGCL yields multiple state-of-the-art results across six public datasets and consistently brings notable performance improvements when applied to various graph CL methods. Code is avilable at https://github.com/wenzhilics/HomoGCL.

Many real-world graphs can be viewed as Heterogeneous Networks or Heterogeneous Information Networks (HINs) for that they comprise a diversity of node types and relation types. Due to the efficient representation ability of Graph Neural Network and the idea of random walk, many recent studies apply graph representation learning to HINs and achieve satisfactory results. However, these works either treat different node types in a metapath equally, which is inconsistent with the original graph semantic information for that different node types should have different statuses, or only consider the first-order (node-level) and second-order (metapath-level, a.k.a. link-level) information aggregation while ignoring the higher-order relations. To tackle these two problems, we propose a novel Star-Shaped Hierarchical Graph Attentional Network (StarGAT) model to boost representation learning in HINs. Specifically, we assume nodes in HINs can be categorized into a star-shaped structure including one center node type and a bunch of auxiliary node types in a specific task; and we encode node-level, link-level and motif-level attentions in a hierarchical manner to capture richer semantic information. Extensive experiments on three datasets illustrate the model effectiveness.