Clustering is a fundamental machine learning task, which aim at assigning instances into groups so that similar samples belong to the same cluster while dissimilar samples belong to different clusters. Shallow clustering methods usually assume that data are collected and expressed as feature vectors within which clustering is performed. However, clustering high-dimensional data, such as images, texts, videos, and graphs, poses significant challenges for clustering tasks, such as indiscriminate representation and intricate relationships among instances. Over the past decades, deep learning has achieved remarkable success in effective representation learning and modeling complex relationships. Motivated by these advancements, Deep Clustering seeks to improve clustering outcomes through deep learning techniques, garnering considerable interest from both academia and industry. Despite many contributions to this vibrant area of research, the lack of systematic analysis and a comprehensive taxonomy has hindered progress in this field. In this survey, we first explore how deep learning can be integrated into deep clustering and identify two fundamental components: the representation learning module and the clustering module. Then, we summarize and analyze the representative design of these two modules. Furthermore, we introduce a novel taxonomy of deep clustering based on how these two modules interact, specifically through multistage, generative, iterative, and simultaneous approaches. In addition, we present well-known benchmark datasets, evaluation metrics, and open-source tools to clearly demonstrate different experimental approaches. Finally, we examine the practical applications of deep clustering and propose challenging areas for future research.

Graph data, prevalent across domains like social networks, biological systems, and recommendation systems, presents significant challenges due to its large scale and complex structure. The advent of Graph Neural Networks (GNNs) has revolutionized graph data mining by effectively capturing node dependencies and neighborhood information. However, the computational complexity of processing large-scale graphs remains a major hurdle, as real-world graphs often consist of millions or even billions of nodes and edges. Efficient techniques like message passing and sampling have helped mitigate this issue, but memory and processing constraints persist. A promising approach to addressing these challenges is learning to reduce the size of large-scale graphs while retaining essential information, thus facilitating faster and more efficient graph data mining tasks, such as graph condensation, reduction, coarsening, summarization, and so on. Despite the differences in terminology, approaches under these topics share the same motivation: to generate smaller yet informative graphs that can replace the original large-scale datasets. In this article, we unify these approaches under the concept of Graph Scaling (GS), highlighting the shared motivation across multiple topics. Alongside this definition, to clarify the question of what principles should be followed when scaling a graph and how a scaled graph was formulated, we propose a taxonomy to methodically categorize and understand existing methods. Moreover, by organizing the dataset and evaluation metrics, we aim to provide a more comprehensive understanding of the GS methods from a practical perspective. Moving forward, we delve into the limitations and challenges of GS methods, identifying the shortcomings and potential in the literature. Finally, we conclude this article by outlining future directions and offering concise guidelines to inspire future research in this field. A full paper list and online resources about GS are available at https://github.com/Frostland12138/Awesome-Graph-Scaling .

Graph data mining techniques in real-world scenarios often encounter significant computational challenges, especially when the graph contains a large number of nodes and edges. Recently, Graph Condensation (GC) has emerged to offer data-centric solutions that address the challenge of graph volume, enhancing the efficiency of graph data mining and storage. Current methods in GC rely solely on optimizing heuristic metrics of one-way maintenance of key information in the condensed graph. However, the maintenance of key information may be insufficient due to the significant condensation ratio, yet these methods lack an effective mechanism to verify and compensate for that. To this end, this paper aims to enhance the maintenance of key information through a reconstruction-based alignment mechanism. More specifically, inspired by the Kolmogorov Complexity, we revisit the theoretical foundations of GC and propose a way-back mechanism that introduces a feedback loop of learning to reconstruct the original graph from the condensed graph, with the objective of key information alignment, namely the WbGC. We modify several GC methods with our mechanism, and the experiments show that our approach provides an enhanced solution for GC.