Graph Neural Networks and Clustering Algorithms: Mathematical Foundations and Applications

Dear Colleagues,

Within the field of machine learning, graph neural networks (GNNs) provide a rigorous framework for representing and analyzing complex structured data, while clustering algorithms offer effective means for identifying latent patterns in high-dimensional datasets. Consequently, these approaches have become foundational research areas in contemporary artificial intelligence. GNNs, in particular, integrate relational topology with node and edge attributes, enabling the extraction of representations that preserve both structural dependencies and feature interactions. Clustering algorithms group samples according to similarity measures derived from their statistical or geometric properties. In doing so, they reveal intrinsic data structures and pattern formations without requiring labels. These approaches have driven significant progress in fields such as computer vision, pattern recognition, path planning, fault diagnosis, system control, and transportation system optimization, while also opening new research avenues in multimodal learning and explainable artificial intelligence.

We invite researchers and practitioners to submit original research articles that advance the mathematical foundations, model innovations, and practical applications within this field.

Topics of interest include, but are not limited to, the following:

• Fundamental innovation and optimization of GNNs and clustering algorithms;
• Graph representation and structure discovery;
• Applications of spectrum clustering in deep learning;
• Integration of GNNs with clustering for complex data analysis;
• Scalable and efficient graph neural network architectures;
• Applications in visual, pattern recognition, and path planning;
• Predictive maintenance and condition monitoring;
• Control and optimization in transportation systems.

Dr. Tao Li
Dr. Uchenna Diala
Dr. Yunpeng Zhu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• graph neural networks
• clustering algorithms
• spectral graph theory
• graph signal processing
• optimization-based clustering
• mathematical foundations
• unsupervised learning
• fractional optimization
• industrial applications with GNNs or clustering algorithms