Disruptive Innovations in Data Mining and Knowledge Discovery

Dear Colleagues,

The exponential growth of data generation driven by advances in sensor networks, the Industrial Internet of Things (IIoT), and emerging paradigms such as quantum computing has introduced significant challenges in extracting meaningful knowledge from complex, high-dimensional, and often noisy data. Addressing these challenges requires not only advanced computational techniques but also rigorous mathematical foundations, novel algorithmic frameworks, and interdisciplinary methodologies.

This Special Issue aims to highlight disruptive and mathematically grounded innovations in data mining and knowledge discovery that advance the development of efficient, scalable, robust, and explainable models. Particular emphasis is placed on contributions that provide solid theoretical analysis, formal guarantees, and principled mathematical insights alongside practical relevance.

We invite high-quality submissions of original research articles and comprehensive review papers addressing both theoretical and applied aspects of data mining through a mathematical lens. Topics of interest include, but are not limited to, the following:

Mathematical Foundations of Data Mining:

• Statistical learning theory and generalization bounds;
• Optimization methods for learning and inference;
• Probabilistic graphical models and Bayesian inference;
• Topological data analysis and persistent homology;
• Algebraic and geometric methods in pattern recognition.

Data Mining for Streaming and Time-Series Data:

• Online and incremental algorithms with provable performance guarantees;
• Real-time signal processing and adaptive filtering;
• Change-point detection and time-series forecasting;
• Functional and stochastic data analysis;
• Quantum computing for data analysis;
• Quantum algorithms for clustering, classification, and regression;
• Quantum linear algebra for large-scale data mining;
• Complexity theory in quantum machine learning;
• Mathematical modeling of quantum-enhanced learning systems.

Interpretable and Explainable Artificial Intelligence:

• Model simplification and surrogate modeling;
• Formal verification and robustness analysis of learning models;
• Shapley values and game-theoretic interpretability frameworks;
• Information-theoretic approaches to explainability.

Federated and Privacy-Preserving Learning:

• Cryptographic protocols and secure multi-party computation;
• Differential privacy and formal privacy guarantees;
• Decentralized optimization and convergence analysis.

Graph Mining and Network Analysis:

• Spectral graph theory and Laplacian-based learning;
• Graph kernels and structural pattern recognition;
• Network embeddings and mathematical graph representations;
• Percolation theory, community detection, and network dynamics.

Text Mining and Natural Language Processing:

• Tensor factorization and latent semantic analysis;
• Language modeling using formal grammars and automata;
• Statistical and algebraic methods for text classification;
• Mathematical frameworks for knowledge graph construction;
• Large language models and mathematical modeling;
• Probabilistic and statistical modeling of transformer architectures;
• Sparse approximation and attention mechanisms;
• Theoretical limits, expressivity, and capacity of deep language models;
• Logic-based and formal semantic approaches.

By fostering the exchange of mathematically rigorous ideas, this Special Issue seeks to stimulate fundamental advances and guide future research directions in data mining, machine learning, and data-driven sciences.

We look forward to receiving your valuable contributions and to advancing the state of the art in this rapidly evolving interdisciplinary field.

Dr. Nabil Belacel
Guest Editor

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.

• mathematical data mining
• statistical learning theory
• optimization and metaheuristics for classification
• preference learning and classification
• explainable artificial intelligence
• streaming and time-series analysis
• graph mining and network analysis
• quantum machine learning