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Advances in Mathematical Methods for Distributed Learning and High-Dimensional Data...
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Advances in Mathematical Methods for Distributed Learning and High-Dimensional Data Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 1 September 2025 | Viewed by 1416

Special Issue Editors

Dr. Keren Li

E-Mail Website
Guest Editor
Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL, USA
Interests: statistical learning; distributed learning; federated learning; deep learning; generalized linear models; graphical models; variable selection methods
Prof. Dr. Ji-Ping Wang

E-Mail Website
Guest Editor
1. Department of Statistics, Northwestern University, Evanston, IL 60208, USA
2. NSF-Simons Center for Quantitative Biology, Northwestern University, Evanston, IL 60208, USA
Interests: statistical applications in bioinformatics; computational biology
Dr. Baocheng Geng

E-Mail Website
Guest Editor
Department of Computer Science, University of Alabama at Birmingham, Birmingham, AL, USA
Interests: human decision making; distributed detection and information fusion; optimization for signal processing and machine learning; Internet of Things

Special Issue Information

Dear Colleagues,

We are pleased to invite contributions to our upcoming Special Issue of Mathematics, entitled "Advances in Mathematical Methods for Distributed Learning and High-Dimensional Data Analysis". This Issue seeks to delve into the intricate intersection of distributed learning and high-dimensional data analysis, which presents both unique challenges and groundbreaking opportunities at the vanguard of mathematical research. The importance of this research area lies in its potential to unlock new understandings and applications in fields ranging from computational biology to artificial intelligence, reflecting the evolving complexity of data and computation in the modern world.

This Special Issue aims to address both the theoretical underpinnings of this intersection and its practical implementations, while concurrently advancing the journal’s commitment to advancing significant mathematical breakthroughs. Our goal is to collate research that showcases innovative mathematical models, algorithms, and applications pertinent to distributed learning and high-dimensional data analysis. If successful, this collection will offer a comprehensive perspective on the mathematical challenges and solutions in these intertwined fields, with potential to be published in book form.

In this Special Issue, we welcome original research articles and reviews that cover a range of topics within our scope. Potential themes for submissions include, but are not limited to:

  • Theoretical and practical challenges in merging distributed learning with high-dimensional data.
  • Development of innovative mathematical models and algorithms for distributed environments and complex data structures.
  • Exploration of deep learning techniques within the context of distributed learning and high-dimensional data.
  • Empirical case studies demonstrating the real-world application of these theoretical concepts.

We look forward to receiving your contributions.

Dr. Keren Li
Prof. Dr. Ji-Ping Wang
Dr. Baocheng Geng
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 100 words) can be sent to the Editorial Office for announcement on this website.

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.

Keywords

  • distributed learning
  • high-dimensional data inference
  • high-dimensional data analysis
  • variable selection
  • federated learning
  • online learning
  • deep learning
  • data privacy
  • big data analytics
  • complex data structures

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  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
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Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

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Research

20 pages, 6070 KiB  
Article
Distributed Collaborative Learning with Representative Knowledge Sharing
by Joseph Casey, Qianjiao Chen, Mengchen Fan, Baocheng Geng, Roman Shterenberg, Zhong Chen and Keren Li
Mathematics 2025, 13(6), 1004; https://doi.org/10.3390/math13061004 - 19 Mar 2025
Viewed by 223
Abstract
Distributed Collaborative Learning (DCL) addresses critical challenges in privacy-aware machine learning by enabling indirect knowledge transfer across nodes with heterogeneous feature distributions. Unlike conventional federated learning approaches, DCL assumes non-IID data and prediction task distributions that span beyond local training data, requiring selective [...] Read more.
Distributed Collaborative Learning (DCL) addresses critical challenges in privacy-aware machine learning by enabling indirect knowledge transfer across nodes with heterogeneous feature distributions. Unlike conventional federated learning approaches, DCL assumes non-IID data and prediction task distributions that span beyond local training data, requiring selective collaboration to achieve generalization. In this work, we propose a novel collaborative transfer learning (CTL) framework that utilizes representative datasets and adaptive distillation weights to facilitate efficient and privacy-preserving collaboration. By leveraging Energy Coefficients to quantify node similarity, CTL dynamically selects optimal collaborators and refines local models through knowledge distillation on shared representative datasets. Simulations demonstrate the efficacy of CTL in improving prediction accuracy across diverse tasks while balancing trade-offs between local and global performance. Furthermore, we explore the impact of data spread and dispersion on collaboration, highlighting the importance of tailored node alignment. This framework provides a scalable foundation for cross-domain generalization in distributed machine learning. Full article
(This article belongs to the Special Issue Advances in Mathematical Methods for Distributed Learning and High-Dimensional Data Analysis)
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29 pages, 1577 KiB  
Article
DIAFM: An Improved and Novel Approach for Incremental Frequent Itemset Mining
by Mohsin Shaikh, Sabina Akram, Jawad Khan, Shah Khalid and Youngmoon Lee
Mathematics 2024, 12(24), 3930; https://doi.org/10.3390/math12243930 - 13 Dec 2024
Cited by 1 | Viewed by 756
Abstract
Traditional approaches to data mining are generally designed for small, centralized, and static datasets. However, when a dataset grows at an enormous rate, the algorithms become infeasible in terms of huge consumption of computational and I/O resources. Frequent itemset mining (FIM) is one [...] Read more.
Traditional approaches to data mining are generally designed for small, centralized, and static datasets. However, when a dataset grows at an enormous rate, the algorithms become infeasible in terms of huge consumption of computational and I/O resources. Frequent itemset mining (FIM) is one of the key algorithms in data mining and finds applications in a variety of domains; however, traditional algorithms do face problems in efficiently processing large and dynamic datasets. This research introduces a distributed incremental approximation frequent itemset mining (DIAFM) algorithm that tackles the mentioned challenges using shard-based approximation within the MapReduce framework. DIAFM minimizes the computational overhead of a program by reducing dataset scans, bypassing exact support checks, and incorporating shard-level error thresholds for an appropriate trade-off between efficiency and accuracy. Extensive experiments have demonstrated that DIAFM reduces runtime by 40–60% compared to traditional methods with losses in accuracy within 1–5%, even for datasets over 500,000 transactions. Its incremental nature ensures that new data increments are handled efficiently without needing to reprocess the entire dataset, making it particularly suitable for real-time, large-scale applications such as transaction analysis and IoT data streams. These results demonstrate the scalability, robustness, and practical applicability of DIAFM and establish it as a competitive and efficient solution for mining frequent itemsets in distributed, dynamic environments. Full article
(This article belongs to the Special Issue Advances in Mathematical Methods for Distributed Learning and High-Dimensional Data Analysis)
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