Advances in Numerical Algorithms for Machine Learning

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Logic".

Deadline for manuscript submissions: closed (31 March 2024) | Viewed by 4159

Special Issue Editors


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Guest Editor
Department of Information Technology, University of Criminal Investigation and Police Studies, 11080 Belgrade, Serbia
Interests: machine learning; artificial intelligence; natural language processing; computer vision

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Guest Editor
School of Electrical and Computer Engineering, Academy of Technical and Art Applied Studies, 11000 Beograd, Serbia
Interests: machine learning; artificial intelligence; information security; biometrics; cryptology

Special Issue Information

Dear Colleagues,

Numerical algorithms have an important role in a variety of machine learning domains, including natural language processing, computer vision, biometrics, autonomous systems, etc.

This Special Issue aims to highlight recent advancements in numerical algorithms for machine learning, especially those that tackle open research questions related to methodological novelty, performance or theoretical justification. 

We welcome original research articles related to the field which ideally address the widest possible audience. Research areas may include (but are not limited to) the following: 

  • New and improved numerical algorithms for machine learning;
  • Novel applications of numerical algorithms for machine learning;
  • Novel applications of numerical machine learning algorithms in medicine;
  • Machine learning and music—mathematics meets the fine arts;
  • Feature extraction and representation learning;
  • Complexity, optimization and validation;
  • Contextual awareness and adaptability;
  • Approximation and heuristics;
  • Theoretical results. 

We look forward to receiving your contributions.

Prof. Dr. Milan Gnjatović
Prof. Dr. Nemanja Maček
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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • numerical algorithms
  • machine learning
  • deep learning
  • representation learning
  • complexity, optimization and validation
  • contextual awareness and adaptability
  • natural language processing
  • computer vision
  • biometrics

Published Papers (3 papers)

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Research

36 pages, 1351 KiB  
Article
Cutting-Edge Monte Carlo Framework: Novel “Walk on Equations” Algorithm for Linear Algebraic Systems
by Venelin Todorov and Ivan Dimov
Axioms 2024, 13(1), 53; https://doi.org/10.3390/axioms13010053 - 15 Jan 2024
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Abstract
In this paper, we introduce the “Walk on Equations” (WE) Monte Carlo algorithm, a novel approach for solving linear algebraic systems. This algorithm shares similarities with the recently developed WE MC method by Ivan Dimov, Sylvain Maire, and Jean Michel Sellier. This method [...] Read more.
In this paper, we introduce the “Walk on Equations” (WE) Monte Carlo algorithm, a novel approach for solving linear algebraic systems. This algorithm shares similarities with the recently developed WE MC method by Ivan Dimov, Sylvain Maire, and Jean Michel Sellier. This method is particularly effective for large matrices, both real- and complex-valued, and shows significant improvements over traditional methods. Our comprehensive comparison with the Gauss–Seidel method highlights the WE algorithm’s superior performance, especially in reducing relative errors within fewer iterations. We also introduce a unique dominancy number, which plays a crucial role in the algorithm’s efficiency. A pivotal outcome of our research is the convergence theorem we established for the WE algorithm, demonstrating its optimized performance through a balanced iteration matrix. Furthermore, we incorporated a sequential Monte Carlo method, enhancing the algorithm’s efficacy. The most-notable application of our algorithm is in solving a large system derived from a finite-element approximation in constructive mechanics, specifically for a beam structure problem. Our findings reveal that the proposed WE Monte Carlo algorithm, especially when combined with sequential MC, converges significantly faster than well-known deterministic iterative methods such as the Jacobi method. This enhanced convergence is more pronounced in larger matrices. Additionally, our comparative analysis with the preconditioned conjugate gradient (PCG) method shows that the WE MC method can outperform traditional methods for certain matrices. The introduction of a new random variable as an unbiased estimator of the solution vector and the analysis of the relative stochastic error structure further illustrate the potential of our novel algorithm in computational mathematics. Full article
(This article belongs to the Special Issue Advances in Numerical Algorithms for Machine Learning)
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21 pages, 612 KiB  
Article
Measure of Similarity between GMMs Based on Autoencoder-Generated Gaussian Component Representations
by Vladimir Kalušev, Branislav Popović, Marko Janev, Branko Brkljač and Nebojša Ralević
Axioms 2023, 12(6), 535; https://doi.org/10.3390/axioms12060535 - 30 May 2023
Viewed by 1005
Abstract
A novel similarity measure between Gaussian mixture models (GMMs), based on similarities between the low-dimensional representations of individual GMM components and obtained using deep autoencoder architectures, is proposed in this paper. Two different approaches built upon these architectures are explored and utilized to [...] Read more.
A novel similarity measure between Gaussian mixture models (GMMs), based on similarities between the low-dimensional representations of individual GMM components and obtained using deep autoencoder architectures, is proposed in this paper. Two different approaches built upon these architectures are explored and utilized to obtain low-dimensional representations of Gaussian components in GMMs. The first approach relies on a classical autoencoder, utilizing the Euclidean norm cost function. Vectorized upper-diagonal symmetric positive definite (SPD) matrices corresponding to Gaussian components in particular GMMs are used as inputs to the autoencoder. Low-dimensional Euclidean vectors obtained from the autoencoder’s middle layer are then used to calculate distances among the original GMMs. The second approach relies on a deep convolutional neural network (CNN) autoencoder, using SPD representatives to generate embeddings corresponding to multivariate GMM components given as inputs. As the autoencoder training cost function, the Frobenious norm between the input and output layers of such network is used and combined with regularizer terms in the form of various pieces of information, as well as the Riemannian manifold-based distances between SPD representatives corresponding to the computed autoencoder feature maps. This is performed assuming that the underlying probability density functions (PDFs) of feature-map observations are multivariate Gaussians. By employing the proposed method, a significantly better trade-off between the recognition accuracy and the computational complexity is achieved when compared with other measures calculating distances among the SPD representatives of the original Gaussian components. The proposed method is much more efficient in machine learning tasks employing GMMs and operating on large datasets that require a large overall number of Gaussian components. Full article
(This article belongs to the Special Issue Advances in Numerical Algorithms for Machine Learning)
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17 pages, 7797 KiB  
Article
A Clustering-Based Approach to Detecting Critical Traffic Road Segments in Urban Areas
by Ivan Košanin, Milan Gnjatović, Nemanja Maček and Dušan Joksimović
Axioms 2023, 12(6), 509; https://doi.org/10.3390/axioms12060509 - 24 May 2023
Viewed by 887
Abstract
This paper introduces a parameter-free clustering-based approach to detecting critical traffic road segments in urban areas, i.e., road segments of spatially prolonged and high traffic accident risk. In addition, it proposes a novel domain-specific criterion for evaluating the clustering results, which promotes the [...] Read more.
This paper introduces a parameter-free clustering-based approach to detecting critical traffic road segments in urban areas, i.e., road segments of spatially prolonged and high traffic accident risk. In addition, it proposes a novel domain-specific criterion for evaluating the clustering results, which promotes the stability of the clustering results through time and inter-period accident spatial collocation, and penalizes the size of the selected clusters. To illustrate the proposed approach, it is applied to data on traffic accidents with injuries or death that occurred in three of the largest cities of Serbia over the three-year period. Full article
(This article belongs to the Special Issue Advances in Numerical Algorithms for Machine Learning)
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