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Mathematics
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Optimization Algorithms in Data Science: Methods and Theory
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Optimization Algorithms in Data Science: Methods and Theory

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (31 July 2024) | Viewed by 1924

Special Issue Editor

Dr. Ashkan Panahi

E-Mail Website
Guest Editor
Data Science and AI division, Department of Computer Science and Engineering, Chalmers University of Technologydisabled, SE-412 96 Gothenburg, Sweden
Interests: optimization algorithms; data science

Special Issue Information

Dear Colleagues,

Optimization algorithms lie at the heart of many chief technologies concerning data, for at least two main reasons. On one hand, they serve as one the most versatile computational toolsets of data science. On the other hand, they provide a principled methodology for formulating data-related problems. Many procedures for data processing and inference, especially statistical approaches, rely on mathematical optimization frameworks, the design of which heavily depends on the structure of the data and the underlying tasks. The purpose of this Special Issue it to address recent advances within this area, in various respects, including formulating various applied tasks as optimization problems, designing algorithmic strategies for solving optimization problems, and analyzing optimization algorithmic solutions in data science.

We consider a wide range of contributions, from proposing new algorithmic solutions to various applied questions using optimization tools, to theoretical studies, e.g., about the convergence of optimization algorithms or statistical analysis of the optimal solutions. We are not restricted to certain types of application. The topics of interest include, but are not limited to, the following:

Algorithms for:

  • Convex optimization;
  • Nonconvex optimization;
  • Discrete optimization;
  • Linear and Convex relaxation;
  • Large-scale optimization;
  • Distributed optimization;
  • Stochastic optimization. 

Optimization applied to:

  • Machine learning;
  • Computer vision;
  • Image processing;
  • Signal processing;
  • Natural Language Processing;
  • Neural Networks;
  • Knowledge transfer;
  • Data fusion;
  • Feature extraction. 

Analysis:

  • Relaxation guarantees;
  • Convergence analysis of optimization algorithms;
  • Hardness of optimization problems;
  • Implicit regularization of optimization algorithms.

Dr. Ashkan Panahi
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 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.

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Published Papers (2 papers)

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Research

16 pages, 3087 KiB  
Article
Predicting the Performance of Ensemble Classification Using Conditional Joint Probability
by Iqbal Murtza, Jin-Young Kim and Muhammad Adnan
Mathematics 2024, 12(16), 2586; https://doi.org/10.3390/math12162586 - 21 Aug 2024
Cited by 1 | Viewed by 631
Abstract
In many machine learning applications, there are many scenarios when performance is not satisfactory by single classifiers. In this case, an ensemble classification is constructed using several weak base learners to achieve satisfactory performance. Unluckily, the construction of the ensemble classification is empirical, [...] Read more.
In many machine learning applications, there are many scenarios when performance is not satisfactory by single classifiers. In this case, an ensemble classification is constructed using several weak base learners to achieve satisfactory performance. Unluckily, the construction of the ensemble classification is empirical, i.e., to try an ensemble classification and if performance is not satisfactory then discard it. In this paper, a challenging analytical problem of the estimation of ensemble classification using the prediction performance of the base learners is considered. The proposed formulation is aimed at estimating the performance of ensemble classification without physically developing it, and it is derived from the perspective of probability theory by manipulating the decision probabilities of the base learners. For this purpose, the output of a base learner (which is either true positive, true negative, false positive, or false negative) is considered as a random variable. Then, the effects of logical disjunction-based and majority voting-based decision combination strategies are analyzed from the perspective of conditional joint probability. To evaluate the forecasted performance of ensemble classifier by the proposed methodology, publicly available standard datasets have been employed. The results show the effectiveness of the derived formulations to estimate the performance of ensemble classification. In addition to this, the theoretical and experimental results show that the logical disjunction-based decision outperforms majority voting in imbalanced datasets and cost-sensitive scenarios. Full article
(This article belongs to the Special Issue Optimization Algorithms in Data Science: Methods and Theory)
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16 pages, 1959 KiB  
Article
An Improved K-Means Algorithm Based on Contour Similarity
by Jing Zhao, Yanke Bao, Dongsheng Li and Xinguo Guan
Mathematics 2024, 12(14), 2211; https://doi.org/10.3390/math12142211 - 15 Jul 2024
Cited by 1 | Viewed by 809
Abstract
The traditional k-means algorithm is widely used in large-scale data clustering because of its easy implementation and efficient process, but it also suffers from the disadvantages of local optimality and poor robustness. In this study, a Csk-means algorithm based on contour similarity is [...] Read more.
The traditional k-means algorithm is widely used in large-scale data clustering because of its easy implementation and efficient process, but it also suffers from the disadvantages of local optimality and poor robustness. In this study, a Csk-means algorithm based on contour similarity is proposed to overcome the drawbacks of the traditional k-means algorithm. For the traditional k-means algorithm, which results in local optimality due to the influence of outliers or noisy data and random selection of the initial clustering centers, the Csk-means algorithm overcomes both drawbacks by combining data lattice transformation and dissimilar interpolation. In particular, the Csk-means algorithm employs Fisher optimal partitioning of the similarity vectors between samples for the process of determining the number of clusters. To improve the robustness of the k-means algorithm to the shape of the clusters, the Csk-means algorithm utilizes contour similarity to compute the similarity between samples during the clustering process. Experimental results show that the Csk-means algorithm provides better clustering results than the traditional k-means algorithm and other comparative algorithms. Full article
(This article belongs to the Special Issue Optimization Algorithms in Data Science: Methods and Theory)
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