An algorithm for independent component analysis using a general class of copula-based dependence criteria
The efficiency of Independent Component Analysis ($\rm ICA$) algorithms relies heavily on the choice of objective function and optimization algorithms. The design of objective functions for $\rm ICA$ algorithms necessitate a foundation built upon specific dependence criteria. This paper will investi...
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| Format: | Article |
| Language: | English |
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Shahid Bahonar University of Kerman
2025-01-01
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| Series: | Journal of Mahani Mathematical Research |
| Subjects: | |
| Online Access: | https://jmmrc.uk.ac.ir/article_4593_acdb36790ecc39d0a2a913e1051273e2.pdf |
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| author | Fatemeh Asadi Hamzeh Torabi Hossein Nadeb |
| author_facet | Fatemeh Asadi Hamzeh Torabi Hossein Nadeb |
| author_sort | Fatemeh Asadi |
| collection | DOAJ |
| description | The efficiency of Independent Component Analysis ($\rm ICA$) algorithms relies heavily on the choice of objective function and optimization algorithms. The design of objective functions for $\rm ICA$ algorithms necessitate a foundation built upon specific dependence criteria. This paper will investigate a general class of dependency criteria based on the copula density function. One of the aims of this study is to characterize the independence between two random variables and investigate their properties. Additionally, this paper introduces a novel algorithm for $\rm ICA$ based on estimators derived from the proposed criteria. To compare the performance of the proposed algorithm against existing methods, a Monte Carlo simulation-based approach was employed. The results of this simulation revealed significant improvements in the algorithm's outputs. Finally, the algorithm was tested on a batch of time series data related to the international tourism receipts index. It served as a pre-processing procedure within a hybrid clustering algorithm alongside ${\tt PAM}$. The obtained results demonstrated that the utilization of this algorithm led to improved performance in clustering countries based on their international tourism receipts index. |
| format | Article |
| id | doaj-art-c2027edaece54f0797ceac91b32b8b72 |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-c2027edaece54f0797ceac91b32b8b722025-01-04T19:30:19ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052025-01-0114152755010.22103/jmmr.2024.23031.15914593An algorithm for independent component analysis using a general class of copula-based dependence criteriaFatemeh Asadi0Hamzeh Torabi1Hossein Nadeb2Department of Statistics, Yazd University, Yazd, IranDepartment of Statistics, Yazd University, Yazd, IranDepartment of Statistics, Yazd University, Yazd, IranThe efficiency of Independent Component Analysis ($\rm ICA$) algorithms relies heavily on the choice of objective function and optimization algorithms. The design of objective functions for $\rm ICA$ algorithms necessitate a foundation built upon specific dependence criteria. This paper will investigate a general class of dependency criteria based on the copula density function. One of the aims of this study is to characterize the independence between two random variables and investigate their properties. Additionally, this paper introduces a novel algorithm for $\rm ICA$ based on estimators derived from the proposed criteria. To compare the performance of the proposed algorithm against existing methods, a Monte Carlo simulation-based approach was employed. The results of this simulation revealed significant improvements in the algorithm's outputs. Finally, the algorithm was tested on a batch of time series data related to the international tourism receipts index. It served as a pre-processing procedure within a hybrid clustering algorithm alongside ${\tt PAM}$. The obtained results demonstrated that the utilization of this algorithm led to improved performance in clustering countries based on their international tourism receipts index.https://jmmrc.uk.ac.ir/article_4593_acdb36790ecc39d0a2a913e1051273e2.pdfamari errorclustering, copuladependence criteriamutual information |
| spellingShingle | Fatemeh Asadi Hamzeh Torabi Hossein Nadeb An algorithm for independent component analysis using a general class of copula-based dependence criteria Journal of Mahani Mathematical Research amari error clustering, copula dependence criteria mutual information |
| title | An algorithm for independent component analysis using a general class of copula-based dependence criteria |
| title_full | An algorithm for independent component analysis using a general class of copula-based dependence criteria |
| title_fullStr | An algorithm for independent component analysis using a general class of copula-based dependence criteria |
| title_full_unstemmed | An algorithm for independent component analysis using a general class of copula-based dependence criteria |
| title_short | An algorithm for independent component analysis using a general class of copula-based dependence criteria |
| title_sort | algorithm for independent component analysis using a general class of copula based dependence criteria |
| topic | amari error clustering, copula dependence criteria mutual information |
| url | https://jmmrc.uk.ac.ir/article_4593_acdb36790ecc39d0a2a913e1051273e2.pdf |
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