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Relational Fisher analysis: Dimensionality reduction in relational data with global convergence

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Wang, Li-Na, Zhong, Guoqiang, Shi, Yaxin and Cheriet, Mohamed. 2023. « Relational Fisher analysis: Dimensionality reduction in relational data with global convergence ». Algorithms, vol. 16, nº 11.

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Abstract

Most of the dimensionality reduction algorithms assume that data are independent and identically distributed (i.i.d.). In real-world applications, however, sometimes there exist relationships between data. Some relational learning methods have been proposed, but those with discriminative relationship analysis are lacking yet, as important supervisory information is usually ignored. In this paper, we propose a novel and general framework, called relational Fisher analysis (RFA), which successfully integrates relational information into the dimensionality reduction model. For nonlinear data representation learning, we adopt the kernel trick to RFA and propose the kernelized RFA (KRFA). In addition, the convergence of the RFA optimization algorithm is proved theoretically. By leveraging suitable strategies to construct the relational matrix, we conduct extensive experiments to demonstrate the superiority of our RFA and KRFA methods over related approaches.

Item Type: Peer reviewed article published in a journal
Professor:
Professor
Cheriet, Mohamed
Affiliation: Génie des systèmes
Date Deposited: 18 Dec 2023 19:03
Last Modified: 08 Jan 2024 19:39
URI: https://espace2.etsmtl.ca/id/eprint/28183

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