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

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

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Résumé

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.

Type de document:	Article publié dans une revue, révisé par les pairs
Professeur:	Professeur Cheriet, Mohamed
Affiliation:	Génie des systèmes
Date de dépôt:	18 déc. 2023 19:03
Dernière modification:	08 janv. 2024 19:39
URI:	https://espace2.etsmtl.ca/id/eprint/28183

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