Cross-view learning with scatters and manifold exploitation in geodesic space

Qing Tian; Heng Zhang; Shiyu Xia; Heng Xu; Chuang Ma; Qing Tian; Heng Zhang; Shiyu Xia; Heng Xu; Chuang Ma

doi:10.3934/era.2023275

Electronic Research Archive

2023, Volume 31, Issue 9: 5425-5441. doi: 10.3934/era.2023275

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Research article

Cross-view learning with scatters and manifold exploitation in geodesic space

1.
School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing 210044, China
2.
Engineering Research Center of Digital Forensics, Ministry of Education, Nanjing University of Information Science and Technology, Nanjing 210044, China
3.
State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210023, China
4.
School of Computer Science and Engineering, Southeast University, Nanjing 210096, China

Academic Editor: Dejing Dou
^† These authors contributed equally to this work.

Received: 11 April 2023 Revised: 07 July 2023 Accepted: 23 July 2023 Published: 31 July 2023

Cross-view data correlation analysis is a typical learning paradigm in machine learning and pattern recognition. To associate data from different views, many approaches to correlation learning have been proposed, among which canonical correlation analysis (CCA) is a representative. When data is associated with label information, CCA can be extended to a supervised version by embedding the supervision information. Although most variants of CCA have achieved good performance, nearly all of their objective functions are nonconvex, implying that their optimal solutions are difficult to obtain. More seriously, the discriminative scatters and manifold structures are not exploited simultaneously. To overcome these shortcomings, in this paper we construct a Discriminative Correlation Learning with Manifold Preservation, DCLMP for short, in which, in addition to the within-view supervision information, discriminative knowledge as well as spatial structural information are exploited to benefit subsequent decision making. To pursue a closed-form solution, we remodel the objective of DCLMP from the Euclidean space to a geodesic space and obtain a convex formulation of DCLMP (C-DCLMP). Finally, we have comprehensively evaluated the proposed methods and demonstrated their superiority on both toy and real datasets.
Citation: Qing Tian, Heng Zhang, Shiyu Xia, Heng Xu, Chuang Ma. Cross-view learning with scatters and manifold exploitation in geodesic space[J]. Electronic Research Archive, 2023, 31(9): 5425-5441. doi: 10.3934/era.2023275

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Abstract

Cross-view data correlation analysis is a typical learning paradigm in machine learning and pattern recognition. To associate data from different views, many approaches to correlation learning have been proposed, among which canonical correlation analysis (CCA) is a representative. When data is associated with label information, CCA can be extended to a supervised version by embedding the supervision information. Although most variants of CCA have achieved good performance, nearly all of their objective functions are nonconvex, implying that their optimal solutions are difficult to obtain. More seriously, the discriminative scatters and manifold structures are not exploited simultaneously. To overcome these shortcomings, in this paper we construct a Discriminative Correlation Learning with Manifold Preservation, DCLMP for short, in which, in addition to the within-view supervision information, discriminative knowledge as well as spatial structural information are exploited to benefit subsequent decision making. To pursue a closed-form solution, we remodel the objective of DCLMP from the Euclidean space to a geodesic space and obtain a convex formulation of DCLMP (C-DCLMP). Finally, we have comprehensively evaluated the proposed methods and demonstrated their superiority on both toy and real datasets.

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