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

被引:0
作者
Tian, Qing [1 ,2 ,3 ]
Zhang, Heng [1 ,2 ]
Xia, Shiyu [4 ]
Xu, Heng [1 ,2 ]
Ma, Chuang [1 ,2 ]
机构
[1] Nanjing Univ Informat Sci & Technol, Sch Comp & Software, Nanjing 210044, Peoples R China
[2] Nanjing Univ Informat Sci & Technol, Engn Res Ctr Digital Forens, Minist Educ, Nanjing 210044, Peoples R China
[3] Nanjing Univ, State Key Lab Novel Software Technol, Nanjing 210023, Peoples R China
[4] Southeast Univ, Sch Comp Sci & Engn, Nanjing 210096, Peoples R China
来源
ELECTRONIC RESEARCH ARCHIVE | 2023年 / 31卷 / 09期
基金
中国国家自然科学基金;
关键词
canonical correlation analysis; cross-view data correlation analysis; convex discriminative correlation learning; cross-view representation; CANONICAL CORRELATION-ANALYSIS; FEATURE-EXTRACTION; RECOGNITION; FUSION; DIFFERENCE; KERNEL;
D O I
10.3934/era.2023275
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
收藏
页码:5425 / 5441
页数:17
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