A kernel method for canonical correlation analysis

By Shotaro Akaho. arXiv.org, 2006

563 citations recorded by the source corpus.

Canonical correlation analysis is a technique to extract common features from a pair of multivariate data. In complex situations, however, it does not extract useful features because of its linearity. On the other hand, kernel method used in support vector machine is an efficient approach to improve such a linear method. In this paper, we investigate the effectiveness of applying kernel method to canonical correlation analysis. Keyword: multivariate analysis, multimodal data, kernel method, regularization

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/793462a25db9514b942d6df93ab20ee0a7c3f257

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Citations in the corpus

Canonical Correlation Analysis: An Overview with Application to Learning Methods (2004, methodology): “KCCA has been applied in some preliminary work by Fyfe and Lai (2001) and Akaho (2001) and the recent Vinokourov, Shawe-Taylor, and Cristianini (2002) with improved results. During recent years, there has been a vast increase in the amount of multimedia content available both off-line and online, th”
On Deep Multi-View Representation Learning (2015, methodology): “To overcome the limiting power of linear projections, a nonlinear extension–kernel canonical correlation analysis (KCCA)–has also been proposed (Lai and Fyfe, 2000; Akaho, 2001; Melzer et al., 2001; Bach and Jordan, 2002; Hardoon et al., 2004).”
Deep Canonical Correlation Analysis (2013, methodology): “Kernel canonical correlation analysis (KCCA) (Akaho, 2001; Melzer et al., 2001; Bach & Jordan, 2002; Hardoon et al., 2004) is an extension of CCA in which maximally correlated nonlinear projections, restricted to reproducing kernel Hilbert spaces with corresponding kernels, are found.”
Scalable Deep Multimodal Learning for Cross-Modal Retrieval (2019, background): “At the first thought, they can be easily extended to nonlinear models with the kernel trick, such as Kernel CCA (KCCA) [1].”
Kernel Methods for Measuring Independence (2005, background): “Further discussion and applications of the kernel canonical correlation include Akaho (2001); Bach and Jordan (2002a); Hardoon et al. (2004); Kuss (2001); Lai and Fyfe (2000); Melzer et al. (2001); Shawe-Taylor and Cristianini (2004); van Gestel et al.”
An Overview of Cross-Media Retrieval: Concepts, Methodologies, Benchmarks, and Challenges (2017, background): “CCA and its variants such as [22]–[26], are the most popular baseline methods for cross-media retrieval.”
Deep multi-view learning methods: A review (2021, methodology): “To tackle this problem, some nonlinear extensions of CCA are proposed, such as Kernel CCA [23, 24, 18, 25], locality preserving CCA [96, 97] and deep CCA [20].”
Linking Image and Text with 2-Way Nets (2016, methodology): “C V ] 1 0 Fe b 20 17 While CCA is restricted to linear projections, KCCA is restricted to a fixed kernel.”
Protein network inference from multiple genomic data: a supervised approach (2004, methodology): “Equation (2) with decreasing eigenvalue ρ. This problem is usually called kernel canonical correlation analysis (CCA) ( Akaho, 2001 ).”
Multi-View Intact Space Learning (2015, background): “A number of works exploit the shared latent subspace across diverse views, such as canonical correlation analysis (CCA) [28], [29], its kernel extension [30], its probabilistic interpretation [31], and its sparse formulation [32].”
Deep Multimodal Representation Learning: A Survey (2019, methodology): “One of the non-linear extensions is kernel CCA [111] which transforms the data into a higher dimensional Hilbert space before applying the CCA method.”
Deep Partial Multi-View Learning (2020, methodology): “Projecting different views into a common space ( e.g. , CCA: Canonical Correlation Analysis and its variants [9], [10], [11]) is impeded by view-missing issue.”
A Comprehensive Survey on Pose-Invariant Face Recognition (2015, methodology): “…[Li et al. 2009], PLS [Sharma and Jacobs 2011], GMLDA [Sharma et al. 2012b], Tied Factor Analysis [Prince et al. 2008] Nonlinear models Kernel CCA [Akaho 2006], Deep CCA [Andrew et al. 2013] Face synthesis based on 2D methods 2D pose normalization Piece-wise Warping [Cootes et al. 2001],…”
Trusted Multi-View Classification With Dynamic Evidential Fusion (2022, unknown): “CCA-based multiview models [36], [37], [38], [39], [40], [41] are representative”
Learning Relationships between Text, Audio, and Video via Deep Canonical Correlation for Multimodal Language Analysis (2019, methodology): “Kernel-CCA can be used exactly like CCA.”