Kernel and Nonlinear Canonical Correlation Analysis

By P. L. Lai, Colin Fyfe. 2000

541 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Signal Processing

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Citations in the corpus

The Incomplete Rosetta Stone problem: Identifiability results for Multi-view Nonlinear ICA (2019, background): “Nonlinear extensions of the basic CCA framework have been proposed [26, 13, 3, 29], but identifiability results in the sense we consider in this paper are lacking.”
Deep Multimodal Feature Analysis for Action Recognition in RGB+D Videos (2016, methodology): “Kernel canonical correlation analysis (KCCA) [25] extended this idea into nonlinear kernel-based projections, which is still limited to the representation capacity of the kernel’s space and is not able to disentangle the high-level nonlinear complexities between the input modalities.”
Learning the Relative Importance of Objects from Tagged Images for Retrieval and Cross-Modal Search (2012, methodology): “We propose an unsupervised approach based on Kernel Canonical Correlation Analysis (KCCA) (Akaho 2001; Fyfe and Lai 2001; Hardoon et al. 2004) to discover a “semantic space” that captures the relationship between those tag cues and the image content itself, and show how it can be used to more effect”
Multi-view Super Vector for Action Recognition (2014, background): “(6) The joint distribution of x and y is p(x, y) = ∫ p(x|z)p(y|z)p(z)dz (7) which is Gaussian, with mean and covariance matrix µ = ( µx µy ) , (8) Σ = [ WxW > x + Ψx, WxW > y WyW > x , WyW > y + Ψy ] , (9)”
The Geometry Of Kernel Canonical Correlation Analysis (2003, methodology): “Furthermore, several authors have studied the construction of a kernel variant of CCA and proposed quite different algorithms (Lai and Fyfe 2000; Melzer et al. 2001; van Gestel et al. 2001; Bach and Jordan 2002).”
Inferring a Semantic Representation of Text via Cross-Language Correlation Analysis (2002, methodology): “We employ kernel Canonical Correlati on Analysis (KCCA) [1] [7] to learn a representation of text that captures aspects of its s emantic.”
Randomized Nonlinear Component Analysis (2014, methodology): “Second, McWilliams et al. (2013) used the Nystr¨om method to deﬁne a randomized feature map and performed CCA to achieve state-of-the-art semi-supervised learning.”
Multi-view learning overview: Recent progress and new challenges (2017, methodology): “Kernel canonical correlation analysis (KCCA) [68–71] is an kerel extension of CCA for pursuing maximally correlated nonlinear rojections.”
A Survey of Multi-View Representation Learning (2016, unknown): “Since kernerlization is a principled trick for introducing non-linearity into linear methods, kernel CCA [82, 83] provides an alternative solution.”
Multi-omic and multi-view clustering algorithms: review and cancer benchmark (2018, background): “An additional expansion to perform CCA in high dimension is Kernel CCA [35].”
Canonical Correlation Analysis: An Overview with Application to Learning Methods (2004, methodology): “KCCA has been applied in some preliminary work by Fyfe & Lai [8], Akaho [1] and the recently Vinokourov et al.”
Large-scale kernel methods for independence testing (2016, methodology): “More specifically, they develop randomised canonical correlation analysis (RCCA) (see also Lopez-Paz 2014, 2016) approximating the nonlinear kernel-based generalisation of the canonical correlation analysis (Lai and Fyfe 2000; Bach and Jordan 2002) and using a further copula transformation, construc”
Efficient leave-one-out cross-validation of kernel fisher discriminant classifiers (2003, methodology): “…many linear methods borrowed from classical statistics (e.g. [2, 3]), including ridge-regression [4], principal component analysis [5] and canonical correlation analysis [6] as well as more recent developments such as the maximal margin classiﬂer [7] (giving rise to the support vector machine [8]).”
From Dependence to Causation (2016, methodology): “Fourth, RDC is consistent with respect to KCCA.”
Kernel Methods for Measuring Independence (2005, background): “For instance, one well known measure of statistical depen nce between two random variables is themutual information(Cover and Thomas, 1991), which for random vectors x,y is zero if and only if the random vectors are independent.”
Kernel Sliced Inverse Regression with Applications to Classification (2008, methodology): “As a result, KSIR also has a link to the KCCA and KFDA variates.”