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John Shawetaylor - One of the best experts on this subject based on the ideXlab platform.
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a tutorial on Canonical Correlation methods
ACM Computing Surveys, 2017Co-Authors: Viivi Uurtio, Joao M Monteiro, Jaz S Kandola, John Shawetaylor, Delmiro Fernandezreyes, Juho RousuAbstract:Canonical Correlation analysis is a family of multivariate statistical methods for the analysis of paired sets of variables. Since its proposition, Canonical Correlation analysis has, for instance, been extended to extract relations between two sets of variables when the sample size is insufficient in relation to the data dimensionality, when the relations have been considered to be non-linear, and when the dimensionality is too large for human interpretation. This tutorial explains the theory of Canonical Correlation analysis, including its regularised, kernel, and sparse variants. Additionally, the deep and Bayesian CCA extensions are briefly reviewed. Together with the numerical examples, this overview provides a coherent compendium on the applicability of the variants of Canonical Correlation analysis. By bringing together techniques for solving the optimisation problems, evaluating the statistical significance and generalisability of the Canonical Correlation model, and interpreting the relations, we hope that this article can serve as a hands-on tool for applying Canonical Correlation methods in data analysis.
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sparse Canonical Correlation analysis
Machine Learning, 2011Co-Authors: David R Hardoon, John ShawetaylorAbstract:We present a novel method for solving Canonical Correlation Analysis (CCA) in a sparse convex framework using a least squares approach. The presented method focuses on the scenario when one is interested in (or limited to) a primal representation for the first view while having a dual representation for the second view. Sparse CCA (SCCA) minimises the number of features used in both the primal and dual projections while maximising the Correlation between the two views. The method is compared to alternative sparse solutions as well as demonstrated on paired corpuses for mate-retrieval. We are able to observe, in the mate-retrieval, that when the number of the original features is large SCCA outperforms Kernel CCA (KCCA), learning the common semantic space from a sparse set of features.
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sparse Canonical Correlation analysis
arXiv: Machine Learning, 2009Co-Authors: David R Hardoon, John ShawetaylorAbstract:We present a novel method for solving Canonical Correlation Analysis (CCA) in a sparse convex framework using a least squares approach. The presented method focuses on the scenario when one is interested in (or limited to) a primal representation for the first view while having a dual representation for the second view. Sparse CCA (SCCA) minimises the number of features used in both the primal and dual projections while maximising the Correlation between the two views. The method is demonstrated on two paired corpuses of English-French and English-Spanish for mate-retrieval. We are able to observe, in the mate-retreival, that when the number of the original features is large SCCA outperforms Kernel CCA (KCCA), learning the common semantic space from a sparse set of features.
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convergence analysis of kernel Canonical Correlation analysis theory and practice
Machine Learning, 2009Co-Authors: David R Hardoon, John ShawetaylorAbstract:Canonical Correlation Analysis is a technique for finding pairs of basis vectors that maximise the Correlation of a set of paired variables, these pairs can be considered as two views of the same object. This paper provides a convergence analysis of Canonical Correlation Analysis by defining a pattern function that captures the degree to which the features from the two views are similar. We analyse the convergence using Rademacher complexity, hence deriving the error bound for new data. The analysis provides further justification for the regularisation of kernel Canonical Correlation Analysis and is corroborated by experiments on real world data.
David R Hardoon - One of the best experts on this subject based on the ideXlab platform.
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sparse Canonical Correlation analysis
Machine Learning, 2011Co-Authors: David R Hardoon, John ShawetaylorAbstract:We present a novel method for solving Canonical Correlation Analysis (CCA) in a sparse convex framework using a least squares approach. The presented method focuses on the scenario when one is interested in (or limited to) a primal representation for the first view while having a dual representation for the second view. Sparse CCA (SCCA) minimises the number of features used in both the primal and dual projections while maximising the Correlation between the two views. The method is compared to alternative sparse solutions as well as demonstrated on paired corpuses for mate-retrieval. We are able to observe, in the mate-retrieval, that when the number of the original features is large SCCA outperforms Kernel CCA (KCCA), learning the common semantic space from a sparse set of features.
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sparse Canonical Correlation analysis
arXiv: Machine Learning, 2009Co-Authors: David R Hardoon, John ShawetaylorAbstract:We present a novel method for solving Canonical Correlation Analysis (CCA) in a sparse convex framework using a least squares approach. The presented method focuses on the scenario when one is interested in (or limited to) a primal representation for the first view while having a dual representation for the second view. Sparse CCA (SCCA) minimises the number of features used in both the primal and dual projections while maximising the Correlation between the two views. The method is demonstrated on two paired corpuses of English-French and English-Spanish for mate-retrieval. We are able to observe, in the mate-retreival, that when the number of the original features is large SCCA outperforms Kernel CCA (KCCA), learning the common semantic space from a sparse set of features.
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convergence analysis of kernel Canonical Correlation analysis theory and practice
Machine Learning, 2009Co-Authors: David R Hardoon, John ShawetaylorAbstract:Canonical Correlation Analysis is a technique for finding pairs of basis vectors that maximise the Correlation of a set of paired variables, these pairs can be considered as two views of the same object. This paper provides a convergence analysis of Canonical Correlation Analysis by defining a pattern function that captures the degree to which the features from the two views are similar. We analyse the convergence using Rademacher complexity, hence deriving the error bound for new data. The analysis provides further justification for the regularisation of kernel Canonical Correlation Analysis and is corroborated by experiments on real world data.
Chao Xu - One of the best experts on this subject based on the ideXlab platform.
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Tensor Canonical Correlation analysis for multi-view dimension reduction
2016 IEEE 32nd International Conference on Data Engineering (ICDE), 2016Co-Authors: Kotagiri Ramamohanarao, Chao XuAbstract:Canonical Correlation analysis (CCA) has proven an effective tool for two-view dimension reduction due to its profound theoretical foundation and success in practical applications. In respect of multi-view learning, however, it is limited by its capability of only handling data represented by two-view features, while in many real-world applications, the number of views is frequently many more. Although the ad hoc way of simultaneously exploring all possible pairs of features can numerically deal with multi-view data, it ignores the high order statistics (Correlation information) which can only be discovered by simultaneously exploring all features. Therefore, in this work, we develop tensor CCA (TCCA) which straightforwardly yet naturally generalizes CCA to handle the data of an arbitrary number of views by analyzing the covariance tensor of the different views. TCCA aims to directly maximize the Canonical Correlation of multiple (more than two) views. Crucially, we prove that the main problem of multiview Canonical Correlation maximization is equivalent to finding the best rank-1 approximation of the data covariance tensor, which can be solved efficiently using the well-known alternating least squares (ALS) algorithm. As a consequence, the high order Correlation information contained in the different views is explored and thus a more reliable common subspace shared by all features can be obtained.
Colin Fyfe - One of the best experts on this subject based on the ideXlab platform.
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Sparsiflcation of Probabilistic Canonical Correlation Analysis
2020Co-Authors: Daniel Livingstone, Colin FyfeAbstract:We have recently developed several ways of performing Canonical Correlation Analysis (1, 5, 7, 4) with probabilistic methods rather than the standard statistical tools. How- ever, the computational demands of training such methods scales with the square of the number of samples, making these methods uncompetitive with e.g. artiflcial neural network methods (3, 2). In this paper, we examine a recent development which sparsifles a probabilistic method of performing principal component analysis and then use this method to sparsify a new proba- bilistic method of performing Canonical Correlation analysis.
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Gaussian processes for Canonical Correlation analysis
Neurocomputing, 2008Co-Authors: Colin Fyfe, Gayle LeenAbstract:We consider several stochastic process methods for performing Canonical Correlation analysis (CCA). The first uses a Gaussian process formulation of regression in which we use the current projection of one data set as the target for the other and then repeat with the second projection as the target for adapting the parameters of the first. The second uses a method which relies on probabilistically sphering the data, concatenating the two streams and then performing a probabilistic PCA. The third gets the Canonical Correlation projections directly without having to calculate the filters first. We also investigate the use of nonlinearity and a method for sparsification of these algorithms.
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kernel and nonlinear Canonical Correlation analysis
International Journal of Neural Systems, 2000Co-Authors: Colin FyfeAbstract:We have previously [4] derived a neural network implementation of the statistical technique of Canonical Correlation Analysis (CCA). We extend this to nonlinear CCA either by adding a nonlinearity to our neural method or by nonlinearly transforming the data to a feature space and then performing linear CCA in this feature space. We give comparative results on both artificial and real data sets.
Kotagiri Ramamohanarao - One of the best experts on this subject based on the ideXlab platform.
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Tensor Canonical Correlation analysis for multi-view dimension reduction
2016 IEEE 32nd International Conference on Data Engineering (ICDE), 2016Co-Authors: Kotagiri Ramamohanarao, Chao XuAbstract:Canonical Correlation analysis (CCA) has proven an effective tool for two-view dimension reduction due to its profound theoretical foundation and success in practical applications. In respect of multi-view learning, however, it is limited by its capability of only handling data represented by two-view features, while in many real-world applications, the number of views is frequently many more. Although the ad hoc way of simultaneously exploring all possible pairs of features can numerically deal with multi-view data, it ignores the high order statistics (Correlation information) which can only be discovered by simultaneously exploring all features. Therefore, in this work, we develop tensor CCA (TCCA) which straightforwardly yet naturally generalizes CCA to handle the data of an arbitrary number of views by analyzing the covariance tensor of the different views. TCCA aims to directly maximize the Canonical Correlation of multiple (more than two) views. Crucially, we prove that the main problem of multiview Canonical Correlation maximization is equivalent to finding the best rank-1 approximation of the data covariance tensor, which can be solved efficiently using the well-known alternating least squares (ALS) algorithm. As a consequence, the high order Correlation information contained in the different views is explored and thus a more reliable common subspace shared by all features can be obtained.