Canonical Correlation Analysis as a General Linear Model: A Heuristic Lesson for Teachers and Students

Local canonical correlation analysis (CCA) is a multivariate method that has been proposed to more accurately determine activation patterns in fMRI data. In its conventional formulation, CCA has several drawbacks that limit its usefulness in fMRI. A major drawback is that, unlike the general linear model (GLM), a test of general linear contrasts of the temporal regressors has not been incorporated into the CCA formalism. To overcome this drawback, a novel directional test statistic was derived using the equivalence of multivariate multiple regression (MVMR) and CCA. This extension will allow CCA to be used for inference of general linear contrasts in more complicated fMRI designs without reparameterization of the design matrix and without reestimating the CCA solutions for each particular contrast of interest. With the proper constraints on the spatial coefficients of CCA, this test statistic can yield a more powerful test on the inference of evoked brain regional activations from noisy fMRI data than the conventionalt-test in the GLM. The quantitative results from simulated and pseudoreal data and activation maps from fMRI data were used to demonstrate the advantage of this novel test statistic.

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Understanding Canonical Correlation through the General Linear Model and Principal Components

The American Statistician ◽

10.2307/2683082 ◽

1982 ◽

Vol 36 (4) ◽

pp. 342 ◽

Cited By ~ 7

Author(s):

Keith E. Muller

Keyword(s):

Linear Model ◽

Principal Components ◽

Canonical Correlation ◽

General Linear Model ◽

General Linear

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EEG-fMRI: Including sleep-induced potentials in the general linear model improves spatial accordance with epileptic focus

Neuropediatrics ◽

10.1055/s-0030-1265591 ◽

2010 ◽

Vol 41 (02) ◽

Author(s):

J Möhring ◽

D Coropceanu ◽

F Möller ◽

S Wolff ◽

R Boor ◽

...

Keyword(s):

Linear Model ◽

General Linear Model ◽

General Linear ◽

Epileptic Focus

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Analysis of Maximum Expiratory Flow Volume Curves Using Canonical Correlation Analysis

Methods of Information in Medicine ◽

10.1055/s-0038-1635359 ◽

1985 ◽

Vol 24 (02) ◽

pp. 91-100 ◽

Cited By ~ 3

Author(s):

W. van Pelt ◽

Ph. H. Quanjer ◽

M. E. Wise ◽

E. van der Burg ◽

R. van der Lende

Keyword(s):

Correlation Analysis ◽

Canonical Correlation Analysis ◽

Canonical Correlation ◽

Flow Volume ◽

Non Linear ◽

Maximum Expiratory Flow ◽

Expiratory Flow ◽

Relationship Of ◽

The Relationship ◽

Age And Sex

SummaryAs part of a population study on chronic lung disease in the Netherlands, an investigation is made of the relationship of both age and sex with indices describing the maximum expiratory flow-volume (MEFV) curve. To determine the relationship, non-linear canonical correlation was used as realized in the computer program CANALS, a combination of ordinary canonical correlation analysis (CCA) and non-linear transformations of the variables. This method enhances the generality of the relationship to be found and has the advantage of showing the relative importance of categories or ranges within a variable with respect to that relationship. The above is exemplified by describing the relationship of age and sex with variables concerning respiratory symptoms and smoking habits. The analysis of age and sex with MEFV curve indices shows that non-linear canonical correlation analysis is an efficient tool in analysing size and shape of the MEFV curve and can be used to derive parameters concerning the whole curve.

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