Back to PLS Helpcorrelation Vs covariance
Posted on 01/16/09 10:22:41
Number of posts: 29
j crofts
Hi, in the 1996 paper the you emphasise the importance of using the covariance rather than the correlation - I am not sure I understand, unless your data consists of vastly differing scales, what difference this will make to the analysis; I guess this is my first question. My second (quite related to the first), concerns your 2004 paper and the definition of behavioural PLS. When constructing the matrix R, it is the correlations between behavioural and imaging data which are used not the covariance! I'm confused, I thought PLS dealt with covariances and canonical correlation analysis dealt with correlations. Any help would be appreciated. Cheers Jonathan
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Untitled Post
Posted on 01/16/09 17:39:04
Number of posts: 394
quote:
Hi, in the 1996 paper the you emphasise the importance of using the covariance rather than the correlation - I am not sure I understand, unless your data consists of vastly differing scales, what difference this will make to the analysis; I guess this is my first question. My second (quite related to the first), concerns your 2004 paper and the definition of behavioural PLS. When constructing the matrix R, it is the correlations between behavioural and imaging data which are used not the covariance! I'm confused, I thought PLS dealt with covariances and canonical correlation analysis dealt with correlations. Any help would be appreciated. Cheers Jonathan
Hi, what the covariance refers to is how the PLS matrix operations can be conceptualized in relation to something like canonical correlation.Hi, in the 1996 paper the you emphasise the importance of using the covariance rather than the correlation - I am not sure I understand, unless your data consists of vastly differing scales, what difference this will make to the analysis; I guess this is my first question. My second (quite related to the first), concerns your 2004 paper and the definition of behavioural PLS. When constructing the matrix R, it is the correlations between behavioural and imaging data which are used not the covariance! I'm confused, I thought PLS dealt with covariances and canonical correlation analysis dealt with correlations. Any help would be appreciated. Cheers Jonathan
Consider the following:
matrix Rxy is a correlation between matrix X and Y. To identify the dominant dimensions relating the two we do:
SVD(Rxy) for PLS
and
adjRxy = (Rxx^-0.5)'*Rxy*(Ryy^-0.5)
SVD(adjRxy) for Canonical Correlation
the singular/eigenvalues from the SVD(Rxy) are the covariances betweeen X and Y, while the singular/eigenvalues from SVD(adjRxy) are the correlations between X and Y. The SVD in PLS thus identifies the maximum covariation while the SVD in Canonical Correlation identifies the maximum correlation.
Does this help (hopefully the symbols make sense)?
Randy
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