Canonical Correlation - MATLAB Canoncorr - MathWorks India
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Canonical correlation canoncorr Syntax [A,B] = canoncorr(X,Y) [A,B,r] = canoncorr(X,Y) [A,B,r,U,V] = canoncorr(X,Y) [A,B,r,U,V,stats] = canoncorr(X,Y) Description [A,B] = canoncorr(X,Y) computes the sample canonical coefficients for the nbyd1 and nbyd2 data matrices X and Y. X and Y must have the same number of observations (rows) but can have different numbers of variables (columns). A and B are d1byd and d2byd matrices, where d = min(rank(X),rank(Y)). The jth columns of A and B contain the canonical coefficients, i.e., the linear combination of variables making up the jth canonical variable for X and Y, respectively. Columns of A and B are scaled to make the covariance matrices of the canonical variables the identity matrix (see U and V below). If X or Y is less than full rank, canoncorr gives a warning and returns zeros in the rows of A or B corresponding to dependent columns of X or Y. [A,B,r] = canoncorr(X,Y) also returns a 1byd vector containing the sample canonical correlations. The jth element of r is the correlation between the j th columns of U and V (see below). [A,B,r,U,V] = canoncorr(X,Y) also returns the canonical variables, scores. U and V are nbyd matrices computed as U = (X-repmat(mean(X),N,1))*A V = (Y-repmat(mean(Y),N,1))*B [A,B,r,U,V,stats] = canoncorr(X,Y) also returns a structure stats containing information relating to the sequence of d null hypotheses , that the (k+1)st through dth correlations are all zero, for k = 0:(d-1). stats contains seven fields, each a 1byd vector with elements corresponding to the values of k, as described in the following table: Field Description Wilks Wilks' lambda (likelihood ratio) statistic df1 Degrees of freedom for the chisquared statistic, and the numerator degrees of freedom for the F statistic df2 Denominator degrees of freedom for the F statistic F Rao's approximate F statistic for pF Righttail significance level for F chisq Bartlett's approximate chisquared statistic for with Lawley's modification pChisq Righttail significance level for chisq stats has two other fields (dfe and p) which are equal to df1 and pChisq, respectively, and exist for historical reasons. Examples load carbig; X = [Displacement Horsepower Weight Acceleration MPG]; nans = sum(isnan(X),2) > 0; [A B r U V] = canoncorr(X(~nans,1:3),X(~nans,4:5)); plot(U(:,1),V(:,1),'.') xlabel('0.0025*Disp+0.020*HP-0.000025*Wgt') ylabel('-0.17*Accel-0.092*MPG')
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Transcript of Canonical Correlation - MATLAB Canoncorr - MathWorks India
12/19/13 Canonical correlation - MATLAB canoncorr - MathWorks India
www.mathworks.in/help/stats/canoncorr.html?searchHighlight=canonical+correlation 1/2
Canonical correlationcanoncorr
Syntax[A,B] = canoncorr(X,Y)[A,B,r] = canoncorr(X,Y)[A,B,r,U,V] = canoncorr(X,Y)[A,B,r,U,V,stats] = canoncorr(X,Y)
Description
[A,B] = canoncorr(X,Y) computes the sample canonical coefficients for the nbyd1 and nbyd2 data matrices X and Y. Xand Y must have the same number of observations (rows) but can have different numbers of variables (columns). A and B ared1byd and d2byd matrices, where d = min(rank(X),rank(Y)). The jth columns of A and B contain the canonicalcoefficients, i.e., the linear combination of variables making up the jth canonical variable for X and Y, respectively. Columns ofA and B are scaled to make the covariance matrices of the canonical variables the identity matrix (see U and V below). If X or Yis less than full rank, canoncorr gives a warning and returns zeros in the rows of A or B corresponding to dependent columnsof X or Y.
[A,B,r] = canoncorr(X,Y) also returns a 1byd vector containing the sample canonical correlations. The jth element of ris the correlation between the jth columns of U and V (see below).
[A,B,r,U,V] = canoncorr(X,Y) also returns the canonical variables, scores. U and V are nbyd matrices computed as
U = (X-repmat(mean(X),N,1))*AV = (Y-repmat(mean(Y),N,1))*B
[A,B,r,U,V,stats] = canoncorr(X,Y) also returns a structure stats containing information relating to the sequence of d
null hypotheses , that the (k+1)st through dth correlations are all zero, for k = 0:(d-1). stats contains seven fields,
each a 1byd vector with elements corresponding to the values of k, as described in the following table:
Field Description
Wilks Wilks' lambda (likelihood ratio) statistic
df1 Degrees of freedom for the chisquared statistic, and the numerator degrees of freedom for theF statistic
df2 Denominator degrees of freedom for the F statistic
F Rao's approximate F statistic for
pF Righttail significance level for F
chisq Bartlett's approximate chisquared statistic for with Lawley's modification
pChisq Righttail significance level for chisq
stats has two other fields (dfe and p) which are equal to df1 and pChisq, respectively, and exist for historical reasons.
Examples
load carbig;X = [Displacement Horsepower Weight Acceleration MPG];nans = sum(isnan(X),2) > 0;[A B r U V] = canoncorr(X(~nans,1:3),X(~nans,4:5));
plot(U(:,1),V(:,1),'.')xlabel('0.0025*Disp+0.020*HP-0.000025*Wgt')ylabel('-0.17*Accel-0.092*MPG')
12/19/13 Canonical correlation - MATLAB canoncorr - MathWorks India
www.mathworks.in/help/stats/canoncorr.html?searchHighlight=canonical+correlation 2/2
References
[1] Krzanowski, W. J. Principles of Multivariate Analysis: A User's Perspective. New York: Oxford University Press, 1988.
[2] Seber, G. A. F. Multivariate Observations. Hoboken, NJ: John Wiley & Sons, Inc., 1984.
See Also
manova1 | pca
