Statistics Toolbox | ![]() ![]() |
Canonical correlation analysis
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 n
-by-d1
and n
-by-d2
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 d1
-by-d
and d2
-by-d
matrices, where d = min(rank(X),rank(Y))
. The j
th columns of A
and B
contain the canonical coefficients, i.e., the linear combination of variables making up the j
th canonical variable for X
and Y
, respectively. Columns of A
and B
are scaled to make the covariances of the canonical variables, or scores, 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 1-by-d
vector containing the sample canonical correlations. The j
th element of r
is 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, known also as scores. U
and V
are n
-by-d
matrices computed as
[A,B,r,U,V,stats] = canoncorr(X,Y)
also returns a structure containing information relating to the sequence of d
null hypotheses , that the (
k+1
)st through d
th correlations are all zero, for k = 0:(d-1)
. stats
contains three fields, each a 1
-by-d
vector with elements corresponding to the values of k
:
dfe |
Error degrees of freedom, i.e., (d1-k)*(d2-k) |
chisq |
Bartlett's approximate chi-squared statistic for ![]() |
p |
Right-tail significance level for ![]() |
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')
See Also
References
[1] Krzanowski, W.J., Principles of Multivariate Analysis, Oxford University Press, Oxford, 1988.
[2] Seber, G.A.F., Multivariate Observations, Wiley, New York, 1984.
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