CCA Canonical Correlation Analysis.
CCA inherits from PLS with mode='B' and deflation_mode='canonical'.
Read more in the :ref:`User Guide <cross_decomposition>`.
Parameters ---------- n_components : int, (default 2). number of components to keep.
scale : boolean, (default True) whether to scale the data?
max_iter : an integer, (default 500) the maximum number of iterations of the NIPALS inner loop
tol : non-negative real, default 1e-06. the tolerance used in the iterative algorithm
copy : boolean Whether the deflation be done on a copy. Let the default value to True unless you don't care about side effects
Attributes ---------- x_weights_ : array, p, n_components
X block weights vectors.
y_weights_ : array, q, n_components
Y block weights vectors.
x_loadings_ : array, p, n_components
X block loadings vectors.
y_loadings_ : array, q, n_components
Y block loadings vectors.
x_scores_ : array, n_samples, n_components
X scores.
y_scores_ : array, n_samples, n_components
Y scores.
x_rotations_ : array, p, n_components
X block to latents rotations.
y_rotations_ : array, q, n_components
Y block to latents rotations.
coef_ : array of shape (p, q) The coefficients of the linear model: ``Y = X coef_ + Err``
n_iter_ : array-like Number of iterations of the NIPALS inner loop for each component.
Notes ----- For each component k, find the weights u, v that maximizes max corr(Xk u, Yk v), such that ``|u| = |v| = 1``
Note that it maximizes only the correlations between the scores.
The residual matrix of X (Xk+1) block is obtained by the deflation on the current X score: x_score.
The residual matrix of Y (Yk+1) block is obtained by deflation on the current Y score.
Examples -------- >>> from sklearn.cross_decomposition import CCA >>> X = [0., 0., 1.], [1.,0.,0.], [2.,2.,2.], [3.,5.,4.]
>>> Y = [0.1, -0.2], [0.9, 1.1], [6.2, 5.9], [11.9, 12.3]
>>> cca = CCA(n_components=1) >>> cca.fit(X, Y) CCA(n_components=1) >>> X_c, Y_c = cca.transform(X, Y)
References ----------
Jacob A. Wegelin. A survey of Partial Least Squares (PLS) methods, with emphasis on the two-block case. Technical Report 371, Department of Statistics, University of Washington, Seattle, 2000.
In french but still a reference: Tenenhaus, M. (1998). La regression PLS: theorie et pratique. Paris: Editions Technic.
See also -------- PLSCanonical PLSSVD