kcca                 package:kernlab                 R Documentation

_K_e_r_n_e_l _C_a_n_o_n_i_c_a_l _C_o_r_r_e_l_a_t_i_o_n _A_n_a_l_y_s_i_s

_D_e_s_c_r_i_p_t_i_o_n:

     Computes the canonical correlation analysis in feature space.

_U_s_a_g_e:

     ## S4 method for signature 'matrix':
     kcca(x, y, kernel="rbfdot", kpar=list(sigma=0.1), ...)

_A_r_g_u_m_e_n_t_s:

       x: a matrix containing data index by row

       y: a matrix containing data index by row

  kernel: the kernel function used in training and predicting. This
          parameter can be set to any function, of class kernel, which
          computes a inner product in feature space between two vector
          arguments. kernlab provides the most popular kernel functions
          which can be used by setting the kernel parameter to the
          following strings:

             *  'rbfdot' Radial Basis kernel function "Gaussian"

             *  'polydot' Polynomial kernel function

             *  'vanilladot' Linear kernel function

             *  'tanhdot' Hyperbolic tangent kernel function

             *  'laplacedot' Laplacian kernel function

             *  'besseldot' Bessel kernel function

             *  'anovadot' ANOVA RBF kernel function

             *  'splinedot' Spline kernel 

          The kernel parameter can also be set to a user defined
          function of class kernel by passing the function name as an
          argument. 

    kpar: the list of hyper-parameters (kernel parameters). This is a
          list which contains the parameters to be used with the kernel
          function. Valid parameters for existing kernels are :

             *  'sigma' inverse kernel width for the Radial Basis
                kernel function "rbfdot" and the Laplacian kernel
                "laplacedot".

             *  'degree, scale, offset' for the Polynomial kernel
                "polydot"

             *  'scale, offset' for the Hyperbolic tangent kernel
                function "tanhdot"

             *  'sigma, order, degree' for the Bessel kernel
                "besseldot". 

             *  'sigma, degree' for the ANOVA kernel "anovadot".

          Hyper-parameters for user defined kernels can be passed
          through the kpar parameter as well.

     ...: adittional parameters for the 'kpca' function

_D_e_t_a_i_l_s:

     The kernel version of canonical correlation analysis. Kernel
     Canonical Correlation Analysis (KCCA) is a non-linear extension of
     CCA. Given two random variables, KCCA aims at extracting the
     information which is shared by the two random variables. More
     precisely given x and y the purpose of KCCA is to provide
     nonlinear mappings f(x) and g(y) such that their correlation is
     maximized.

_V_a_l_u_e:

     An S4 object containg the following slots: 

    kcor: Correlation coefficients in feature space

   xcoef: estimated coefficients for the 'x' variables in the feature
          space

   ycoef: estimated coefficients for the 'y' variables in the feature
          space

    xvar: The canonical variates for 'x'

    yvar: The canonical variates for 'y'

_A_u_t_h_o_r(_s):

     Alexandros Karatzoglou 
      alexandros.karatzoglou@ci.tuwien.ac.at

_R_e_f_e_r_e_n_c_e_s:

     Malte Kuss, Thore Graepel 
       _The Geometry Of Kernel Canonical Correlation Analysis_
      <URL:
     http://www.kyb.tuebingen.mpg.de/publications/pdfs/pdf2233.pdf>

_S_e_e _A_l_s_o:

     'cancor', 'kpca', 'kfa', 'kha'

_E_x_a_m_p_l_e_s:

