kha                 package:kernlab                 R Documentation

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

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

     Kernel Hebbian Algorithm is a nonlinear iterative algorithm for
     principal component analysis.

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

     ## S4 method for signature 'formula':
     kha(x, data = NULL, na.action, ...)

     ## S4 method for signature 'matrix':
     kha(x, kernel = "rbfdot", kpar = list(sigma = 0.1), features = 5, 
              eta = 0.005, th = 1e-4, maxiter = 10000, verbose = FALSE,
             na.action = na.omit...)

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

       x: The data matrix indexed by row or a formula descibing the
          model. Note, that an intercept is always included, whether
          given in the formula or not.

    data: an optional data frame containing the variables in the model
          (when using a formula).

  kernel: the kernel function used in training and predicting. This
          parameter can be set to any function, of class kernel, which
          computes the inner product in feature space between two
          vector arguments (see 'kernels'). '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.

features: Number of features (principal components) to return.
          (default: 5)

     eta: The hebbian learning rate (default : 0.005)

      th: the smallest value of the convergence step (default : 0.0001) 

 maxiter: the maximum number of iterations.

 verbose: print convergence every 100 iterations. (default : FALSE)

na.action: A function to specify the action to be taken if 'NA's are
          found. The default action is 'na.omit', which leads to
          rejection of cases with missing values on any required
          variable. An alternative is 'na.fail', which causes an error
          if 'NA' cases are found. (NOTE: If given, this argument must
          be named.)

     ...: additional parameters

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

     The original form of KPCA can only be used on small data sets
     since it requieres the estimation of the eigenvectors of a full
     kernel matrix. The Kernel Hebbian Algorithm iteratively estimates
     the Kernel Principal Components with only linear order memory
     complexity. (see ref. for more details)

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

     An S4 object containing the principal component vectors along with
     the corresponding normalization values.  

     pcv: a matrix containing the principal component vectors (column
          wise)

     eig: The normalization values

 xmatrix: The original data matrix


     all the slots of the object can be accessed by accessor functions.

_N_o_t_e:

     The predict function can be used to embed new data on the new
     space

_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:

     Kwang In Kim, M.O. Franz and B. Schlkopf
      _Kernel Hebbian Algorithm for Iterative Kernel Principal
     Component Analysis_
      Max-Planck-Institut fr biologische Kybernetik, Tbingen (109)
      <URL:
     http://www.kyb.tuebingen.mpg.de/publications/pdfs/pdf2302.pdf>

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

     'kpca', 'kfa', 'kcca', 'pca'

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

     # another example using the iris
     data(iris)
     test <- sample(1:150,20)

     kpc <- kha(~.,data=iris[-test,-5],kernel="rbfdot",kpar=list(sigma=0.2),features=2)

     #print the principal component vectors
     pcv(kpc)

     #plot the data projection on the components
     plot(predict(kpc,iris[,-5]),col=as.integer(iris[,5]),xlab="1st Principal Component",ylab="2nd Principal Component")

