csi-class              package:kernlab              R Documentation

_C_l_a_s_s "_c_s_i"

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

     The reduced Cholesky decomposition object

_O_b_j_e_c_t_s _f_r_o_m _t_h_e _C_l_a_s_s:

     Objects can be created by calls of the form 'new("csi", ...)'. or
     by calling the  'csi' function.

_S_l_o_t_s:


     '._D_a_t_a': Object of class '"matrix"' contains the decomposed matrix

     '_p_i_v_o_t_s': Object of class '"vector"' contains the pivots performed

     '_d_i_a_g_r_e_s_i_d_u_e_s': Object of class '"vector"' contains the diagonial
          residues

     '_m_a_x_r_e_s_i_d_u_a_l_s': Object of class '"vector"' contains the maximum
          residues

     _p_r_e_d_g_a_i_n Object of class '"vector"' contains the predicted gain
          before adding each column

     _t_r_u_e_g_a_i_n Object of class '"vector"' contains the actual gain after
          adding each column

     _Q Object of class '"matrix"' contains Q from the QR decomposition
          of the kernel matrix

     _R Object of class '"matrix"' contains R from the QR decomposition
          of the kernel matrix

_E_x_t_e_n_d_s:

     Class '"matrix"', directly.

_M_e_t_h_o_d_s:


     _d_i_a_g_r_e_s_i_d_u_e_s 'signature(object = "csi")': returns the diagonial
          residues

     _m_a_x_r_e_s_i_d_u_a_l_s 'signature(object = "csi")': returns the maximum
          residues

     _p_i_v_o_t_s 'signature(object = "csi")': returns the pivots performed

     _p_r_e_d_g_a_i_n 'signature(object = "csi")': returns the predicted gain
          before adding each column

     _t_r_u_e_g_a_i_n 'signature(object = "csi")': returns the actual gain
          after adding each column

     _Q 'signature(object = "csi")': returns Q from the QR decomposition
          of the kernel matrix

     _R 'signature(object = "csi")': returns R from the QR decomposition
          of the kernel matrix

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

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

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

     'csi', 'inchol-class'

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

     data(iris)

     ## create multidimensional y matrix
     yind <- t(matrix(1:3,3,150))
     ymat <- matrix(0, 150, 3)
     ymat[yind==as.integer(iris[,5])] <- 1

     datamatrix <- as.matrix(iris[,-5])
     # initialize kernel function
     rbf <- rbfdot(sigma=0.1)
     rbf
     Z <- csi(datamatrix,ymat, kernel=rbf, rank = 30)
     dim(Z)
     pivots(Z)
     # calculate kernel matrix
     K <- crossprod(t(Z))
     # difference between approximated and real kernel matrix
     (K - kernelMatrix(kernel=rbf, datamatrix))[6,]

