acpgen                 package:amap                 R Documentation

_G_e_n_e_r_a_l_i_s_e_d _p_r_i_n_c_i_p_a_l _c_o_m_p_o_n_e_n_t _a_n_a_l_y_s_i_s

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

     Generalised principal component analysis

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

     acpgen(x,h1,h2,center=TRUE,reduce=TRUE,kernel="gaussien")
     K(u,kernel="gaussien")
     W(x,h,D=NULL,kernel="gaussien")

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

       x: Matrix or data frame

       h: Scalar: bandwidth of the Kernel

      h1: Scalar: bandwidth of the Kernel for W

      h2: Scalar: bandwidth of the Kernel for U

  kernel: The kernel used. This must be one of '"gaussien"', 
          '"quartic"', '"triweight"', '"epanechikov"' ,  '"cosinus"' or
          '"uniform"' 

  center: A logical value indicating whether we center data

  reduce: A logical value indicating whether we "reduce" data i.e. 
          divide each column by standard deviation

       D: A product scalar matrix / une matrice de produit scalaire

       u: Vector

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

     'acpgen' compute generalised pca. i.e. spectral analysis of  Un /
     Wn, and project Xi with 1/Wn on the principal vector sub-spaces.

     Xi a column vector of p variables of individu  i  (input data)

     'W' compute estimation of noise in the variance. 

                           W: see latex doc


     with Vn variance estimation;

     'U' compute robust variance. 1/Un = 1/Sn - 1 / (h Vn)


                           S: see latex doc


     with mu_n estimator of the mean.

     'K' compute   kernel, i.e.

     gaussien: 

                       1/sqrt(2pi)  exp(-u^2/2)


     quartic: 

                     15/16 (1-u^2)^2  if |u| < 1


     triweight: 

                     35/32 (1-u^2)^3  if |u| < 1


     epanechikov: 

                       3/4 (1-u^2)  if |u| < 1


     cosinus: 

                   pi/4 cos (u * pi/2)  if |u| < 1

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

     An object of class *acp*  The object is a list with components:

    sdev: the standard deviations of the principal components.

loadings: the matrix of variable loadings (i.e., a matrix whose columns
          contain the eigenvectors).  This is of class '"loadings"':
          see 'loadings' for its 'print' method.

  scores: if 'scores = TRUE', the scores of the supplied data on the
          principal components.

     eig: Eigen values

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

     Antoine Lucas, <URL:
     http://mulcyber.toulouse.inra.fr/projects/amap/>

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

     H. Caussinus, M. Fekri, S. Hakam and A. Ruiz-Gazen, _A monitoring
     display of multivariate outliers_ Computational Statistics & Data
     Analysis, Volume 44, Issues 1-2, 28 October 2003, Pages 237-252

     Caussinus, H and Ruiz-Gazen, A. (1993): _Projection Pursuit and
     Generalized Principal Component Analyses, in New Directions in
     Statistical Data Analysis and Robustness_ (eds.  Morgenthaler et
     al.), pp. 35-46. Birk\"auser Verlag Basel.

     Caussinus, H. and Ruiz-Gazen, A. (1995). _Metrics for Finding
     Typical Structures by Means of Principal Component Analysis. In
     Data Science and its Applications_ (eds Y. Escoufier and C.
     Hayashi), pp. 177-192. Tokyo: Academic Press.

     Antoine Lucas and Sylvain Jasson, _Using amap and ctc Packages for
     Huge Clustering_, R News, 2006, vol 6, issue 5 pages 58-60.

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

     acp acprob princomp

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

     data(lubisch)
     lubisch <- lubisch[,-c(1,8)]
     p <- acpgen(lubisch,h1=1,h2=1/sqrt(2))
     plot(p,main='ACP robuste des individus')

     # See difference with acp

     p <- princomp(lubisch)
     class(p)<- "acp"

