concorgmcano             package:concor             R Documentation

_C_a_n_o_n_i_c_a_l _a_n_a_l_y_s_i_s _o_f _s_u_b_s_e_t_s _Y_j _w_i_t_h _s_u_b_s_e_t_s _X_i

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

     Canonical analysis of subsets Yj with subsets Xi. Relative
     valuations by squared correlations of the proximities of subsets
     Xi with subsets Yj. SUCCESSIVE SOLUTIONS

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

     concorgmcano(x,px,y,py,r)

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

       x: is a n x p matrix of p centered variables

       y: is a n x q matrix of q centered variables

      px: is a row vector which contains the numbers pi, i=1,...,kx, of
          the kx subsets xi of x : sum_i p_i=sum(px)=p. px is the
          partition vector of x

      py: is the partition vector of y with ky subsets yj, j=1,...,ky

       r: is the wanted number of successive solutions rmax <=
          min(min(px),min(py),n)

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

     For the first solution, sum_i sum_j mbox{rho2}(cx_i[,1],cy_j[,1])
     is the optimized criterion. The other solutions are calculated
     from the same criterion, but with orthogonalities for having two
     by two zero correlated the canonical components defined for each
     xi, and also for those defined for each yj.  Each solution
     associates kx canonical components to ky canonical components. 
     When kx =1 (px=p), take concorcano function

     This function uses the concorgm function

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

     list with following components 

      cx: is a n.kx x r matrix of kx row blocks cxi (n x r). Each row
          block contains r partial canonical components

      cy: is a n.ky x r matrix of ky row blocks cyj (n x r). Each row
          block contains r partial canonical components

    rho2: is a kx x ky x r array; for a fixed solution k, rho2[,,k]
          contains kxky squared correlations
          rho2(cx[n*(i-1)+1:n*i,k],cy[n*(j-1)+1:n*j,k]), simultaneously
          calculated between all the yj with all the xi

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

     Kissita G., Analyse canonique generalisee avec tableau de
     reference generalisee. Thesis, Ceremade Paris 9 Dauphine (2003).

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

     x<-matrix(runif(50),10,5);y<-matrix(runif(90),10,9)
     x<-scale(x);y<-scale(y)
     cc<-concorgmcano(x,c(2,3),y,c(3,2,4),2)
     diag(t(cc$cx[1:10,])%*%cc$cy[1:10,]/10)^2
     cc$rho2[1,1,] 

