Page 63 - Rapid Learning in Robotics
P. 63

4.2 The Continuous Associative Completion                                                49








                  a)                   b)              c)                  d)
                      x 3
                                                           x 3
                                                                              x 3
                  x 2
                                                       x 2
                                       s 2
                                    x 1                                                x 2
                                                                            x 1
                                           s 1

                                        S
                 Figure 4.5: a–d: PSOM associative completion or recall procedure (I   f    g,
                 P=diag(1,0,1)) for a rectangular spaced set of           x           x tuples to  x         ,  x
                 together with the original training set of Fig. 4.1,4.5. (a) the input space in the x

                   plane, (b) the resulting (Eq. 4.4) mapping coordinates s 	 S, (c) the completed
                 data set in X, (d) the desired output space projection (looking down x   ).

















                        x 3                                 x 3
                                                                              x 3

                    x 2                                  x 2
                                         s 2
                                                                                       x 2
                                     x 1                                  x 1
                                             s 1



                 Figure 4.6: a–d: PSOM associative completion procedure, but in contrast to

                 Fig. 4.5 here mapping from the input subspace x      with the input components
                 I   f   
g (P=diag(1,1,0)).
   58   59   60   61   62   63   64   65   66   67   68