landmarkreg               package:fda               R Documentation

_R_e_g_i_s_t_r_a_t_i_o_n _o_f _F_u_n_c_t_i_o_n_a_l _O_b_s_e_r_v_a_t_i_o_n_s _U_s_i_n_g _L_a_n_d_m_a_r_k_s

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

     It is common to see that among a set of functions certain
     prominent features such peaks and valleys, called landmarks, do
     not occur at the same times, or other argument values. This is
     called phase variation, and it can be essential to align these
     features before proceeding with further functional data analyses.
     This function uses the timings of these features to align or
     register the curves. The registration involves estimating a
     nonlinear transformation of the argument continuum for each
     functional observation. This transformation is called a warping
     function. It must be strictly increasing and smooth.

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

     landmarkreg(fd, fd0, ximarks, x0marks=xmeanmarks, wbasis=basis, Lfd=0, sparval=1e-010, monwrd=FALSE)

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

     fd : A functional data object containing the curves to be
          registered. 

    fd0 : A functional data object with a single observation defining a
          template or gold standard function to which the other
          functions are registered. 

ximarks : A matrix containing the timings or argument values associated
          with the landmarks for the observations in fd to be
          registered. The number of rows equals the number of
          observations, and the number of columns equals the number of
          landmarks. 

x0marks : A vector containing the timings or argument values associated
          with the landmarks for the template or gold standard function
          in fd0. 

 wbasis : A basis object used to define the warping functions. 

    Lfd : Either a nonnegative integer of a linear differential
          operator to be applied to the functions before registering
          them. 

sparval : A smoothing parameter controlling the smoothness of the
          estimated warping functions. 

 monwrd : If TRUE, the warping function is estimated using a monotone
          smoothing methhod; otherwise, a regular smoothing method is
          used, which is not guaranteed to give strictly monotonic
          warping functions. 

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

     It is essential that the location of every landmark be clearly
     defined in each of the curves as well as the template function. If
     this is not the case, consider using the continuous registration
     function register.fd. 

     Although requiring that a monotone smoother be used to estimate
     the warping functions is safer, it adds considerably to the
     computatation time since monotone smoothing is itself an iterative
     process. It is usually better to try an initial registration with
     this feature to see if there are any failures of monotonicity.
     Moreover, monotonicity failures can usually be cured by increasing
     the smoothing parameter sparval. 

     Not much curvature is usually required in the warping functions,
     so a rather low power basis, usually B-splines, is suitable for
     argument wbasis. 

     A registration with a few prominent landmarks is often a good
     preliminary to using the more sophisticated but more lengthy
     process in register.fd.

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

     A list with these entries is returned.  "fdreg" a functional data
     object for the registered curves  "warpfd" A functional data
     object for the warping functions

_N_o_t_e:

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

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

     Ramsay, J. O. and Silverman, B. W. (1997) Functional Data
     Analysis. New York: Springer. Registration is described in Chapter
     5.

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

     register.fd

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

