ccl_error_poe

 [nPOE, vPOE, uPOE] = ccl_error_poe(U_t, N_p, Pi)

 Compute the normalised projected observation error (nPOE). To evaluate the fit without the
 true nullspace policy, an alternative criterion must be used. This indicates
 the quality of the learnt projection matrix in capturing the image space of
 the observations. i.e., how well the learnt N satisfy Nu = u

 Input:

    U_t                                    True observation
    N_p                                    Learnt projection matrix
    P_i                                    True nullspace policy

 Output:

    nPPE                                   Normalised projected observation error
    vPPE                                   Variance of the nullspace policy
    uPPE                                   Projected observation error

0001 function [nPOE, vPOE, uPOE] = ccl_error_poe(U_t, N_p, Pi)
0002 % [nPOE, vPOE, uPOE] = ccl_error_poe(U_t, N_p, Pi)
0003 %
0004 % Compute the normalised projected observation error (nPOE). To evaluate the fit without the
0005 % true nullspace policy, an alternative criterion must be used. This indicates
0006 % the quality of the learnt projection matrix in capturing the image space of
0007 % the observations. i.e., how well the learnt N satisfy Nu = u
0008 %
0009 % Input:
0010 %
0011 %    U_t                                    True observation
0012 %    N_p                                    Learnt projection matrix
0013 %    P_i                                    True nullspace policy
0014 %
0015 % Output:
0016 %
0017 %    nPPE                                   Normalised projected observation error
0018 %    vPPE                                   Variance of the nullspace policy
0019 %    uPPE                                   Projected observation error
0020 
0021 
0022 
0023 
0024 % CCL: A MATLAB library for Constraint Consistent Learning
0025 % Copyright (C) 2007  Matthew Howard
0026 % Contact: matthew.j.howard@kcl.ac.uk
0027 %
0028 % This library is free software; you can redistribute it and/or
0029 % modify it under the terms of the GNU Lesser General Public
0030 % License as published by the Free Software Foundation; either
0031 % version 2.1 of the License, or (at your option) any later version.
0032 %
0033 % This library is distributed in the hope that it will be useful,
0034 % but WITHOUT ANY WARRANTY; without even the implied warranty of
0035 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
0036 % Lesser General Public License for more details.
0037 %
0038 % You should have received a copy of the GNU Library General Public
0039 % License along with this library; if not, write to the Free
0040 % Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
0041 
0042 dim_n   = size(U_t,2) ;
0043 U_p     = zeros(size(U_t)) ;
0044 for n = 1:dim_n
0045     U_p(:,n) = N_p*U_t(:,n) ;
0046 end
0047 uPOE = sum((U_t-U_p).^2,2) / dim_n ;
0048 vPOE = var(Pi, 0, 2);
0049 nPOE = sum(uPOE) / sum(vPOE);
0050 end