approxPca

 approximation by principal component analysis

 THIS IS NO USER FUNCTION

• approximateDec shape approximation based on sample points and decomposition data
• obtainGrassStruct collect information required for computeProjectionFromGrass

0001 function out = approxPca(hcMatrix, par)
0002 % approximation by principal component analysis
0003 %
0004 % THIS IS NO USER FUNCTION
0005 
0006 % The elk-library: convex geometry applied to crystallization modeling.
0007 %   Copyright (C) 2013 Alexander Reinhold
0008 %
0009 % This program is free software: you can redistribute it and/or modify it
0010 %   under the terms of the GNU General Public License as published by the
0011 %   Free Software Foundation, either version 3 of the License, or (at your
0012 %   option) any later version.
0013 %
0014 % This program is distributed in the hope that it will be useful, but
0015 %   WITHOUT ANY WARRANTY; without even the implied warranty of
0016 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
0017 %   General Public License for more details.
0018 %
0019 % You should have received a copy of the GNU General Public License along
0020 %   with this program.  If not, see <http://www.gnu.org/licenses/>.
0021 
0022 %% perform PCA
0023 % svd with covariance matrix
0024 % X = [dataOriginal.positionMatrix, -1*dataOriginal.positionMatrix];
0025 % [u,s,v] = svd(X*X', 0);
0026 [u,s,v] = svd(hcMatrix);
0027 % [u,s,v] = svd(dataOriginal.positionMatrix', 0);
0028 out.mappingReducedToEmbedding = u(:, 1:par.targetDim);
0029 out.projectionMatrix = u(:, 1:par.targetDim) * u(:, 1:par.targetDim)';
0030 
0031 
0032 % v(:, 1:par.targetDim)
0033 % v(:, 1:par.targetDim)'*v(:, 1:par.targetDim)
0034 % v(:, 1:par.targetDim)*v(:, 1:par.targetDim)'
0035 % v = orth(out.projectionMatrix)
0036 % v'*v
0037 % pinv(orth(out.projectionMatrix))
0038 
0039 end