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/*Copyright (C) 2015 Olivier Delaneau, Halit Ongen, Emmanouil T. Dermitzakis
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.*/
#ifndef _PCA_H
#define _PCA_H
//STL INCLUDES
#include <vector>
#include <string>
//EIGEN INCLUDES
#include <Eigen/Dense>
#include <Eigen/SVD>
#include <iterator>
//EIGEN NAMESPACE
using namespace Eigen;
using namespace std;
class pca {
public:
unsigned int _nrows; // Number of rows in matrix x.
unsigned int _ncols; // Number of cols in matrix x.
bool _is_center; // Whether the variables should be shifted to be zero centered
bool _is_scale; // Whether the variables should be scaled to have unit variance
bool _is_corr; // PCA with correlation matrix, not covariance
vector < unsigned int > _eliminated_columns; // Numbers of eliminated columns
vector < float > _sd; // Standard deviation of each component
vector < float > _prop_of_var; // Proportion of variance
vector < float > _cum_prop; // Cumulative proportion
vector < float > _scores; // Rotated values
unsigned int _kaiser; // Number of PC according Kaiser criterion
unsigned int _thresh995; // Number of PC according 95% variance threshol
Eigen::MatrixXf _xXf; // Initial matrix as Eigen MatrixXf structure
Eigen::MatrixXf _pcs;
pca(int nrows, int ncols): _nrows(nrows), _ncols(ncols), _is_center(true), _is_scale (true), _is_corr(false), _kaiser(0), _thresh995(1) {
_xXf.resize(nrows, ncols);
};
~pca() { _xXf.resize(0, 0); };
void fill (vector < vector < float > > & values, vector < unsigned int > & indexes) {
for (int i = 0; i < indexes.size() ; i++) for (int s = 0 ; s < values[0].size() ; s++) _xXf(s, i) = values[indexes[i]][s];
}
void get(int i_pc, vector < float > & values) {
for (int s = 0 ; s < _nrows ; s ++) values[s] = _pcs(i_pc, s);
}
float getVariance (unsigned int k) { return _prop_of_var[k]; }
bool run(const bool is_corr, const bool is_center, const bool is_scale) {
_ncols = _xXf.cols();
_nrows = _xXf.rows();
_is_corr = is_corr;
_is_center = is_center;
_is_scale = is_scale;
if ((1 == _ncols) || (1 == _nrows)) return false;
// Mean and standard deviation for each column
VectorXf mean_vector(_ncols);
mean_vector = _xXf.colwise().mean();
VectorXf sd_vector(_ncols);
unsigned int zero_sd_num = 0;
float denom = static_cast<float>((_nrows > 1)? _nrows - 1: 1);
for (unsigned int i = 0; i < _ncols; ++i) {
VectorXf curr_col = VectorXf::Constant(_nrows, mean_vector(i)); // mean(x) for column x
curr_col = _xXf.col(i) - curr_col; // x - mean(x)
curr_col = curr_col.array().square(); // (x-mean(x))^2
sd_vector(i) = sqrt((curr_col.sum())/denom);
if (0 == sd_vector(i)) {
zero_sd_num++;
}
}
if (1 > _ncols-zero_sd_num) return false;
// Delete columns where sd == 0
MatrixXf tmp(_nrows, _ncols-zero_sd_num);
VectorXf tmp_mean_vector(_ncols-zero_sd_num);
unsigned int curr_col_num = 0;
for (unsigned int i = 0; i < _ncols; ++i) {
if (0 != sd_vector(i)) {
tmp.col(curr_col_num) = _xXf.col(i);
tmp_mean_vector(curr_col_num) = mean_vector(i);
curr_col_num++;
} else {
_eliminated_columns.push_back(i);
}
}
_ncols -= zero_sd_num;
_xXf = tmp;
mean_vector = tmp_mean_vector;
tmp.resize(0, 0); tmp_mean_vector.resize(0);
// Shift to zero
if (true == _is_center) {
for (unsigned int i = 0; i < _ncols; ++i) {
_xXf.col(i) -= VectorXf::Constant(_nrows, mean_vector(i));
}
}
// Scale to unit variance
if ( true == _is_scale) {
for (unsigned int i = 0; i < _ncols; ++i) {
_xXf.col(i) /= sqrt(_xXf.col(i).array().square().sum()/denom);
}
}
// When _nrows < _ncols then svd will be used.
// If corr is true and _nrows > _ncols then will be used correlation matrix
// (TODO): What about covariance?
if ((_nrows < _ncols) || (false == _is_corr)) { // Singular Value Decomposition is on
JacobiSVD<MatrixXf> svd(_xXf, ComputeThinV);
VectorXf eigen_singular_values = svd.singularValues();
VectorXf tmp_vec = eigen_singular_values.array().square();
float tmp_sum = tmp_vec.sum();
tmp_vec /= tmp_sum;
// PC's standard deviation and
// PC's proportion of variance
_kaiser = 0;
unsigned int lim = (_nrows < _ncols)? _nrows : _ncols;
for (unsigned int i = 0; i < lim; ++i) {
_sd.push_back(eigen_singular_values(i)/sqrt(denom));
if (_sd[i] >= 1) {
_kaiser = i + 1;
}
_prop_of_var.push_back(tmp_vec(i));
}
tmp_vec.resize(0);
// PC's cumulative proportion
_thresh995 = 1;
_cum_prop.push_back(_prop_of_var[0]);
for (unsigned int i = 1; i < _prop_of_var.size(); ++i) {
_cum_prop.push_back(_cum_prop[i-1]+_prop_of_var[i]);
if (_cum_prop[i] < 0.995) {
_thresh995 = i+1;
}
}
// Scores
MatrixXf eigen_scores = _xXf * svd.matrixV();
_pcs = eigen_scores.transpose();
eigen_scores.resize(0, 0);
} else { // COR OR COV MATRICES ARE HERE
// Calculate covariance matrix
MatrixXf eigen_cov; // = MatrixXf::Zero(_ncols, _ncols);
VectorXf sds;
// (TODO) Should be weighted cov matrix, even if is_center == false
eigen_cov = (1.0 /(_nrows/*-1*/)) * _xXf.transpose() * _xXf;
sds = eigen_cov.diagonal().array().sqrt();
MatrixXf outer_sds = sds * sds.transpose();
eigen_cov = eigen_cov.array() / outer_sds.array();
outer_sds.resize(0, 0);
// ?If data matrix is scaled, covariance matrix is equal to correlation matrix
EigenSolver<MatrixXf> edc(eigen_cov);
VectorXf eigen_eigenvalues = edc.eigenvalues().real();
MatrixXf eigen_eigenvectors = edc.eigenvectors().real();
// The eigenvalues and eigenvectors are not sorted in any particular order.
// So, we should sort them
typedef pair<float, int> eigen_pair;
vector<eigen_pair> ep;
for (unsigned int i = 0 ; i < _ncols; ++i) {
ep.push_back(make_pair(eigen_eigenvalues(i), i));
}
sort(ep.begin(), ep.end()); // Ascending order by default
// Sort them all in descending order
MatrixXf eigen_eigenvectors_sorted = MatrixXf::Zero(eigen_eigenvectors.rows(), eigen_eigenvectors.cols());
VectorXf eigen_eigenvalues_sorted = VectorXf::Zero(_ncols);
int colnum = 0;
int i = ep.size()-1;
for (; i > -1; i--) {
eigen_eigenvalues_sorted(colnum) = ep[i].first;
eigen_eigenvectors_sorted.col(colnum++) += eigen_eigenvectors.col(ep[i].second);
}
// We don't need not sorted arrays anymore
eigen_eigenvalues.resize(0);
eigen_eigenvectors.resize(0, 0);
_sd.clear(); _prop_of_var.clear(); _kaiser = 0;
float tmp_sum = eigen_eigenvalues_sorted.sum();
for (unsigned int i = 0; i < _ncols; ++i) {
_sd.push_back(sqrt(eigen_eigenvalues_sorted(i)));
if (_sd[i] >= 1) {
_kaiser = i + 1;
}
_prop_of_var.push_back(eigen_eigenvalues_sorted(i)/tmp_sum);
}
// PC's cumulative proportion
_cum_prop.clear(); _thresh995 = 1;
_cum_prop.push_back(_prop_of_var[0]);
for (unsigned int i = 1; i < _prop_of_var.size(); ++i) {
_cum_prop.push_back(_cum_prop[i-1]+_prop_of_var[i]);
if (_cum_prop[i] < 0.995) {
_thresh995 = i+1;
}
}
// Scores for PCA with correlation matrix
// Scale before calculating new values
for (unsigned int i = 0; i < _ncols; ++i) {
_xXf.col(i) /= sds(i);
}
sds.resize(0);
MatrixXf eigen_scores = _xXf * eigen_eigenvectors_sorted;
_pcs = eigen_scores.transpose();
eigen_scores.resize(0, 0);
}
return true;
};
};
#endif
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