// Copyright (C) 2014 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#ifndef DLIB_LDA_Hh_
#define DLIB_LDA_Hh_
#include "lda_abstract.h"
#include "../algs.h"
#include <map>
#include "../matrix.h"
#include <vector>
namespace dlib
{
// ----------------------------------------------------------------------------------------
namespace impl
{
inline std::map<unsigned long,unsigned long> make_class_labels(
const std::vector<unsigned long>& row_labels
)
{
std::map<unsigned long,unsigned long> class_labels;
for (unsigned long i = 0; i < row_labels.size(); ++i)
{
const unsigned long next = class_labels.size();
if (class_labels.count(row_labels[i]) == 0)
class_labels[row_labels[i]] = next;
}
return class_labels;
}
// ------------------------------------------------------------------------------------
template <
typename T
>
matrix<T,0,1> center_matrix (
matrix<T>& X
)
{
matrix<T,1> mean;
for (long r = 0; r < X.nr(); ++r)
mean += rowm(X,r);
mean /= X.nr();
for (long r = 0; r < X.nr(); ++r)
set_rowm(X,r) -= mean;
return trans(mean);
}
}
// ----------------------------------------------------------------------------------------
template <
typename T
>
void compute_lda_transform (
matrix<T>& X,
matrix<T,0,1>& mean,
const std::vector<unsigned long>& row_labels,
unsigned long lda_dims = 500,
unsigned long extra_pca_dims = 200
)
{
std::map<unsigned long,unsigned long> class_labels = impl::make_class_labels(row_labels);
// LDA can only give out at most class_labels.size()-1 dimensions so don't try to
// compute more than that.
lda_dims = std::min<unsigned long>(lda_dims, class_labels.size()-1);
// make sure requires clause is not broken
DLIB_CASSERT(class_labels.size() > 1,
"\t void compute_lda_transform()"
<< "\n\t You can't call this function if the number of distinct class labels is less than 2."
);
DLIB_CASSERT(X.size() != 0 && (long)row_labels.size() == X.nr() && lda_dims != 0,
"\t void compute_lda_transform()"
<< "\n\t Invalid inputs were given to this function."
<< "\n\t X.size(): " << X.size()
<< "\n\t row_labels.size(): " << row_labels.size()
<< "\n\t lda_dims: " << lda_dims
);
mean = impl::center_matrix(X);
// Do PCA to reduce dims
matrix<T> pu,pw,pv;
svd_fast(X, pu, pw, pv, lda_dims+extra_pca_dims, 4);
pu.set_size(0,0); // free RAM, we don't need pu.
X = X*pv;
matrix<T> class_means(class_labels.size(), X.nc());
class_means = 0;
matrix<T,0,1> class_counts(class_labels.size());
class_counts = 0;
// First compute the means of each class
for (unsigned long i = 0; i < row_labels.size(); ++i)
{
const unsigned long class_idx = class_labels[row_labels[i]];
set_rowm(class_means,class_idx) += rowm(X,i);
class_counts(class_idx)++;
}
class_means = inv(diagm(class_counts))*class_means;
// subtract means from the data
for (unsigned long i = 0; i < row_labels.size(); ++i)
{
const unsigned long class_idx = class_labels[row_labels[i]];
set_rowm(X,i) -= rowm(class_means,class_idx);
}
// Note that we are using the formulas from the paper Using Discriminant
// Eigenfeatures for Image Retrieval by Swets and Weng.
matrix<T> Sw = trans(X)*X;
matrix<T> Sb = trans(class_means)*class_means;
matrix<T> A, H;
matrix<T,0,1> W;
svd3(Sw, A, W, H);
W = sqrt(W);
W = reciprocal(lowerbound(W,max(W)*1e-5));
A = trans(H*diagm(W))*Sb*H*diagm(W);
matrix<T> v,s,u;
svd3(A, v, s, u);
matrix<T> tform = H*diagm(W)*u;
// pick out only the number of dimensions we are supposed to for the output, unless
// we should just keep them all, then don't do anything.
if ((long)lda_dims <= tform.nc())
{
rsort_columns(tform, s);
tform = colm(tform, range(0, lda_dims-1));
}
X = trans(pv*tform);
mean = X*mean;
}
// ----------------------------------------------------------------------------------------
struct roc_point
{
double true_positive_rate;
double false_positive_rate;
double detection_threshold;
};
inline std::vector<roc_point> compute_roc_curve (
const std::vector<double>& true_detections,
const std::vector<double>& false_detections
)
{
DLIB_CASSERT(true_detections.size() != 0);
DLIB_CASSERT(false_detections.size() != 0);
std::vector<std::pair<double,int> > temp;
temp.reserve(true_detections.size()+false_detections.size());
// We use -1 for true labels and +1 for false so when we call std::sort() below it will sort
// runs with equal detection scores so false come first. This will avoid it seeming like we
// can separate true from false when scores are equal in the loop below.
const int true_label = -1;
const int false_label = +1;
for (unsigned long i = 0; i < true_detections.size(); ++i)
temp.push_back(std::make_pair(true_detections[i], true_label));
for (unsigned long i = 0; i < false_detections.size(); ++i)
temp.push_back(std::make_pair(false_detections[i], false_label));
std::sort(temp.rbegin(), temp.rend());
std::vector<roc_point> roc_curve;
roc_curve.reserve(temp.size());
double num_false_included = 0;
double num_true_included = 0;
for (unsigned long i = 0; i < temp.size(); ++i)
{
if (temp[i].second == true_label)
num_true_included++;
else
num_false_included++;
roc_point p;
p.true_positive_rate = num_true_included/true_detections.size();
p.false_positive_rate = num_false_included/false_detections.size();
p.detection_threshold = temp[i].first;
roc_curve.push_back(p);
}
return roc_curve;
}
// ----------------------------------------------------------------------------------------
inline std::pair<double,double> equal_error_rate (
const std::vector<double>& low_vals,
const std::vector<double>& high_vals
)
{
if (low_vals.size() == 0 && high_vals.size() == 0)
return std::make_pair(0,0);
else if (low_vals.size() == 0)
return std::make_pair(0, min(mat(high_vals)));
else if (high_vals.size() == 0)
return std::make_pair(0, max(mat(low_vals))+1);
// Find the point of equal error rates
double best_thresh = 0;
double best_error = 0;
double best_delta = std::numeric_limits<double>::infinity();
for (const auto& pt : compute_roc_curve(high_vals, low_vals))
{
const double false_negative_rate = 1-pt.true_positive_rate;
const double delta = std::abs(false_negative_rate - pt.false_positive_rate);
if (delta < best_delta)
{
best_delta = delta;
best_error = std::max(false_negative_rate, pt.false_positive_rate);
best_thresh = pt.detection_threshold;
}
}
return std::make_pair(best_error, best_thresh);
}
// ----------------------------------------------------------------------------------------
}
#endif // DLIB_LDA_Hh_