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525 lines (407 loc) · 17.6 KB
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#include "classifier.hpp"
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <iostream>
using namespace std;
/* SVM Classifier: Methods to initialize parameters, fit model and predict labels -- START */
template <typename T>
SVC<T>::SVC(double C, double tol, double eps, double (*kernelFunction)(vector<T>, vector<T>))
{
SVC::C = C;
SVC::tol = tol;
SVC::kernelFunction = kernelFunction;
SVC::eps = eps;
}
template <typename T>
void SVC<T>::fit(const Dataset<T>& dataset)
{
// Copy the dataset to classifier
SVC::dataset = dataset;
int i, j;
alphas = (double *)malloc(sizeof(double) * dataset.n_data);
fill_n(alphas, dataset.n_data, 0);
b = 0;
// Calculate the error for each data sample
errors = (double *)malloc(sizeof(double) * dataset.n_data);
// #pragma omp parallel for default(none) private(i) shared(dataset, errors)
#pragma omp parallel for private(i)
for(i=0; i<dataset.n_data; ++i)
errors[i] = -1 * dataset.target[i];
// Perform optimization of alpha pairs using SMO (Sequential Minimal Optimization)
int examine_all = 1, num_changed = 0;
double kkt_parameter;
while((num_changed > 0) || (examine_all == 1))
{
num_changed = 0;
for(j=0; j<dataset.n_data; ++j)
{
// Iterates alternatively single scans through entire dataset and multiple scans through non-bound training examples
if( (examine_all == 1) || ((alphas[j] > 0) && (alphas[j] < C)) )
{
// Identify the training examples (alpha j) that violate KKT conditions
kkt_parameter = dataset.target[j] * errors[j];
if( ((kkt_parameter < -1*tol) && (alphas[j] < C)) || ((kkt_parameter > tol) && (alphas[j] > 0)) )
num_changed += findUpdateAlphaPair(j);
}
}
if(examine_all == 1)
examine_all = 0;
else if(num_changed == 0)
examine_all = 1;
}
free(errors);
}
template <typename T>
int SVC<T>::predict(const vector<T>& data)
{
double output = 0;
int i;
// #pragma omp parallel for default(none) private(i) shared(dataset, alphas, kernelFunction, data) reduction(+:output)
#pragma omp parallel for private(i) reduction(+:output)
for(i=0; i<dataset.n_data; ++i)
if(alphas[i] > 0)
output += alphas[i] * dataset.target[i] * kernelFunction(dataset.data[i], data);
output -= b;
if(output >= 0)
return 1;
else
return -1;
}
template <typename T>
int SVC<T>::findUpdateAlphaPair(int alpha2_index)
{
int i;
double estimated_step, max_estimated_step = -1;
int alpha1_index = -1;
// Iterate through all non-bound training examples to find other example for optimization using heuristic
for(i=0; i<dataset.n_data; ++i)
if((i!=alpha2_index) && (alphas[i] > 0) && (alphas[i] < C))
{
// Estimated step size of optimization
estimated_step = errors[i] - errors[alpha2_index];
if(estimated_step < 0)
estimated_step *= -1;
if(estimated_step > max_estimated_step)
#pragma omp critical
if(estimated_step > max_estimated_step)
{
max_estimated_step = estimated_step;
alpha1_index = i;
}
}
if((alpha1_index >= 0) && updateAlphaPair(alpha1_index, alpha2_index))
return 1;
// int random_offset = random() % dataset.n_data;
// Parallely search across non-bound alphas for alpha1 that makes positive step
valid_alpha1_found = 0;
// #pragma omp parallel for default(none) private(i, alpha1_index) shared(dataset, alphas, alpha2_index, C)
# pragma omp parallel
{
#pragma omp for private(i, alpha1_index)
for(i=0; i<dataset.n_data; ++i)
{
#pragma omp cancellation point for
// alpha1_index = (i + random_offset) % dataset.n_data;
alpha1_index = i;
if((valid_alpha1_found == 0) && (alpha1_index != alpha2_index) && (alphas[alpha1_index] > 0) && (alphas[alpha1_index] < C))
{
// SVC<T>::updateAlphaPair has been expanded to circumvent oprphaned cancellation point problem
#pragma omp cancellation point for
if(valid_alpha1_found == 0)
{
double alpha1_value, alpha2_value, updated_alpha1_value, updated_alpha2_value, old_b_value;
alpha1_value = alphas[alpha1_index];
alpha2_value = alphas[alpha2_index];
old_b_value = b;
int s = dataset.target[alpha1_index] * dataset.target[alpha2_index];
double L, H;
if(s > 0)
{
L = max(0.0, alpha2_value + alpha1_value - C);
H = min(C, alpha2_value + alpha1_value);
}
else
{
L = max(0.0, alpha2_value - alpha1_value);
H = min(C, C + alpha2_value - alpha1_value);
}
if(L < H)
{
#pragma omp cancellation point for
if(valid_alpha1_found == 0)
{
double k11, k12, k22, eta;
k11 = kernelFunction(dataset.data[alpha1_index], dataset.data[alpha1_index]);
k12 = kernelFunction(dataset.data[alpha1_index], dataset.data[alpha2_index]);
k22 = kernelFunction(dataset.data[alpha2_index], dataset.data[alpha2_index]);
eta = k11 + k22 - 2*k12;
if(eta > 0)
{
updated_alpha2_value = alpha2_value + dataset.target[alpha2_index]*(errors[alpha1_index] - errors[alpha2_index])/eta;
if(updated_alpha2_value < L) updated_alpha2_value = L;
else if(updated_alpha2_value > H) updated_alpha2_value = H;
}
else
{
double f1, f2, L1, H1, Lobj, Hobj;
f1 = dataset.target[alpha1_index]*(errors[alpha1_index]+b) - alpha1_value*k11 - s*alpha2_value*k12;
f2 = dataset.target[alpha2_index]*(errors[alpha2_index]+b) - s*alpha1_value*k12 - alpha2_value*k22;
L1 = alpha1_value + s*(alpha2_value - L);
H1 = alpha1_value + s*(alpha2_value - H);
Lobj = L1*f1 + L*f2 + (L1*L1*k11)/2 + (L*L*k22)/2 + s*L*L1*k12;
Hobj = H1*f1 + H*f2 + (H1*H1*k11)/2 + (H*H*k22)/2 + s*H*H1*k12;
if(Lobj < Hobj-eps)
updated_alpha2_value = L;
else if(Lobj > Hobj+eps)
updated_alpha2_value = H;
else
updated_alpha2_value = alpha2_value;
}
if(fabs(updated_alpha2_value - alpha2_value) >= eps*(updated_alpha2_value + alpha2_value + eps))
{
int thread_valid_alpha1_found = -1;
#pragma omp critical
{
if(valid_alpha1_found == 0)
{
valid_alpha1_found = 1;
thread_valid_alpha1_found = 1;
updated_alpha1_value = alpha1_value + s*(alpha2_value - updated_alpha2_value);
// update the threshold value b
if((updated_alpha1_value > 0) && (updated_alpha1_value < C))
b += errors[alpha1_index] + dataset.target[alpha1_index]*(updated_alpha1_value - alpha1_value)*k11 + dataset.target[alpha2_index]*(updated_alpha2_value - alpha2_value)*k12;
else if((updated_alpha2_value > 0) && (updated_alpha2_value < C))
b += errors[alpha2_index] + dataset.target[alpha1_index]*(updated_alpha1_value - alpha1_value)*k12 + dataset.target[alpha2_index]*(updated_alpha2_value - alpha2_value)*k22;
else
b += (errors[alpha1_index] + errors[alpha2_index])/2 + dataset.target[alpha1_index]*(updated_alpha1_value - alpha1_value)*(k11+k12)/2 + dataset.target[alpha2_index]*(updated_alpha2_value - alpha2_value)*(k12+k22)/2;
// update the error cache using new langrange multipliers
double errors_delta_b, errors_delta_alpha1, errors_delta_alpha2;
errors_delta_b = old_b_value - b;
errors_delta_alpha1 = (updated_alpha1_value - alpha1_value) * dataset.target[alpha1_index];
errors_delta_alpha2 = (updated_alpha2_value - alpha2_value) * dataset.target[alpha2_index];
int i;
// #pragma omp parallel for default(none) private(i) shared(dataset, errors, errors_delta_b, errors_delta_alpha1, errors_delta_alpha2, kernelFunction)
#pragma omp parallel for private(i)
for(i=0; i<dataset.n_data; ++i)
{
errors[i] += errors_delta_b;
errors[i] += errors_delta_alpha1 * kernelFunction(dataset.data[alpha1_index], dataset.data[i]);
errors[i] += errors_delta_alpha2 * kernelFunction(dataset.data[alpha2_index], dataset.data[i]);
}
// store alpha values in alphas array
alphas[alpha1_index] = updated_alpha1_value;
alphas[alpha2_index] = updated_alpha2_value;
} // end of inner most if(valid_alpha1_found == 0)
} // end of #pragma omp critical
if(thread_valid_alpha1_found)
{
#pragma omp cancel for
}
}
} // end of inner if(valid_alpha1_found == 0)
} // end of if(L < H)
} // end of outter if(valid_alpha1_found == 0)
}
}
}
if(valid_alpha1_found)
return 1;
// Parallely search across all alphas for alpha1 that makes positive step
valid_alpha1_found = 0;
// #pragma omp parallel for default(none) private(i, alpha1_index) shared(dataset, alphas, alpha2_index, C)
#pragma omp parallel
{
#pragma omp for private(i, alpha1_index)
for(i=0; i<dataset.n_data; ++i)
{
#pragma omp cancellation point for
// alpha1_index = (i + random_offset) % dataset.n_data;
alpha1_index = i;
if((valid_alpha1_found == 0) && (alpha1_index != alpha2_index) && ((alphas[alpha1_index] == 0) || (alphas[alpha1_index] == C)) )
{
// SVC<T>::updateAlphaPair has been expanded to circumvent oprphaned cancellation point problem
#pragma omp cancellation point for
if(valid_alpha1_found == 0)
{
double alpha1_value, alpha2_value, updated_alpha1_value, updated_alpha2_value, old_b_value;
alpha1_value = alphas[alpha1_index];
alpha2_value = alphas[alpha2_index];
old_b_value = b;
int s = dataset.target[alpha1_index] * dataset.target[alpha2_index];
double L, H;
if(s > 0)
{
L = max(0.0, alpha2_value + alpha1_value - C);
H = min(C, alpha2_value + alpha1_value);
}
else
{
L = max(0.0, alpha2_value - alpha1_value);
H = min(C, C + alpha2_value - alpha1_value);
}
if(L < H)
{
#pragma omp cancellation point for
if(valid_alpha1_found == 0)
{
double k11, k12, k22, eta;
k11 = kernelFunction(dataset.data[alpha1_index], dataset.data[alpha1_index]);
k12 = kernelFunction(dataset.data[alpha1_index], dataset.data[alpha2_index]);
k22 = kernelFunction(dataset.data[alpha2_index], dataset.data[alpha2_index]);
eta = k11 + k22 - 2*k12;
if(eta > 0)
{
updated_alpha2_value = alpha2_value + dataset.target[alpha2_index]*(errors[alpha1_index] - errors[alpha2_index])/eta;
if(updated_alpha2_value < L) updated_alpha2_value = L;
else if(updated_alpha2_value > H) updated_alpha2_value = H;
}
else
{
double f1, f2, L1, H1, Lobj, Hobj;
f1 = dataset.target[alpha1_index]*(errors[alpha1_index]+b) - alpha1_value*k11 - s*alpha2_value*k12;
f2 = dataset.target[alpha2_index]*(errors[alpha2_index]+b) - s*alpha1_value*k12 - alpha2_value*k22;
L1 = alpha1_value + s*(alpha2_value - L);
H1 = alpha1_value + s*(alpha2_value - H);
Lobj = L1*f1 + L*f2 + (L1*L1*k11)/2 + (L*L*k22)/2 + s*L*L1*k12;
Hobj = H1*f1 + H*f2 + (H1*H1*k11)/2 + (H*H*k22)/2 + s*H*H1*k12;
if(Lobj < Hobj-eps)
updated_alpha2_value = L;
else if(Lobj > Hobj+eps)
updated_alpha2_value = H;
else
updated_alpha2_value = alpha2_value;
}
if(fabs(updated_alpha2_value - alpha2_value) >= eps*(updated_alpha2_value + alpha2_value + eps))
{
int thread_valid_alpha1_found = -1;
#pragma omp critical
{
if(valid_alpha1_found == 0)
{
valid_alpha1_found = 1;
thread_valid_alpha1_found = 1;
updated_alpha1_value = alpha1_value + s*(alpha2_value - updated_alpha2_value);
// update the threshold value b
if((updated_alpha1_value > 0) && (updated_alpha1_value < C))
b += errors[alpha1_index] + dataset.target[alpha1_index]*(updated_alpha1_value - alpha1_value)*k11 + dataset.target[alpha2_index]*(updated_alpha2_value - alpha2_value)*k12;
else if((updated_alpha2_value > 0) && (updated_alpha2_value < C))
b += errors[alpha2_index] + dataset.target[alpha1_index]*(updated_alpha1_value - alpha1_value)*k12 + dataset.target[alpha2_index]*(updated_alpha2_value - alpha2_value)*k22;
else
b += (errors[alpha1_index] + errors[alpha2_index])/2 + dataset.target[alpha1_index]*(updated_alpha1_value - alpha1_value)*(k11+k12)/2 + dataset.target[alpha2_index]*(updated_alpha2_value - alpha2_value)*(k12+k22)/2;
// update the error cache using new langrange multipliers
double errors_delta_b, errors_delta_alpha1, errors_delta_alpha2;
errors_delta_b = old_b_value - b;
errors_delta_alpha1 = (updated_alpha1_value - alpha1_value) * dataset.target[alpha1_index];
errors_delta_alpha2 = (updated_alpha2_value - alpha2_value) * dataset.target[alpha2_index];
int i;
// #pragma omp parallel for default(none) private(i) shared(dataset, errors, errors_delta_b, errors_delta_alpha1, errors_delta_alpha2, kernelFunction)
#pragma omp parallel for private(i)
for(i=0; i<dataset.n_data; ++i)
{
errors[i] += errors_delta_b;
errors[i] += errors_delta_alpha1 * kernelFunction(dataset.data[alpha1_index], dataset.data[i]);
errors[i] += errors_delta_alpha2 * kernelFunction(dataset.data[alpha2_index], dataset.data[i]);
}
// store alpha values in alphas array
alphas[alpha1_index] = updated_alpha1_value;
alphas[alpha2_index] = updated_alpha2_value;
} // end of inner most if(valid_alpha1_found == 0)
} // end of #pragma omp critical
if(thread_valid_alpha1_found)
{
#pragma omp cancel for
}
}
} // end of inner if(valid_alpha1_found == 0)
} // end of if(L < H)
} // end of outter if(valid_alpha1_found == 0)
}
}
}
if(valid_alpha1_found)
return 1;
return 0;
}
template <typename T>
int SVC<T>::updateAlphaPair(int alpha1_index, int alpha2_index)
{
double alpha1_value, alpha2_value, updated_alpha1_value, updated_alpha2_value, old_b_value;
alpha1_value = alphas[alpha1_index];
alpha2_value = alphas[alpha2_index];
old_b_value = b;
int s = dataset.target[alpha1_index] * dataset.target[alpha2_index];
double L, H;
if(s > 0)
{
L = max(0.0, alpha2_value + alpha1_value - C);
H = min(C, alpha2_value + alpha1_value);
}
else
{
L = max(0.0, alpha2_value - alpha1_value);
H = min(C, C + alpha2_value - alpha1_value);
}
if(L == H)
return 0;
double k11, k12, k22, eta;
k11 = kernelFunction(dataset.data[alpha1_index], dataset.data[alpha1_index]);
k12 = kernelFunction(dataset.data[alpha1_index], dataset.data[alpha2_index]);
k22 = kernelFunction(dataset.data[alpha2_index], dataset.data[alpha2_index]);
eta = k11 + k22 - 2*k12;
if(eta > 0)
{
updated_alpha2_value = alpha2_value + dataset.target[alpha2_index]*(errors[alpha1_index] - errors[alpha2_index])/eta;
if(updated_alpha2_value < L) updated_alpha2_value = L;
else if(updated_alpha2_value > H) updated_alpha2_value = H;
}
else
{
double f1, f2, L1, H1, Lobj, Hobj;
f1 = dataset.target[alpha1_index]*(errors[alpha1_index]+b) - alpha1_value*k11 - s*alpha2_value*k12;
f2 = dataset.target[alpha2_index]*(errors[alpha2_index]+b) - s*alpha1_value*k12 - alpha2_value*k22;
L1 = alpha1_value + s*(alpha2_value - L);
H1 = alpha1_value + s*(alpha2_value - H);
Lobj = L1*f1 + L*f2 + (L1*L1*k11)/2 + (L*L*k22)/2 + s*L*L1*k12;
Hobj = H1*f1 + H*f2 + (H1*H1*k11)/2 + (H*H*k22)/2 + s*H*H1*k12;
if(Lobj < Hobj-eps)
updated_alpha2_value = L;
else if(Lobj > Hobj+eps)
updated_alpha2_value = H;
else
updated_alpha2_value = alpha2_value;
}
if(fabs(updated_alpha2_value - alpha2_value) < eps*(updated_alpha2_value + alpha2_value + eps))
return 0;
updated_alpha1_value = alpha1_value + s*(alpha2_value - updated_alpha2_value);
// update the threshold value b
if((updated_alpha1_value > 0) && (updated_alpha1_value < C))
b += errors[alpha1_index] + dataset.target[alpha1_index]*(updated_alpha1_value - alpha1_value)*k11 + dataset.target[alpha2_index]*(updated_alpha2_value - alpha2_value)*k12;
else if((updated_alpha2_value > 0) && (updated_alpha2_value < C))
b += errors[alpha2_index] + dataset.target[alpha1_index]*(updated_alpha1_value - alpha1_value)*k12 + dataset.target[alpha2_index]*(updated_alpha2_value - alpha2_value)*k22;
else
b += (errors[alpha1_index] + errors[alpha2_index])/2 + dataset.target[alpha1_index]*(updated_alpha1_value - alpha1_value)*(k11+k12)/2 + dataset.target[alpha2_index]*(updated_alpha2_value - alpha2_value)*(k12+k22)/2;
// update the error cache using new langrange multipliers
double errors_delta_b, errors_delta_alpha1, errors_delta_alpha2;
errors_delta_b = old_b_value - b;
errors_delta_alpha1 = (updated_alpha1_value - alpha1_value) * dataset.target[alpha1_index];
errors_delta_alpha2 = (updated_alpha2_value - alpha2_value) * dataset.target[alpha2_index];
int i;
// #pragma omp parallel for default(none) private(i) shared(dataset, errors, errors_delta_b, errors_delta_alpha1, errors_delta_alpha2, kernelFunction)
#pragma omp parallel for private(i)
for(i=0; i<dataset.n_data; ++i)
{
errors[i] += errors_delta_b;
errors[i] += errors_delta_alpha1 * kernelFunction(dataset.data[alpha1_index], dataset.data[i]);
errors[i] += errors_delta_alpha2 * kernelFunction(dataset.data[alpha2_index], dataset.data[i]);
}
// store alpha values in alphas array
alphas[alpha1_index] = updated_alpha1_value;
alphas[alpha2_index] = updated_alpha2_value;
return 1;
}
/* SVM Classifier: Methods to initialize parameters, fit model and predict labels -- END */
// explicit instantiation of template class and function
template class SVC<int>;
template class SVC<float>;
template class SVC<double>;