/// <summary>
/// Solves the SMO considering no previous knowledge about the problem
/// </summary>
/// <param name="problemSolution">Solution of the problem</param>
/// <returns>Solution of the problem with alphas and threshold</returns>
public static SVM solveSMOStartingFromZero(SVM problemSolution)
{
problemSolution.initializeWithZeros();
// Solve it
return solveSMOStartingFromPreviousSolution(problemSolution);
}
/// <summary>
/// Solves the SMO considering no previous knowledge about the problem
/// </summary>
/// <param name="problemSolution">Known solution</param>
/// <returns>Solution of the problem with alphas and threshold</returns>
public static SVM solveSMOStartingFromPreviousSolution(SVM problemSolution)
{
System.Diagnostics.Stopwatch swTotalTime = new System.Diagnostics.Stopwatch();
System.Diagnostics.Stopwatch swHeuristica = new System.Diagnostics.Stopwatch();
System.Diagnostics.Stopwatch swComputeKernel = new System.Diagnostics.Stopwatch();
System.Diagnostics.Stopwatch swUpdateError = new System.Diagnostics.Stopwatch();
swTotalTime.Start();
ProblemConfig problemConfig = problemSolution.ProblemCfg;
if (problemSolution.alphaList == null) problemSolution.initializeWithZeros();
ProblemSolver.calculateErrors(problemSolution);
//Initializes GPU error vector
if (OpenTKWrapper.CLCalc.CLAcceleration == OpenTKWrapper.CLCalc.CLAccelerationType.UsingCL)
WriteCLErr(problemSolution);
TrainingSet trainingSet = problemSolution.TrainingSet;
int passes = 0;
int m = trainingSet.getN;
while (passes < problemConfig.maxPasses)
{
int changedAlphas = 0;
for (int i = 0; i < m; i++)
{
float yi = trainingSet.trainingArray[i].y;
float alpha_i = problemSolution.alphaList[i];
// Error between the SVM output on the ith training unit and the true ith output
float ei = trainingSet.errors[i];
// KKT conditions for ith element
if (
((yi * ei < -problemConfig.tol && alpha_i < problemConfig.c) || (yi * ei > problemConfig.tol && alpha_i > 0))
)
{
swHeuristica.Start();
#region Computes J using maximum variation heuristics
// Get a number from 0 to m - 1 not equal to i
int j = 0;
if (trainingSet.errors[i] >= 0)
{
if (OpenTKWrapper.CLCalc.CLAcceleration == OpenTKWrapper.CLCalc.CLAccelerationType.UsingCL)
{
j = CLFindMinError(problemSolution);
}
else
{
float minError = trainingSet.errors[0];
for (int k = 1; k < trainingSet.getN; k++)
{
if (minError > trainingSet.errors[k])
{
minError = trainingSet.errors[k];
j = k;
}
}
}
}
else
{
if (OpenTKWrapper.CLCalc.CLAcceleration == OpenTKWrapper.CLCalc.CLAccelerationType.UsingCL)
{
j = CLFindMaxError(problemSolution);
}
else
{
float maxError = trainingSet.errors[0];
for (int k = 1; k < trainingSet.getN; k++)
{
if (maxError < trainingSet.errors[k])
{
maxError = trainingSet.errors[k];
j = k;
}
}
}
}
#endregion
swHeuristica.Stop();
float yj = trainingSet.trainingArray[j].y;
float alpha_j = problemSolution.alphaList[j];
// Error between the SVM output on the jth training unit and the true jth output
float ej = trainingSet.errors[j];
// Save old alphas
float oldAlpha_i = problemSolution.alphaList[i];
float oldAlpha_j = problemSolution.alphaList[j];
#region Compute lower and higher bounds of alpha_j
float lowerBound;
float higherBound;
if (yi != yj)
{
lowerBound = Math.Max(0, alpha_j - alpha_i);
higherBound = Math.Min(problemConfig.c, problemConfig.c + alpha_j - alpha_i);
}
else
{
lowerBound = Math.Max(0, alpha_j + alpha_i - problemConfig.c);
higherBound = Math.Min(problemConfig.c, alpha_j + alpha_i);
}
#endregion
// Nothing to adjust if we can't set any value between those bounds
if (lowerBound == higherBound) continue;
#region Compute eta
float kernel_xi_xj;
float kernel_xi_xi;
float kernel_xj_xj;
if (trainingSet.IsKernelCalculated[i])
kernel_xi_xj = trainingSet.kernels[i][j];
else if (trainingSet.IsKernelCalculated[j])
kernel_xi_xj = trainingSet.kernels[j][i];
else kernel_xi_xj = calculateSingleKernel(trainingSet.trainingArray[i], trainingSet.trainingArray[j], problemSolution);//trainingSet.kernels[i][j];
if (trainingSet.IsKernelCalculated[i])
kernel_xi_xi = trainingSet.kernels[i][i];
else kernel_xi_xi = calculateSingleKernel(trainingSet.trainingArray[i], trainingSet.trainingArray[i], problemSolution);//trainingSet.kernels[i][i];
if (trainingSet.IsKernelCalculated[j])
kernel_xj_xj = trainingSet.kernels[j][j];
else kernel_xj_xj = calculateSingleKernel(trainingSet.trainingArray[j], trainingSet.trainingArray[j], problemSolution);//trainingSet.kernels[j][j];
float eta = 2 * kernel_xi_xj - kernel_xi_xi - kernel_xj_xj;
#endregion
if (eta >= 0) continue;
// Compute new alpha_j
alpha_j = alpha_j - yj * (ei - ej) / eta;
// Clip alpha_j if necessary
if (alpha_j > higherBound) alpha_j = higherBound;
else if (alpha_j < lowerBound) alpha_j = lowerBound;
// If the changes are not big enough, just continue
if (Math.Abs(oldAlpha_j - alpha_j) < MIN_ALPHA_CHANGE) continue;
swComputeKernel.Start();
//Needs to compute lines K[i][] and K[j][] since the alphas will change
if (OpenTKWrapper.CLCalc.CLAcceleration == OpenTKWrapper.CLCalc.CLAccelerationType.UsingCL)
{
CLComputeKernels(problemSolution, i);
CLComputeKernels(problemSolution, j);
}
else
{
ComputeKernels(problemSolution, i);
ComputeKernels(problemSolution, j);
}
swComputeKernel.Stop();
// Compute value for alpha_i
alpha_i = alpha_i + yi * yj * (oldAlpha_j - alpha_j);
// Compute b1, b2 and new b (threshold)
float oldB = problemSolution.b;
if (0 < alpha_i && alpha_i < problemConfig.c)
{
// b1 is enough in this case
float b1 = problemSolution.b - ei - yi * (alpha_i - oldAlpha_i) * kernel_xi_xi - yj * (alpha_j - oldAlpha_j) * kernel_xi_xj;
problemSolution.b = b1;
}
else if (0 < alpha_j && alpha_j < problemConfig.c)
{
// b2 is enough in this case
float b2 = problemSolution.b - ej - yi * (alpha_i - oldAlpha_i) * kernel_xi_xj - yj * (alpha_j - oldAlpha_j) * kernel_xj_xj;
problemSolution.b = b2;
}
else
{
// b is the average between b1 and b2
float b1 = problemSolution.b - ei - yi * (alpha_i - oldAlpha_i) * kernel_xi_xi - yj * (alpha_j - oldAlpha_j) * kernel_xi_xj;
float b2 = problemSolution.b - ej - yi * (alpha_i - oldAlpha_i) * kernel_xi_xj - yj * (alpha_j - oldAlpha_j) * kernel_xj_xj;
problemSolution.b = (b1 + b2) * 0.5f;
}
// Update the changed alphas in the solution
problemSolution.alphaList[i] = alpha_i;
problemSolution.alphaList[j] = alpha_j;
// Update errors cache
swUpdateError.Start();
if (OpenTKWrapper.CLCalc.CLAcceleration == OpenTKWrapper.CLCalc.CLAccelerationType.UsingCL)
CLupdateErrorsCache(trainingSet, problemSolution, oldAlpha_i, alpha_i, i, oldAlpha_j, alpha_j, j, oldB, problemSolution.b);
else
updateErrorsCache(trainingSet, problemSolution, oldAlpha_i, alpha_i, i, oldAlpha_j, alpha_j, j, oldB, problemSolution.b);
swUpdateError.Stop();
changedAlphas++;
}
}
if (changedAlphas == 0)
{ passes++; }
else
{ passes = 0; }
}
return problemSolution;
}
