svmprecomputed.cpp

一个包含丰富内容的流形学习算法工具包

				}
			}
			else
			{
				if(alpha[i] < 0)
				{
					alpha[i] = 0;
					alpha[j] = sum;
				}
			}
		}

		// update G

		double delta_alpha_i = alpha[i] - old_alpha_i;
		double delta_alpha_j = alpha[j] - old_alpha_j;
		
		for(int k=0;k<active_size;k++)
		{
			G[k] += Q_i[k]*delta_alpha_i + Q_j[k]*delta_alpha_j;
		}

		// update alpha_status and G_bar

		{
			bool ui = is_upper_bound(i);
			bool uj = is_upper_bound(j);
			update_alpha_status(i);
			update_alpha_status(j);
			int k;
			if(ui != is_upper_bound(i))
			{
				Q_i = Q.get_Q(i,l);
				if(ui)
					for(k=0;k<l;k++)
						G_bar[k] -= C_i * Q_i[k];
				else
					for(k=0;k<l;k++)
						G_bar[k] += C_i * Q_i[k];
			}

			if(uj != is_upper_bound(j))
			{
				Q_j = Q.get_Q(j,l);
				if(uj)
					for(k=0;k<l;k++)
						G_bar[k] -= C_j * Q_j[k];
				else
					for(k=0;k<l;k++)
						G_bar[k] += C_j * Q_j[k];
			}
		}
	}

	// calculate rho

	si->rho = calculate_rho();

	// calculate objective value
	{
		double v = 0;
		int i;
		for(i=0;i<l;i++)
			v += alpha[i] * (G[i] + b[i]);

		si->obj = v/2;
	}

	// put back the solution
	{
		for(int i=0;i<l;i++)
			alpha_[active_set[i]] = alpha[i];
	}

	// juggle everything back
	/*{
		for(int i=0;i<l;i++)
			while(active_set[i] != i)
				swap_index(i,active_set[i]);
				// or Q.swap_index(i,active_set[i]);
	}*/

	si->upper_bound_p = Cp;
	si->upper_bound_n = Cn;

	info("\noptimization finished, #iter = %d\n",iter);

	delete[] b;
	delete[] y;
	delete[] alpha;
	delete[] alpha_status;
	delete[] active_set;
	delete[] G;
	delete[] G_bar;
}

// return 1 if already optimal, return 0 otherwise
int Solver::select_working_set(int &out_i, int &out_j)
{
	// return i,j which maximize -grad(f)^T d , under constraint
	// if alpha_i == C, d != +1
	// if alpha_i == 0, d != -1

	double Gmax1 = -INF;		// max { -grad(f)_i * d | y_i*d = +1 }
	int Gmax1_idx = -1;

	double Gmax2 = -INF;		// max { -grad(f)_i * d | y_i*d = -1 }
	int Gmax2_idx = -1;

	for(int i=0;i<active_size;i++)
	{
		if(y[i]==+1)	// y = +1
		{
			if(!is_upper_bound(i))	// d = +1
			{
				if(-G[i] > Gmax1)
				{
					Gmax1 = -G[i];
					Gmax1_idx = i;
				}
			}
			if(!is_lower_bound(i))	// d = -1
			{
				if(G[i] > Gmax2)
				{
					Gmax2 = G[i];
					Gmax2_idx = i;
				}
			}
		}
		else		// y = -1
		{
			if(!is_upper_bound(i))	// d = +1
			{
				if(-G[i] > Gmax2)
				{
					Gmax2 = -G[i];
					Gmax2_idx = i;
				}
			}
			if(!is_lower_bound(i))	// d = -1
			{
				if(G[i] > Gmax1)
				{
					Gmax1 = G[i];
					Gmax1_idx = i;
				}
			}
		}
	}

	if(Gmax1+Gmax2 < eps)
 		return 1;

	out_i = Gmax1_idx;
	out_j = Gmax2_idx;
	return 0;
}

void Solver::do_shrinking()
{
	int i,j,k;
	if(select_working_set(i,j)!=0) return;
	double Gm1 = -y[j]*G[j];
	double Gm2 = y[i]*G[i];

	// shrink
	
	for(k=0;k<active_size;k++)
	{
		if(is_lower_bound(k))
		{
			if(y[k]==+1)
			{
				if(-G[k] >= Gm1) continue;
			}
			else	if(-G[k] >= Gm2) continue;
		}
		else if(is_upper_bound(k))
		{
			if(y[k]==+1)
			{
				if(G[k] >= Gm2) continue;
			}
			else	if(G[k] >= Gm1) continue;
		}
		else continue;

		--active_size;
		swap_index(k,active_size);
		--k;	// look at the newcomer
	}

	// unshrink, check all variables again before final iterations

	if(unshrinked || -(Gm1 + Gm2) > eps*10) return;
	
	unshrinked = true;
	reconstruct_gradient();

	for(k=l-1;k>=active_size;k--)
	{
		if(is_lower_bound(k))
		{
			if(y[k]==+1)
			{
				if(-G[k] < Gm1) continue;
			}
			else	if(-G[k] < Gm2) continue;
		}
		else if(is_upper_bound(k))
		{
			if(y[k]==+1)
			{
				if(G[k] < Gm2) continue;
			}
			else	if(G[k] < Gm1) continue;
		}
		else continue;

		swap_index(k,active_size);
		active_size++;
		++k;	// look at the newcomer
	}
}

double Solver::calculate_rho()
{
	double r;
	int nr_free = 0;
	double ub = INF, lb = -INF, sum_free = 0;
	for(int i=0;i<active_size;i++)
	{
		double yG = y[i]*G[i];

		if(is_lower_bound(i))
		{
			if(y[i] > 0)
				ub = min(ub,yG);
			else
				lb = max(lb,yG);
		}
		else if(is_upper_bound(i))
		{
			if(y[i] < 0)
				ub = min(ub,yG);
			else
				lb = max(lb,yG);
		}
		else
		{
			++nr_free;
			sum_free += yG;
		}
	}

	if(nr_free>0)
		r = sum_free/nr_free;
	else
		r = (ub+lb)/2;

	return r;
}

//
// Solver for nu-svm classification and regression
//
// additional constraint: e^T \alpha = constant
//
class Solver_NU : public Solver
{
public:
	Solver_NU() {}
	void Solve(int l, const Kernel& Q, const double *b, const schar *y,
		   double *alpha, double Cp, double Cn, double eps,
		   SolutionInfo* si, int shrinking)
	{
		this->si = si;
		Solver::Solve(l,Q,b,y,alpha,Cp,Cn,eps,si,shrinking);
	}
private:
	SolutionInfo *si;
	int select_working_set(int &i, int &j);
	double calculate_rho();
	void do_shrinking();
};

int Solver_NU::select_working_set(int &out_i, int &out_j)
{
	// return i,j which maximize -grad(f)^T d , under constraint
	// if alpha_i == C, d != +1
	// if alpha_i == 0, d != -1

	double Gmax1 = -INF;	// max { -grad(f)_i * d | y_i = +1, d = +1 }
	int Gmax1_idx = -1;

	double Gmax2 = -INF;	// max { -grad(f)_i * d | y_i = +1, d = -1 }
	int Gmax2_idx = -1;

	double Gmax3 = -INF;	// max { -grad(f)_i * d | y_i = -1, d = +1 }
	int Gmax3_idx = -1;

	double Gmax4 = -INF;	// max { -grad(f)_i * d | y_i = -1, d = -1 }
	int Gmax4_idx = -1;

	for(int i=0;i<active_size;i++)
	{
		if(y[i]==+1)	// y == +1
		{
			if(!is_upper_bound(i))	// d = +1
			{
				if(-G[i] > Gmax1)
				{
					Gmax1 = -G[i];
					Gmax1_idx = i;
				}
			}
			if(!is_lower_bound(i))	// d = -1
			{
				if(G[i] > Gmax2)
				{
					Gmax2 = G[i];
					Gmax2_idx = i;
				}
			}
		}
		else		// y == -1
		{
			if(!is_upper_bound(i))	// d = +1
			{
				if(-G[i] > Gmax3)
				{
					Gmax3 = -G[i];
					Gmax3_idx = i;
				}
			}
			if(!is_lower_bound(i))	// d = -1
			{
				if(G[i] > Gmax4)
				{
					Gmax4 = G[i];
					Gmax4_idx = i;
				}
			}
		}
	}

	if(max(Gmax1+Gmax2,Gmax3+Gmax4) < eps)
 		return 1;

	if(Gmax1+Gmax2 > Gmax3+Gmax4)
	{
		out_i = Gmax1_idx;
		out_j = Gmax2_idx;
	}
	else
	{
		out_i = Gmax3_idx;
		out_j = Gmax4_idx;
	}
	return 0;
}

void Solver_NU::do_shrinking()
{
	double Gmax1 = -INF;	// max { -grad(f)_i * d | y_i = +1, d = +1 }
	double Gmax2 = -INF;	// max { -grad(f)_i * d | y_i = +1, d = -1 }
	double Gmax3 = -INF;	// max { -grad(f)_i * d | y_i = -1, d = +1 }
	double Gmax4 = -INF;	// max { -grad(f)_i * d | y_i = -1, d = -1 }

	int k;
	for(k=0;k<active_size;k++)
	{
		if(!is_upper_bound(k))
		{
			if(y[k]==+1)
			{
				if(-G[k] > Gmax1) Gmax1 = -G[k];
			}
			else	if(-G[k] > Gmax3) Gmax3 = -G[k];
		}
		if(!is_lower_bound(k))
		{
			if(y[k]==+1)
			{	
				if(G[k] > Gmax2) Gmax2 = G[k];
			}
			else	if(G[k] > Gmax4) Gmax4 = G[k];
		}
	}

	double Gm1 = -Gmax2;
	double Gm2 = -Gmax1;
	double Gm3 = -Gmax4;
	double Gm4 = -Gmax3;

	for(k=0;k<active_size;k++)
	{
		if(is_lower_bound(k))
		{
			if(y[k]==+1)
			{
				if(-G[k] >= Gm1) continue;
			}
			else	if(-G[k] >= Gm3) continue;
		}
		else if(is_upper_bound(k))
		{
			if(y[k]==+1)
			{
				if(G[k] >= Gm2) continue;
			}
			else	if(G[k] >= Gm4) continue;
		}
		else continue;

		--active_size;
		swap_index(k,active_size);
		--k;	// look at the newcomer
	}

	// unshrink, check all variables again before final iterations

	if(unshrinked || max(-(Gm1+Gm2),-(Gm3+Gm4)) > eps*10) return;
	
	unshrinked = true;
	reconstruct_gradient();

	for(k=l-1;k>=active_size;k--)
	{
		if(is_lower_bound(k))
		{
			if(y[k]==+1)
			{
				if(-G[k] < Gm1) continue;
			}
			else	if(-G[k] < Gm3) continue;
		}
		else if(is_upper_bound(k))
		{
			if(y[k]==+1)
			{
				if(G[k] < Gm2) continue;
			}
			else	if(G[k] < Gm4) continue;
		}
		else continue;

		swap_index(k,active_size);
		active_size++;
		++k;	// look at the newcomer
	}
}

double Solver_NU::calculate_rho()
{
	int nr_free1 = 0,nr_free2 = 0;
	double ub1 = INF, ub2 = INF;
	double lb1 = -INF, lb2 = -INF;
	double sum_free1 = 0, sum_free2 = 0;

	for(int i=0;i<active_size;i++)
	{
		if(y[i]==+1)
		{
			if(is_lower_bound(i))
				ub1 = min(ub1,G[i]);
			else if(is_upper_bound(i))
				lb1 = max(lb1,G[i]);
			else
			{
				++nr_free1;
				sum_free1 += G[i];
			}
		}
		else
		{
			if(is_lower_bound(i))
				ub2 = min(ub2,G[i]);
			else if(is_upper_bound(i))
				lb2 = max(lb2,G[i]);
			else
			{
				++nr_free2;
				sum_free2 += G[i];
			}
		}
	}

	double r1,r2;
	if(nr_free1 > 0)
		r1 = sum_free1/nr_free1;
	else
		r1 = (ub1+lb1)/2;
	
	if(nr_free2 > 0)
		r2 = sum_free2/nr_free2;
	else
		r2 = (ub2+lb2)/2;
	
	si->r = (r1+r2)/2;
	return (r1-r2)/2;
}

//
// Q matrices for various formulations
//
class SVC_Q: public Kernel
{ 
public:
	SVC_Q(const svm_problem& prob, const svm_parameter& param, const schar *y_)
	:Kernel(prob.l, prob.x, param)
	{
		clone(y,y_,prob.l);
		this->kernel_type = param.kernel_type;
		cache = new Cache(prob.l,(int)(param.cache_size*(1<<20)));
	}
	
	Qfloat *get_Q(int i, int len) const
	{
		Qfloat *data;
		int start;
		if((start = cache->get_data(i,&data,len)) < len)
		{
			if( kernel_type== MATRIX)
			{
				for(int j=start;j<len;j++)                                          	
                        		data[j] = (Qfloat)(y[i]*y[j]*(x[i][(int)(x[j][0].value)].value));
			}
			else
			{
				for(int j=start;j<len;j++)
					data[j] = (Qfloat)(y[i]*y[j]*(this->*kernel_function)(i,j));
			}
		}
		return data;
	}

	void swap_index(int i, int j) const
	{
		cache->swap_index(i,j);
		Kernel::swap_index(i,j);
		swap(y[i],y[j]);
	}

	~SVC_Q()
	{
		delete[] y;
		delete cache;
	}
private:
	schar *y;
	Cache *cache;
	int kernel_type;
};

class ONE_CLASS_Q: public Kernel
{
public:
	ONE_CLASS_Q(const svm_problem& prob, const svm_parameter& param)
	:Kernel(prob.l, prob.x, param)
	{
		this->kernel_type = param.kernel_type;	
		cache = new Cache(prob.l,(int)(param.cache_size*(1<<20)));
	}
	
	Qfloat *get_Q(int i, int len) const
	{
		Qfloat *data;
		int start;
		if((start = cache->get_data(i,&data,len)) < len)
		{
			if( kernel_type== MATRIX)
			{
				for(int j=start;j<len;j++)
                        		data[j] = (Qfloat)((x[i][(int)(x[j][0].value)].value));
			}                                                                                			
			else
			{                                                                                			
				for(int j=start;j<len;j++)
					data[j] = (Qfloat)(this->*kernel_function)(i,j);
			}
		}
		return data;
	}

	void swap_index(int i, int j) const
	{
		cache->swap_index(i,j);
		Kernel::swap_index(i,j);
	}

	~ONE_CLASS_Q()
	{
		delete cache;
	}
private:
	Cache *cache;
	int kernel_type;
};

class SVR_Q: public Kernel
{ 
public:
	SVR_Q(const svm_problem& prob, const svm_parameter& param)
	:Kernel(prob.l, prob.x, param)
	{
		l = prob.l;