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2837 lines (2502 loc) · 54.8 KB
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#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdarg.h>
#include <locale.h>
#include "linear.h"
#include "tron.h"
typedef signed char schar;
template <class T> static inline void swap(T& x, T& y) { T t=x; x=y; y=t; }
#ifndef min
template <class T> static inline T min(T x,T y) { return (x<y)?x:y; }
#endif
#ifndef max
template <class T> static inline T max(T x,T y) { return (x>y)?x:y; }
#endif
template <class S, class T> static inline void clone(T*& dst, S* src, int n)
{
dst = new T[n];
memcpy((void *)dst,(void *)src,sizeof(T)*n);
}
#define Malloc(type,n) (type *)malloc((n)*sizeof(type))
#define INF HUGE_VAL
static void print_string_stdout(const char *s)
{
fputs(s,stdout);
fflush(stdout);
}
static void (*liblinear_print_string) (const char *) = &print_string_stdout;
#if 1
static void info(const char *fmt,...)
{
char buf[BUFSIZ];
va_list ap;
va_start(ap,fmt);
vsprintf(buf,fmt,ap);
va_end(ap);
(*liblinear_print_string)(buf);
}
#else
static void info(const char *fmt,...) {}
#endif
class l2r_lr_fun: public function
{
public:
l2r_lr_fun(const problem *prob, double *C);
~l2r_lr_fun();
double fun(double *w);
void grad(double *w, double *g);
void Hv(double *s, double *Hs);
int get_nr_variable(void);
private:
void Xv(double *v, double *Xv);
void XTv(double *v, double *XTv);
double *C;
double *z;
double *D;
const problem *prob;
};
l2r_lr_fun::l2r_lr_fun(const problem *prob, double *C)
{
int l=prob->l;
this->prob = prob;
z = new double[l];
D = new double[l];
this->C = C;
}
l2r_lr_fun::~l2r_lr_fun()
{
delete[] z;
delete[] D;
}
double l2r_lr_fun::fun(double *w)
{
int i;
double f=0;
double *y=prob->y;
int l=prob->l;
int w_size=get_nr_variable();
Xv(w, z);
for(i=0;i<w_size;i++)
f += w[i]*w[i];
f /= 2.0;
for(i=0;i<l;i++)
{
double yz = y[i]*z[i];
if (yz >= 0)
f += C[i]*log(1 + exp(-yz));
else
f += C[i]*(-yz+log(1 + exp(yz)));
}
return(f);
}
void l2r_lr_fun::grad(double *w, double *g)
{
int i;
double *y=prob->y;
int l=prob->l;
int w_size=get_nr_variable();
for(i=0;i<l;i++)
{
z[i] = 1/(1 + exp(-y[i]*z[i]));
D[i] = z[i]*(1-z[i]);
z[i] = C[i]*(z[i]-1)*y[i];
}
XTv(z, g);
for(i=0;i<w_size;i++)
g[i] = w[i] + g[i];
}
int l2r_lr_fun::get_nr_variable(void)
{
return prob->n;
}
void l2r_lr_fun::Hv(double *s, double *Hs)
{
int i;
int l=prob->l;
int w_size=get_nr_variable();
double *wa = new double[l];
Xv(s, wa);
for(i=0;i<l;i++)
wa[i] = C[i]*D[i]*wa[i];
XTv(wa, Hs);
for(i=0;i<w_size;i++)
Hs[i] = s[i] + Hs[i];
delete[] wa;
}
void l2r_lr_fun::Xv(double *v, double *Xv)
{
int i;
int l=prob->l;
feature_node **x=prob->x;
for(i=0;i<l;i++)
{
feature_node *s=x[i];
Xv[i]=0;
while(s->index!=-1)
{
Xv[i]+=v[s->index-1]*s->value;
s++;
}
}
}
void l2r_lr_fun::XTv(double *v, double *XTv)
{
int i;
int l=prob->l;
int w_size=get_nr_variable();
feature_node **x=prob->x;
for(i=0;i<w_size;i++)
XTv[i]=0;
for(i=0;i<l;i++)
{
feature_node *s=x[i];
while(s->index!=-1)
{
XTv[s->index-1]+=v[i]*s->value;
s++;
}
}
}
class l2r_l2_svc_fun: public function
{
public:
l2r_l2_svc_fun(const problem *prob, double *C);
~l2r_l2_svc_fun();
double fun(double *w);
void grad(double *w, double *g);
void Hv(double *s, double *Hs);
int get_nr_variable(void);
protected:
void Xv(double *v, double *Xv);
void subXv(double *v, double *Xv);
void subXTv(double *v, double *XTv);
double *C;
double *z;
double *D;
int *I;
int sizeI;
const problem *prob;
};
l2r_l2_svc_fun::l2r_l2_svc_fun(const problem *prob, double *C)
{
int l=prob->l;
this->prob = prob;
z = new double[l];
D = new double[l];
I = new int[l];
this->C = C;
}
l2r_l2_svc_fun::~l2r_l2_svc_fun()
{
delete[] z;
delete[] D;
delete[] I;
}
double l2r_l2_svc_fun::fun(double *w)
{
int i;
double f=0;
double *y=prob->y;
int l=prob->l;
int w_size=get_nr_variable();
Xv(w, z);
for(i=0;i<w_size;i++)
f += w[i]*w[i];
f /= 2.0;
for(i=0;i<l;i++)
{
z[i] = y[i]*z[i];
double d = 1-z[i];
if (d > 0)
f += C[i]*d*d;
}
return(f);
}
void l2r_l2_svc_fun::grad(double *w, double *g)
{
int i;
double *y=prob->y;
int l=prob->l;
int w_size=get_nr_variable();
sizeI = 0;
for (i=0;i<l;i++)
if (z[i] < 1)
{
z[sizeI] = C[i]*y[i]*(z[i]-1);
I[sizeI] = i;
sizeI++;
}
subXTv(z, g);
for(i=0;i<w_size;i++)
g[i] = w[i] + 2*g[i];
}
int l2r_l2_svc_fun::get_nr_variable(void)
{
return prob->n;
}
void l2r_l2_svc_fun::Hv(double *s, double *Hs)
{
int i;
int w_size=get_nr_variable();
double *wa = new double[sizeI];
subXv(s, wa);
for(i=0;i<sizeI;i++)
wa[i] = C[I[i]]*wa[i];
subXTv(wa, Hs);
for(i=0;i<w_size;i++)
Hs[i] = s[i] + 2*Hs[i];
delete[] wa;
}
void l2r_l2_svc_fun::Xv(double *v, double *Xv)
{
int i;
int l=prob->l;
feature_node **x=prob->x;
for(i=0;i<l;i++)
{
feature_node *s=x[i];
Xv[i]=0;
while(s->index!=-1)
{
Xv[i]+=v[s->index-1]*s->value;
s++;
}
}
}
void l2r_l2_svc_fun::subXv(double *v, double *Xv)
{
int i;
feature_node **x=prob->x;
for(i=0;i<sizeI;i++)
{
feature_node *s=x[I[i]];
Xv[i]=0;
while(s->index!=-1)
{
Xv[i]+=v[s->index-1]*s->value;
s++;
}
}
}
void l2r_l2_svc_fun::subXTv(double *v, double *XTv)
{
int i;
int w_size=get_nr_variable();
feature_node **x=prob->x;
for(i=0;i<w_size;i++)
XTv[i]=0;
for(i=0;i<sizeI;i++)
{
feature_node *s=x[I[i]];
while(s->index!=-1)
{
XTv[s->index-1]+=v[i]*s->value;
s++;
}
}
}
class l2r_l2_svr_fun: public l2r_l2_svc_fun
{
public:
l2r_l2_svr_fun(const problem *prob, double *C, double p);
double fun(double *w);
void grad(double *w, double *g);
private:
double p;
};
l2r_l2_svr_fun::l2r_l2_svr_fun(const problem *prob, double *C, double p):
l2r_l2_svc_fun(prob, C)
{
this->p = p;
}
double l2r_l2_svr_fun::fun(double *w)
{
int i;
double f=0;
double *y=prob->y;
int l=prob->l;
int w_size=get_nr_variable();
double d;
Xv(w, z);
for(i=0;i<w_size;i++)
f += w[i]*w[i];
f /= 2;
for(i=0;i<l;i++)
{
d = z[i] - y[i];
if(d < -p)
f += C[i]*(d+p)*(d+p);
else if(d > p)
f += C[i]*(d-p)*(d-p);
}
return(f);
}
void l2r_l2_svr_fun::grad(double *w, double *g)
{
int i;
double *y=prob->y;
int l=prob->l;
int w_size=get_nr_variable();
double d;
sizeI = 0;
for(i=0;i<l;i++)
{
d = z[i] - y[i];
// generate index set I
if(d < -p)
{
z[sizeI] = C[i]*(d+p);
I[sizeI] = i;
sizeI++;
}
else if(d > p)
{
z[sizeI] = C[i]*(d-p);
I[sizeI] = i;
sizeI++;
}
}
subXTv(z, g);
for(i=0;i<w_size;i++)
g[i] = w[i] + 2*g[i];
}
// A coordinate descent algorithm for
// multi-class support vector machines by Crammer and Singer
//
// min_{\alpha} 0.5 \sum_m ||w_m(\alpha)||^2 + \sum_i \sum_m e^m_i alpha^m_i
// s.t. \alpha^m_i <= C^m_i \forall m,i , \sum_m \alpha^m_i=0 \forall i
//
// where e^m_i = 0 if y_i = m,
// e^m_i = 1 if y_i != m,
// C^m_i = C if m = y_i,
// C^m_i = 0 if m != y_i,
// and w_m(\alpha) = \sum_i \alpha^m_i x_i
//
// Given:
// x, y, C
// eps is the stopping tolerance
//
// solution will be put in w
//
// See Appendix of LIBLINEAR paper, Fan et al. (2008)
#define GETI(i) ((int) prob->y[i])
// To support weights for instances, use GETI(i) (i)
class Solver_MCSVM_CS
{
public:
Solver_MCSVM_CS(const problem *prob, int nr_class, double *C, double eps=0.1, int max_iter=100000);
~Solver_MCSVM_CS();
void Solve(double *w);
private:
void solve_sub_problem(double A_i, int yi, double C_yi, int active_i, double *alpha_new);
bool be_shrunk(int i, int m, int yi, double alpha_i, double minG);
double *B, *C, *G;
int w_size, l;
int nr_class;
int max_iter;
double eps;
const problem *prob;
};
Solver_MCSVM_CS::Solver_MCSVM_CS(const problem *prob, int nr_class, double *weighted_C, double eps, int max_iter)
{
this->w_size = prob->n;
this->l = prob->l;
this->nr_class = nr_class;
this->eps = eps;
this->max_iter = max_iter;
this->prob = prob;
this->B = new double[nr_class];
this->G = new double[nr_class];
this->C = weighted_C;
}
Solver_MCSVM_CS::~Solver_MCSVM_CS()
{
delete[] B;
delete[] G;
}
int compare_double(const void *a, const void *b)
{
if(*(double *)a > *(double *)b)
return -1;
if(*(double *)a < *(double *)b)
return 1;
return 0;
}
void Solver_MCSVM_CS::solve_sub_problem(double A_i, int yi, double C_yi, int active_i, double *alpha_new)
{
int r;
double *D;
clone(D, B, active_i);
if(yi < active_i)
D[yi] += A_i*C_yi;
qsort(D, active_i, sizeof(double), compare_double);
double beta = D[0] - A_i*C_yi;
for(r=1;r<active_i && beta<r*D[r];r++)
beta += D[r];
beta /= r;
for(r=0;r<active_i;r++)
{
if(r == yi)
alpha_new[r] = min(C_yi, (beta-B[r])/A_i);
else
alpha_new[r] = min((double)0, (beta - B[r])/A_i);
}
delete[] D;
}
bool Solver_MCSVM_CS::be_shrunk(int i, int m, int yi, double alpha_i, double minG)
{
double bound = 0;
if(m == yi)
bound = C[GETI(i)];
if(alpha_i == bound && G[m] < minG)
return true;
return false;
}
void Solver_MCSVM_CS::Solve(double *w)
{
int i, m, s;
int iter = 0;
double *alpha = new double[l*nr_class];
double *alpha_new = new double[nr_class];
int *index = new int[l];
double *QD = new double[l];
int *d_ind = new int[nr_class];
double *d_val = new double[nr_class];
int *alpha_index = new int[nr_class*l];
int *y_index = new int[l];
int active_size = l;
int *active_size_i = new int[l];
double eps_shrink = max(10.0*eps, 1.0); // stopping tolerance for shrinking
bool start_from_all = true;
// Initial alpha can be set here. Note that
// sum_m alpha[i*nr_class+m] = 0, for all i=1,...,l-1
// alpha[i*nr_class+m] <= C[GETI(i)] if prob->y[i] == m
// alpha[i*nr_class+m] <= 0 if prob->y[i] != m
// If initial alpha isn't zero, uncomment the for loop below to initialize w
for(i=0;i<l*nr_class;i++)
alpha[i] = 0;
for(i=0;i<w_size*nr_class;i++)
w[i] = 0;
for(i=0;i<l;i++)
{
for(m=0;m<nr_class;m++)
alpha_index[i*nr_class+m] = m;
feature_node *xi = prob->x[i];
QD[i] = 0;
while(xi->index != -1)
{
double val = xi->value;
QD[i] += val*val;
// Uncomment the for loop if initial alpha isn't zero
// for(m=0; m<nr_class; m++)
// w[(xi->index-1)*nr_class+m] += alpha[i*nr_class+m]*val;
xi++;
}
active_size_i[i] = nr_class;
y_index[i] = (int)prob->y[i];
index[i] = i;
}
while(iter < max_iter)
{
double stopping = -INF;
for(i=0;i<active_size;i++)
{
int j = i+rand()%(active_size-i);
swap(index[i], index[j]);
}
for(s=0;s<active_size;s++)
{
i = index[s];
double Ai = QD[i];
double *alpha_i = &alpha[i*nr_class];
int *alpha_index_i = &alpha_index[i*nr_class];
if(Ai > 0)
{
for(m=0;m<active_size_i[i];m++)
G[m] = 1;
if(y_index[i] < active_size_i[i])
G[y_index[i]] = 0;
feature_node *xi = prob->x[i];
while(xi->index!= -1)
{
double *w_i = &w[(xi->index-1)*nr_class];
for(m=0;m<active_size_i[i];m++)
G[m] += w_i[alpha_index_i[m]]*(xi->value);
xi++;
}
double minG = INF;
double maxG = -INF;
for(m=0;m<active_size_i[i];m++)
{
if(alpha_i[alpha_index_i[m]] < 0 && G[m] < minG)
minG = G[m];
if(G[m] > maxG)
maxG = G[m];
}
if(y_index[i] < active_size_i[i])
if(alpha_i[(int) prob->y[i]] < C[GETI(i)] && G[y_index[i]] < minG)
minG = G[y_index[i]];
for(m=0;m<active_size_i[i];m++)
{
if(be_shrunk(i, m, y_index[i], alpha_i[alpha_index_i[m]], minG))
{
active_size_i[i]--;
while(active_size_i[i]>m)
{
if(!be_shrunk(i, active_size_i[i], y_index[i],
alpha_i[alpha_index_i[active_size_i[i]]], minG))
{
swap(alpha_index_i[m], alpha_index_i[active_size_i[i]]);
swap(G[m], G[active_size_i[i]]);
if(y_index[i] == active_size_i[i])
y_index[i] = m;
else if(y_index[i] == m)
y_index[i] = active_size_i[i];
break;
}
active_size_i[i]--;
}
}
}
if(active_size_i[i] <= 1)
{
active_size--;
swap(index[s], index[active_size]);
s--;
continue;
}
if(maxG-minG <= 1e-12)
continue;
else
stopping = max(maxG - minG, stopping);
for(m=0;m<active_size_i[i];m++)
B[m] = G[m] - Ai*alpha_i[alpha_index_i[m]] ;
solve_sub_problem(Ai, y_index[i], C[GETI(i)], active_size_i[i], alpha_new);
int nz_d = 0;
for(m=0;m<active_size_i[i];m++)
{
double d = alpha_new[m] - alpha_i[alpha_index_i[m]];
alpha_i[alpha_index_i[m]] = alpha_new[m];
if(fabs(d) >= 1e-12)
{
d_ind[nz_d] = alpha_index_i[m];
d_val[nz_d] = d;
nz_d++;
}
}
xi = prob->x[i];
while(xi->index != -1)
{
double *w_i = &w[(xi->index-1)*nr_class];
for(m=0;m<nz_d;m++)
w_i[d_ind[m]] += d_val[m]*xi->value;
xi++;
}
}
}
iter++;
if(iter % 10 == 0)
{
info(".");
}
if(stopping < eps_shrink)
{
if(stopping < eps && start_from_all == true)
break;
else
{
active_size = l;
for(i=0;i<l;i++)
active_size_i[i] = nr_class;
info("*");
eps_shrink = max(eps_shrink/2, eps);
start_from_all = true;
}
}
else
start_from_all = false;
}
info("\noptimization finished, #iter = %d\n",iter);
if (iter >= max_iter)
info("\nWARNING: reaching max number of iterations\n");
// calculate objective value
double v = 0;
int nSV = 0;
for(i=0;i<w_size*nr_class;i++)
v += w[i]*w[i];
v = 0.5*v;
for(i=0;i<l*nr_class;i++)
{
v += alpha[i];
if(fabs(alpha[i]) > 0)
nSV++;
}
for(i=0;i<l;i++)
v -= alpha[i*nr_class+(int)prob->y[i]];
info("Objective value = %lf\n",v);
info("nSV = %d\n",nSV);
delete [] alpha;
delete [] alpha_new;
delete [] index;
delete [] QD;
delete [] d_ind;
delete [] d_val;
delete [] alpha_index;
delete [] y_index;
delete [] active_size_i;
}
// A coordinate descent algorithm for
// L1-loss and L2-loss SVM dual problems
//
// min_\alpha 0.5(\alpha^T (Q + D)\alpha) - e^T \alpha,
// s.t. 0 <= \alpha_i <= upper_bound_i,
//
// where Qij = yi yj xi^T xj and
// D is a diagonal matrix
//
// In L1-SVM case:
// upper_bound_i = Cp if y_i = 1
// upper_bound_i = Cn if y_i = -1
// D_ii = 0
// In L2-SVM case:
// upper_bound_i = INF
// D_ii = 1/(2*Cp) if y_i = 1
// D_ii = 1/(2*Cn) if y_i = -1
//
// Given:
// x, y, Cp, Cn
// eps is the stopping tolerance
//
// solution will be put in w
//
// See Algorithm 3 of Hsieh et al., ICML 2008
#undef GETI
#define GETI(i) (y[i]+1)
// To support weights for instances, use GETI(i) (i)
static void solve_l2r_l1l2_svc(
const problem *prob, double *w, double eps,
double Cp, double Cn, int solver_type)
{
int l = prob->l;
int w_size = prob->n;
int i, s, iter = 0;
double C, d, G;
double *QD = new double[l];
int max_iter = 1000;
int *index = new int[l];
double *alpha = new double[l];
schar *y = new schar[l];
int active_size = l;
// PG: projected gradient, for shrinking and stopping
double PG;
double PGmax_old = INF;
double PGmin_old = -INF;
double PGmax_new, PGmin_new;
// default solver_type: L2R_L2LOSS_SVC_DUAL
double diag[3] = {0.5/Cn, 0, 0.5/Cp};
double upper_bound[3] = {INF, 0, INF};
if(solver_type == L2R_L1LOSS_SVC_DUAL)
{
diag[0] = 0;
diag[2] = 0;
upper_bound[0] = Cn;
upper_bound[2] = Cp;
}
for(i=0; i<l; i++)
{
if(prob->y[i] > 0)
{
y[i] = +1;
}
else
{
y[i] = -1;
}
}
// Initial alpha can be set here. Note that
// 0 <= alpha[i] <= upper_bound[GETI(i)]
for(i=0; i<l; i++)
alpha[i] = 0;
for(i=0; i<w_size; i++)
w[i] = 0;
for(i=0; i<l; i++)
{
QD[i] = diag[GETI(i)];
feature_node *xi = prob->x[i];
while (xi->index != -1)
{
double val = xi->value;
QD[i] += val*val;
w[xi->index-1] += y[i]*alpha[i]*val;
xi++;
}
index[i] = i;
}
while (iter < max_iter)
{
PGmax_new = -INF;
PGmin_new = INF;
for (i=0; i<active_size; i++)
{
int j = i+rand()%(active_size-i);
swap(index[i], index[j]);
}
for (s=0; s<active_size; s++)
{
i = index[s];
G = 0;
schar yi = y[i];
feature_node *xi = prob->x[i];
while(xi->index!= -1)
{
G += w[xi->index-1]*(xi->value);
xi++;
}
G = G*yi-1;
C = upper_bound[GETI(i)];
G += alpha[i]*diag[GETI(i)];
PG = 0;
if (alpha[i] == 0)
{
if (G > PGmax_old)
{
active_size--;
swap(index[s], index[active_size]);
s--;
continue;
}
else if (G < 0)
PG = G;
}
else if (alpha[i] == C)
{
if (G < PGmin_old)
{
active_size--;
swap(index[s], index[active_size]);
s--;
continue;
}
else if (G > 0)
PG = G;
}
else
PG = G;
PGmax_new = max(PGmax_new, PG);
PGmin_new = min(PGmin_new, PG);
if(fabs(PG) > 1.0e-12)
{
double alpha_old = alpha[i];
alpha[i] = min(max(alpha[i] - G/QD[i], 0.0), C);
d = (alpha[i] - alpha_old)*yi;
xi = prob->x[i];
while (xi->index != -1)
{
w[xi->index-1] += d*xi->value;
xi++;
}
}
}
iter++;
if(iter % 10 == 0)
info(".");
if(PGmax_new - PGmin_new <= eps)
{
if(active_size == l)
break;
else
{
active_size = l;
info("*");
PGmax_old = INF;
PGmin_old = -INF;
continue;
}
}
PGmax_old = PGmax_new;
PGmin_old = PGmin_new;
if (PGmax_old <= 0)
PGmax_old = INF;
if (PGmin_old >= 0)
PGmin_old = -INF;
}
info("\noptimization finished, #iter = %d\n",iter);
if (iter >= max_iter)
info("\nWARNING: reaching max number of iterations\nUsing -s 2 may be faster (also see FAQ)\n\n");
// calculate objective value
double v = 0;
int nSV = 0;
for(i=0; i<w_size; i++)
v += w[i]*w[i];
for(i=0; i<l; i++)
{
v += alpha[i]*(alpha[i]*diag[GETI(i)] - 2);
if(alpha[i] > 0)
++nSV;
}
info("Objective value = %lf\n",v/2);
info("nSV = %d\n",nSV);
delete [] QD;
delete [] alpha;
delete [] y;
delete [] index;
}
// A coordinate descent algorithm for
// L1-loss and L2-loss epsilon-SVR dual problem
//
// min_\beta 0.5\beta^T (Q + diag(lambda)) \beta - p \sum_{i=1}^l|\beta_i| + \sum_{i=1}^l yi\beta_i,
// s.t. -upper_bound_i <= \beta_i <= upper_bound_i,
//
// where Qij = xi^T xj and
// D is a diagonal matrix
//
// In L1-SVM case:
// upper_bound_i = C
// lambda_i = 0
// In L2-SVM case:
// upper_bound_i = INF
// lambda_i = 1/(2*C)
//
// Given:
// x, y, p, C
// eps is the stopping tolerance
//
// solution will be put in w
//
// See Algorithm 4 of Ho and Lin, 2012
#undef GETI
#define GETI(i) (0)
// To support weights for instances, use GETI(i) (i)
static void solve_l2r_l1l2_svr(
const problem *prob, double *w, const parameter *param,
int solver_type)
{
int l = prob->l;