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#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <ctype.h>
#include <float.h>
#include <string.h>
#include <stdarg.h>
#include "svm.h"
int libsvm_version = LIBSVM_VERSION;
typedef double Qfloat;
typedef signed char schar;
#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 T> static inline void swap(T& x, T& y) { T t=x; x=y; y=t; }
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);
}
static inline double powi(double base, int times)
{
double tmp = base, ret = 1.0;
for(int t=times; t>0; t/=2)
{
if(t%2==1) ret*=tmp;
tmp = tmp * tmp;
}
return ret;
}
#define INF HUGE_VAL
#define TAU 1e-12
#define Malloc(type,n) (type *)malloc((n)*sizeof(type))
static void print_string_stdout(const char *s)
{
fputs(s,stdout);
fflush(stdout);
}
void (*svm_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);
(*svm_print_string)(buf);
}
#else
static void info(const char *fmt,...) {}
#endif
//
// Kernel Cache
//
// l is the number of total data items
// size is the cache size limit in bytes
//
class Cache
{
public:
Cache(int l,long int size);
~Cache();
// request data [0,len)
// return some position p where [p,len) need to be filled
// (p >= len if nothing needs to be filled)
int get_data(const int index, Qfloat **data, int len);
void swap_index(int i, int j);
private:
int l;
long int size;
struct head_t
{
head_t *prev, *next; // a circular list
Qfloat *data;
int len; // data[0,len) is cached in this entry
};
head_t *head;
head_t lru_head;
void lru_delete(head_t *h);
void lru_insert(head_t *h);
};
Cache::Cache(int l_,long int size_):l(l_),size(size_)
{
head = (head_t *)calloc(l,sizeof(head_t)); // initialized to 0
size /= sizeof(Qfloat);
size -= l * sizeof(head_t) / sizeof(Qfloat);
size = max(size, 2 * (long int) l); // cache must be large enough for two columns
lru_head.next = lru_head.prev = &lru_head;
}
Cache::~Cache()
{
for(head_t *h = lru_head.next; h != &lru_head; h=h->next)
free(h->data);
free(head);
}
void Cache::lru_delete(head_t *h)
{
// delete from current location
h->prev->next = h->next;
h->next->prev = h->prev;
}
void Cache::lru_insert(head_t *h)
{
// insert to last position
h->next = &lru_head;
h->prev = lru_head.prev;
h->prev->next = h;
h->next->prev = h;
}
int Cache::get_data(const int index, Qfloat **data, int len)
{
head_t *h = &head[index];
if(h->len) lru_delete(h);
int more = len - h->len;
if(more > 0)
{
// free old space
while(size < more)
{
head_t *old = lru_head.next;
lru_delete(old);
free(old->data);
size += old->len;
old->data = 0;
old->len = 0;
}
// allocate new space
h->data = (Qfloat *)realloc(h->data,sizeof(Qfloat)*len);
size -= more;
swap(h->len,len);
}
lru_insert(h);
*data = h->data;
return len;
}
void Cache::swap_index(int i, int j)
{
if(i==j) return;
if(head[i].len) lru_delete(&head[i]);
if(head[j].len) lru_delete(&head[j]);
swap(head[i].data,head[j].data);
swap(head[i].len,head[j].len);
if(head[i].len) lru_insert(&head[i]);
if(head[j].len) lru_insert(&head[j]);
if(i>j) swap(i,j);
for(head_t *h = lru_head.next; h!=&lru_head; h=h->next)
{
if(h->len > i)
{
if(h->len > j)
swap(h->data[i],h->data[j]);
else
{
// give up
lru_delete(h);
free(h->data);
size += h->len;
h->data = 0;
h->len = 0;
}
}
}
}
//
// Kernel evaluation
//
// the static method k_function is for doing single kernel evaluation
// the constructor of Kernel prepares to calculate the l*l kernel matrix
// the member function get_Q is for getting one column from the Q Matrix
//
class QMatrix {
public:
virtual Qfloat *get_Q(int column, int len) const = 0;
virtual Qfloat *get_QD() const = 0;
virtual void swap_index(int i, int j) const = 0;
virtual ~QMatrix() {}
};
class Kernel: public QMatrix {
public:
Kernel(int l, svm_node * const * x, const svm_parameter& param);
virtual ~Kernel();
static double k_function(const svm_node *x, const svm_node *y,
const svm_parameter& param);
virtual Qfloat *get_Q(int column, int len) const = 0;
virtual Qfloat *get_QD() const = 0;
virtual void swap_index(int i, int j) const // no so const...
{
swap(x[i],x[j]);
if(x_square) swap(x_square[i],x_square[j]);
}
protected:
double (Kernel::*kernel_function)(int i, int j) const;
private:
const svm_node **x;
double *x_square;
// svm_parameter
const int kernel_type;
const int degree;
const double gamma;
const double coef0;
static double dot(const svm_node *px, const svm_node *py);
static double dist_1(const svm_node * px, const svm_node * py);
static double dist_2_sqr(const svm_node * px, const svm_node * py);
inline double dist_2_sqr(int i, int j) const
{
double sum = x_square[i]+x_square[j]-2*dot(x[i],x[j]);
return (sum > 0.0 ? sum : 0.0);
}
double kernel_linear(int i, int j) const
{
return dot(x[i],x[j]);
}
double kernel_poly(int i, int j) const
{
return powi(gamma*dot(x[i],x[j])+coef0,degree);
}
double kernel_rbf(int i, int j) const
{
return exp(-gamma*dist_2_sqr(i, j));
}
double kernel_sigmoid(int i, int j) const
{
return tanh(gamma*dot(x[i],x[j])+coef0);
}
double kernel_stump(int i, int j) const
{
return -dist_1(x[i], x[j]) + coef0;
}
double kernel_perc(int i, int j) const
{
return -sqrt(dist_2_sqr(i, j))+coef0;
}
double kernel_laplace(int i, int j) const
{
return exp(-gamma*dist_1(x[i], x[j]));
}
double kernel_expo(int i, int j) const
{
return exp(-gamma*sqrt(dist_2_sqr(i, j)));
}
double kernel_precomputed(int i, int j) const
{
return x[i][(int)(x[j][0].value)].value;
}
};
Kernel::Kernel(int l, svm_node * const * x_, const svm_parameter& param)
:kernel_type(param.kernel_type), degree(param.degree),
gamma(param.gamma), coef0(param.coef0)
{
switch(kernel_type)
{
case LINEAR:
kernel_function = &Kernel::kernel_linear;
break;
case POLY:
kernel_function = &Kernel::kernel_poly;
break;
case GAUSSIAN:
kernel_function = &Kernel::kernel_rbf;
break;
case SIGMOID:
kernel_function = &Kernel::kernel_sigmoid;
break;
case STUMP:
kernel_function = &Kernel::kernel_stump;
break;
case PERC:
kernel_function = &Kernel::kernel_perc;
break;
case LAPLACE:
kernel_function = &Kernel::kernel_laplace;
break;
case EXPO:
kernel_function = &Kernel::kernel_expo;
break;
case PRECOMPUTED:
kernel_function = &Kernel::kernel_precomputed;
break;
}
clone(x,x_,l);
if(kernel_type == GAUSSIAN || kernel_type == PERC || kernel_type == EXPO)
{
x_square = new double[l];
for(int i=0;i<l;i++)
x_square[i] = dot(x[i],x[i]);
}
else
x_square = 0;
}
Kernel::~Kernel()
{
delete[] x;
delete[] x_square;
}
double Kernel::dot(const svm_node *px, const svm_node *py)
{
double sum = 0;
while(px->index != -1 && py->index != -1)
{
if(px->index == py->index)
{
sum += px->value * py->value;
++px;
++py;
}
else
{
if(px->index > py->index)
++py;
else
++px;
}
}
return sum;
}
double Kernel::dist_1(const svm_node * px, const svm_node * py)
{
double sum = 0;
while(px->index != -1 && py->index != -1)
{
if(px->index == py->index)
{
sum += fabs(px->value - py->value);
++px;
++py;
}
else
{
if(px->index > py->index)
{
sum += fabs(py->value);
++py;
}
else
{
sum += fabs(px->value);
++px;
}
}
}
while(px->index != -1)
{
sum += fabs(px->value);
++px;
}
while (py->index != -1)
{
sum += fabs (py->value);
++py;
}
return sum;
}
double Kernel::dist_2_sqr(const svm_node * px, const svm_node * py)
{
double sum = 0;
while(px->index != -1 && py->index != -1)
{
if(px->index == py->index)
{
double d = px->value - py->value;
sum += d * d;
++px;
++py;
}
else
{
if(px->index > py->index)
{
sum += py->value * py->value;
++py;
}
else
{
sum += px->value * px->value;
++px;
}
}
}
while(px->index != -1)
{
sum += px->value * px->value;
++px;
}
while (py->index != -1)
{
sum += py->value * py->value;
++py;
}
return (sum > 0.0 ? sum : 0.0);
}
double Kernel::k_function(const svm_node *x, const svm_node *y,
const svm_parameter& param)
{
switch(param.kernel_type)
{
case LINEAR:
return dot(x,y);
case POLY:
return powi(param.gamma*dot(x,y)+param.coef0,param.degree);
case GAUSSIAN:
return exp(-param.gamma*dist_2_sqr(x, y));
case SIGMOID:
return tanh(param.gamma*dot(x,y)+param.coef0);
case STUMP:
return -dist_1(x, y) + param.coef0;
case PERC:
return -sqrt(dist_2_sqr(x, y)) + param.coef0;
case LAPLACE:
return exp(-param.gamma*dist_1(x, y));
case EXPO:
return exp(-param.gamma*sqrt(dist_2_sqr(x, y)));
case PRECOMPUTED: //x: test (validation), y: SV
return x[(int)(y->value)].value;
default:
return 0; // Unreachable
}
}
// An SMO algorithm in Fan et al., JMLR 6(2005), p. 1889--1918
// Solves:
//
// min 0.5(\alpha^T Q \alpha) + p^T \alpha
//
// y^T \alpha = \delta
// y_i = +1 or -1
// 0 <= alpha_i <= Cp for y_i = 1
// 0 <= alpha_i <= Cn for y_i = -1
//
// Given:
//
// Q, p, y, Cp, Cn, and an initial feasible point \alpha
// l is the size of vectors and matrices
// eps is the stopping tolerance
//
// solution will be put in \alpha, objective value will be put in obj
//
class Solver {
public:
Solver() {};
virtual ~Solver() {};
struct SolutionInfo {
double obj;
double rho;
double upper_bound_p;
double upper_bound_n;
double r; // for Solver_NU
};
void Solve(int l, const QMatrix& Q, const double *p_, const schar *y_,
double *alpha_, double Cp, double Cn, double eps,
SolutionInfo* si, int shrinking);
protected:
int active_size;
schar *y;
double *G; // gradient of objective function
enum { LOWER_BOUND, UPPER_BOUND, FREE };
char *alpha_status; // LOWER_BOUND, UPPER_BOUND, FREE
double *alpha;
const QMatrix *Q;
const Qfloat *QD;
double eps;
double Cp,Cn;
double *p;
int *active_set;
double *G_bar; // gradient, if we treat free variables as 0
int l;
bool unshrink; // XXX
double get_C(int i)
{
return (y[i] > 0)? Cp : Cn;
}
void update_alpha_status(int i)
{
if(alpha[i] >= get_C(i))
alpha_status[i] = UPPER_BOUND;
else if(alpha[i] <= 0)
alpha_status[i] = LOWER_BOUND;
else alpha_status[i] = FREE;
}
bool is_upper_bound(int i) { return alpha_status[i] == UPPER_BOUND; }
bool is_lower_bound(int i) { return alpha_status[i] == LOWER_BOUND; }
bool is_free(int i) { return alpha_status[i] == FREE; }
void swap_index(int i, int j);
void reconstruct_gradient();
virtual int select_working_set(int &i, int &j);
virtual double calculate_rho();
virtual void do_shrinking();
private:
bool be_shrunk(int i, double Gmax1, double Gmax2);
};
void Solver::swap_index(int i, int j)
{
Q->swap_index(i,j);
swap(y[i],y[j]);
swap(G[i],G[j]);
swap(alpha_status[i],alpha_status[j]);
swap(alpha[i],alpha[j]);
swap(p[i],p[j]);
swap(active_set[i],active_set[j]);
swap(G_bar[i],G_bar[j]);
}
void Solver::reconstruct_gradient()
{
// reconstruct inactive elements of G from G_bar and free variables
if(active_size == l) return;
int i,j;
int nr_free = 0;
for(j=active_size;j<l;j++)
G[j] = G_bar[j] + p[j];
for(j=0;j<active_size;j++)
if(is_free(j))
nr_free++;
if(2*nr_free < active_size)
info("\nWarning: using -h 0 may be faster\n");
if (nr_free*l > 2*active_size*(l-active_size))
{
for(i=active_size;i<l;i++)
{
const Qfloat *Q_i = Q->get_Q(i,active_size);
for(j=0;j<active_size;j++)
if(is_free(j))
G[i] += alpha[j] * Q_i[j];
}
}
else
{
for(i=0;i<active_size;i++)
if(is_free(i))
{
const Qfloat *Q_i = Q->get_Q(i,l);
double alpha_i = alpha[i];
for(j=active_size;j<l;j++)
G[j] += alpha_i * Q_i[j];
}
}
}
void Solver::Solve(int l, const QMatrix& Q, const double *p_, const schar *y_,
double *alpha_, double Cp, double Cn, double eps,
SolutionInfo* si, int shrinking)
{
this->l = l;
this->Q = &Q;
QD=Q.get_QD();
clone(p, p_,l);
clone(y, y_,l);
clone(alpha,alpha_,l);
this->Cp = Cp;
this->Cn = Cn;
this->eps = eps;
unshrink = false;
// initialize alpha_status
{
alpha_status = new char[l];
for(int i=0;i<l;i++)
update_alpha_status(i);
}
// initialize active set (for shrinking)
{
active_set = new int[l];
for(int i=0;i<l;i++)
active_set[i] = i;
active_size = l;
}
// initialize gradient
{
G = new double[l];
G_bar = new double[l];
int i;
for(i=0;i<l;i++)
{
G[i] = p[i];
G_bar[i] = 0;
}
for(i=0;i<l;i++)
if(!is_lower_bound(i))
{
const Qfloat *Q_i = Q.get_Q(i,l);
double alpha_i = alpha[i];
int j;
for(j=0;j<l;j++)
G[j] += alpha_i*Q_i[j];
if(is_upper_bound(i))
for(j=0;j<l;j++)
G_bar[j] += get_C(i) * Q_i[j];
}
}
// optimization step
int iter = 0;
int counter = min(l,1000)+1;
while(1)
{
// show progress and do shrinking
if(--counter == 0)
{
counter = min(l,1000);
if(shrinking) do_shrinking();
info(".");
}
int i,j;
if(select_working_set(i,j)!=0)
{
// reconstruct the whole gradient
reconstruct_gradient();
// reset active set size and check
active_size = l;
info("*");
if(select_working_set(i,j)!=0)
break;
else
counter = 1; // do shrinking next iteration
}
++iter;
// update alpha[i] and alpha[j], handle bounds carefully
const Qfloat *Q_i = Q.get_Q(i,active_size);
const Qfloat *Q_j = Q.get_Q(j,active_size);
double C_i = get_C(i);
double C_j = get_C(j);
double old_alpha_i = alpha[i];
double old_alpha_j = alpha[j];
if(y[i]!=y[j])
{
double quad_coef = Q_i[i]+Q_j[j]+2*Q_i[j];
if (quad_coef <= 0)
quad_coef = TAU;
double delta = (-G[i]-G[j])/quad_coef;
double diff = alpha[i] - alpha[j];
alpha[i] += delta;
alpha[j] += delta;
if(diff > 0)
{
if(alpha[j] < 0)
{
alpha[j] = 0;
alpha[i] = diff;
}
}
else
{
if(alpha[i] < 0)
{
alpha[i] = 0;
alpha[j] = -diff;
}
}
if(diff > C_i - C_j)
{
if(alpha[i] > C_i)
{
alpha[i] = C_i;
alpha[j] = C_i - diff;
}
}
else
{
if(alpha[j] > C_j)
{
alpha[j] = C_j;
alpha[i] = C_j + diff;
}
}
}
else
{
double quad_coef = Q_i[i]+Q_j[j]-2*Q_i[j];
if (quad_coef <= 0)
quad_coef = TAU;
double delta = (G[i]-G[j])/quad_coef;
double sum = alpha[i] + alpha[j];
alpha[i] -= delta;
alpha[j] += delta;
if(sum > C_i)
{
if(alpha[i] > C_i)
{
alpha[i] = C_i;
alpha[j] = sum - C_i;
}
}
else
{
if(alpha[j] < 0)
{
alpha[j] = 0;
alpha[i] = sum;
}
}
if(sum > C_j)
{
if(alpha[j] > C_j)
{
alpha[j] = C_j;
alpha[i] = sum - C_j;
}
}
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] + p[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[] p;
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 such that
// i: maximizes -y_i * grad(f)_i, i in I_up(\alpha)
// j: minimizes the decrease of obj value
// (if quadratic coefficeint <= 0, replace it with tau)
// -y_j*grad(f)_j < -y_i*grad(f)_i, j in I_low(\alpha)
double Gmax = -INF;
double Gmax2 = -INF;
int Gmax_idx = -1;
int Gmin_idx = -1;
double obj_diff_min = INF;
for(int t=0;t<active_size;t++)
if(y[t]==+1)
{
if(!is_upper_bound(t))
if(-G[t] >= Gmax)
{
Gmax = -G[t];
Gmax_idx = t;
}
}
else
{
if(!is_lower_bound(t))
if(G[t] >= Gmax)
{
Gmax = G[t];
Gmax_idx = t;
}
}
int i = Gmax_idx;
const Qfloat *Q_i = NULL;
if(i != -1) // NULL Q_i not accessed: Gmax=-INF if i=-1
Q_i = Q->get_Q(i,active_size);
for(int j=0;j<active_size;j++)
{
if(y[j]==+1)
{
if (!is_lower_bound(j))
{
double grad_diff=Gmax+G[j];
if (G[j] >= Gmax2)
Gmax2 = G[j];
if (grad_diff > 0)
{
double obj_diff;
double quad_coef=Q_i[i]+QD[j]-2.0*y[i]*Q_i[j];
if (quad_coef > 0)
obj_diff = -(grad_diff*grad_diff)/quad_coef;
else
obj_diff = -(grad_diff*grad_diff)/TAU;
if (obj_diff <= obj_diff_min)
{
Gmin_idx=j;
obj_diff_min = obj_diff;
}
}
}
}
else
{
if (!is_upper_bound(j))
{
double grad_diff= Gmax-G[j];
if (-G[j] >= Gmax2)
Gmax2 = -G[j];
if (grad_diff > 0)
{
double obj_diff;
double quad_coef=Q_i[i]+QD[j]+2.0*y[i]*Q_i[j];
if (quad_coef > 0)
obj_diff = -(grad_diff*grad_diff)/quad_coef;
else
obj_diff = -(grad_diff*grad_diff)/TAU;
if (obj_diff <= obj_diff_min)
{
Gmin_idx=j;
obj_diff_min = obj_diff;
}
}
}
}
}
if(Gmax+Gmax2 < eps)
return 1;
out_i = Gmax_idx;
out_j = Gmin_idx;
return 0;
}
bool Solver::be_shrunk(int i, double Gmax1, double Gmax2)
{
if(is_upper_bound(i))
{
if(y[i]==+1)
return(-G[i] > Gmax1);
else
return(-G[i] > Gmax2);
}
else if(is_lower_bound(i))
{
if(y[i]==+1)
return(G[i] > Gmax2);
else
return(G[i] > Gmax1);
}
else
return(false);
}
void Solver::do_shrinking()
{
int i;
double Gmax1 = -INF; // max { -y_i * grad(f)_i | i in I_up(\alpha) }
double Gmax2 = -INF; // max { y_i * grad(f)_i | i in I_low(\alpha) }
// find maximal violating pair first
for(i=0;i<active_size;i++)
{
if(y[i]==+1)
{
if(!is_upper_bound(i))
{
if(-G[i] >= Gmax1)
Gmax1 = -G[i];
}
if(!is_lower_bound(i))
{
if(G[i] >= Gmax2)
Gmax2 = G[i];
}
}
else
{
if(!is_upper_bound(i))
{
if(-G[i] >= Gmax2)
Gmax2 = -G[i];
}
if(!is_lower_bound(i))
{
if(G[i] >= Gmax1)
Gmax1 = G[i];
}
}
}
if(unshrink == false && Gmax1 + Gmax2 <= eps*10)
{
unshrink = true;
reconstruct_gradient();
active_size = l;
info("*");
}
for(i=0;i<active_size;i++)
if (be_shrunk(i, Gmax1, Gmax2))
{
active_size--;
while (active_size > i)
{
if (!be_shrunk(active_size, Gmax1, Gmax2))
{
swap_index(i,active_size);
break;
}
active_size--;
}
}
}
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_upper_bound(i))
{
if(y[i]==-1)
ub = min(ub,yG);
else
lb = max(lb,yG);
}
else if(is_lower_bound(i))
{
if(y[i]==+1)
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 QMatrix& Q, const double *p, const schar *y,
double *alpha, double Cp, double Cn, double eps,
SolutionInfo* si, int shrinking)
{
this->si = si;
Solver::Solve(l,Q,p,y,alpha,Cp,Cn,eps,si,shrinking);
}
private:
SolutionInfo *si;
int select_working_set(int &i, int &j);
double calculate_rho();
bool be_shrunk(int i, double Gmax1, double Gmax2, double Gmax3, double Gmax4);
void do_shrinking();
};
// return 1 if already optimal, return 0 otherwise
int Solver_NU::select_working_set(int &out_i, int &out_j)
{
// return i,j such that y_i = y_j and
// i: maximizes -y_i * grad(f)_i, i in I_up(\alpha)
// j: minimizes the decrease of obj value
// (if quadratic coefficeint <= 0, replace it with tau)
// -y_j*grad(f)_j < -y_i*grad(f)_i, j in I_low(\alpha)
double Gmaxp = -INF;
double Gmaxp2 = -INF;
int Gmaxp_idx = -1;
double Gmaxn = -INF;
double Gmaxn2 = -INF;
int Gmaxn_idx = -1;
int Gmin_idx = -1;
double obj_diff_min = INF;
for(int t=0;t<active_size;t++)
if(y[t]==+1)
{
if(!is_upper_bound(t))
if(-G[t] >= Gmaxp)
{
Gmaxp = -G[t];
Gmaxp_idx = t;
}
}
else
{
if(!is_lower_bound(t))
if(G[t] >= Gmaxn)
{
Gmaxn = G[t];
Gmaxn_idx = t;
}
}
int ip = Gmaxp_idx;
int in = Gmaxn_idx;
const Qfloat *Q_ip = NULL;
const Qfloat *Q_in = NULL;
if(ip != -1) // NULL Q_ip not accessed: Gmaxp=-INF if ip=-1
Q_ip = Q->get_Q(ip,active_size);
if(in != -1)
Q_in = Q->get_Q(in,active_size);
for(int j=0;j<active_size;j++)
{
if(y[j]==+1)
{
if (!is_lower_bound(j))
{
double grad_diff=Gmaxp+G[j];
if (G[j] >= Gmaxp2)
Gmaxp2 = G[j];
if (grad_diff > 0)
{
double obj_diff;
double quad_coef = Q_ip[ip]+QD[j]-2*Q_ip[j];
if (quad_coef > 0)
obj_diff = -(grad_diff*grad_diff)/quad_coef;
else
obj_diff = -(grad_diff*grad_diff)/TAU;
if (obj_diff <= obj_diff_min)
{
Gmin_idx=j;
obj_diff_min = obj_diff;
}
}
}
}
else
{
if (!is_upper_bound(j))
{
double grad_diff=Gmaxn-G[j];
if (-G[j] >= Gmaxn2)
Gmaxn2 = -G[j];
if (grad_diff > 0)
{
double obj_diff;
double quad_coef = Q_in[in]+QD[j]-2*Q_in[j];
if (quad_coef > 0)
obj_diff = -(grad_diff*grad_diff)/quad_coef;
else
obj_diff = -(grad_diff*grad_diff)/TAU;
if (obj_diff <= obj_diff_min)
{
Gmin_idx=j;
obj_diff_min = obj_diff;
}
}
}
}
}
if(max(Gmaxp+Gmaxp2,Gmaxn+Gmaxn2) < eps)
return 1;
if (y[Gmin_idx] == +1)
out_i = Gmaxp_idx;
else
out_i = Gmaxn_idx;
out_j = Gmin_idx;
return 0;
}
bool Solver_NU::be_shrunk(int i, double Gmax1, double Gmax2, double Gmax3, double Gmax4)
{
if(is_upper_bound(i))
{
if(y[i]==+1)
return(-G[i] > Gmax1);
else
return(-G[i] > Gmax4);
}
else if(is_lower_bound(i))
{
if(y[i]==+1)
return(G[i] > Gmax2);
else
return(G[i] > Gmax3);
}
else
return(false);
}
void Solver_NU::do_shrinking()
{
double Gmax1 = -INF; // max { -y_i * grad(f)_i | y_i = +1, i in I_up(\alpha) }
double Gmax2 = -INF; // max { y_i * grad(f)_i | y_i = +1, i in I_low(\alpha) }
double Gmax3 = -INF; // max { -y_i * grad(f)_i | y_i = -1, i in I_up(\alpha) }
double Gmax4 = -INF; // max { y_i * grad(f)_i | y_i = -1, i in I_low(\alpha) }
// find maximal violating pair first
int i;
for(i=0;i<active_size;i++)
{
if(!is_upper_bound(i))
{
if(y[i]==+1)
{
if(-G[i] > Gmax1) Gmax1 = -G[i];
}
else if(-G[i] > Gmax4) Gmax4 = -G[i];
}
if(!is_lower_bound(i))
{
if(y[i]==+1)
{
if(G[i] > Gmax2) Gmax2 = G[i];
}
else if(G[i] > Gmax3) Gmax3 = G[i];
}
}
if(unshrink == false && max(Gmax1+Gmax2,Gmax3+Gmax4) <= eps*10)
{
unshrink = true;
reconstruct_gradient();
active_size = l;
}
for(i=0;i<active_size;i++)
if (be_shrunk(i, Gmax1, Gmax2, Gmax3, Gmax4))
{
active_size--;
while (active_size > i)
{
if (!be_shrunk(active_size, Gmax1, Gmax2, Gmax3, Gmax4))
{
swap_index(i,active_size);
break;
}
active_size--;
}
}
}
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_upper_bound(i))
lb1 = max(lb1,G[i]);
else if(is_lower_bound(i))
ub1 = min(ub1,G[i]);
else
{
++nr_free1;
sum_free1 += G[i];
}
}
else
{
if(is_upper_bound(i))
lb2 = max(lb2,G[i]);
else if(is_lower_bound(i))
ub2 = min(ub2,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);
cache = new Cache(prob.l,(long int)(param.cache_size*(1<<20)));
QD = new Qfloat[prob.l];
for(int i=0;i<prob.l;i++)
QD[i]= (Qfloat)(this->*kernel_function)(i,i);
}
Qfloat *get_Q(int i, int len) const
{
Qfloat *data;
int start, j;
if((start = cache->get_data(i,&data,len)) < len)
{
for(j=start;j<len;j++)
data[j] = (Qfloat)(y[i]*y[j]*(this->*kernel_function)(i,j));
}
return data;
}
Qfloat *get_QD() const
{
return QD;
}
void swap_index(int i, int j) const
{
cache->swap_index(i,j);
Kernel::swap_index(i,j);
swap(y[i],y[j]);
swap(QD[i],QD[j]);
}
~SVC_Q()
{
delete[] y;
delete cache;
delete[] QD;
}
private:
schar *y;
Cache *cache;
Qfloat *QD;
};
class SVC_L2_Q: public Kernel
{
public:
SVC_L2_Q(const svm_problem& prob, const svm_parameter& param, const schar *y_)
:Kernel(prob.l, prob.x, param)
{
clone(y,y_,prob.l);
cache = new Cache(prob.l,(long int)(param.cache_size*(1<<20)));
this->C = param.C;
QD = new Qfloat[prob.l];
for(int i=0;i<prob.l;i++)
QD[i]= (Qfloat)(this->*kernel_function)(i,i);
}
Qfloat *get_Q(int i, int len) const
{
Qfloat *data;
int start;
if((start = cache->get_data(i,&data,len)) < len)
{
for(int j=start;j<len;j++)
data[j] = (Qfloat)(y[i]*y[j]*(this->*kernel_function)(i,j));
if(i >= start && i < len)
data[i] += 1/C;
}
return data;
}
Qfloat *get_QD() const
{
return QD;
}
void swap_index(int i, int j) const
{
cache->swap_index(i,j);
Kernel::swap_index(i,j);
swap(y[i],y[j]);
swap(QD[i],QD[j]);
}
~SVC_L2_Q()
{
delete[] y;
delete cache;
delete[] QD;
}
private:
schar *y;
Cache *cache;
Qfloat *QD;
double C;
};
class ONE_CLASS_Q: public Kernel
{
public:
ONE_CLASS_Q(const svm_problem& prob, const svm_parameter& param)
:Kernel(prob.l, prob.x, param)
{
cache = new Cache(prob.l,(long int)(param.cache_size*(1<<20)));
QD = new Qfloat[prob.l];
for(int i=0;i<prob.l;i++)
QD[i]= (Qfloat)(this->*kernel_function)(i,i);
}
Qfloat *get_Q(int i, int len) const
{
Qfloat *data;
int start, j;
if((start = cache->get_data(i,&data,len)) < len)
{
for(j=start;j<len;j++)
data[j] = (Qfloat)(this->*kernel_function)(i,j);
}
return data;
}
Qfloat *get_QD() const
{
return QD;
}
void swap_index(int i, int j) const
{
cache->swap_index(i,j);
Kernel::swap_index(i,j);
swap(QD[i],QD[j]);
}
~ONE_CLASS_Q()
{
delete cache;
delete[] QD;
}
private:
Cache *cache;
Qfloat *QD;
};
class ONE_CLASS_L2_Q: public Kernel
{
public:
ONE_CLASS_L2_Q(const svm_problem& prob, const svm_parameter& param)
:Kernel(prob.l, prob.x, param)
{
cache = new Cache(prob.l,(long int)(param.cache_size*(1<<20)));
QD = new Qfloat[prob.l];
this->C = param.C;
for(int i=0;i<prob.l;i++)
QD[i]= (Qfloat)(this->*kernel_function)(i,i);
}
Qfloat *get_Q(int i, int len) const
{
Qfloat *data;
int start;
if((start = cache->get_data(i,&data,len)) < len)
{
for(int j=start;j<len;j++)
data[j] = (Qfloat)(this->*kernel_function)(i,j);
if(i >= start && i < len)
data[i] += 1/C;
}
return data;
}
Qfloat *get_QD() const
{
return QD;
}
void swap_index(int i, int j) const
{
cache->swap_index(i,j);
Kernel::swap_index(i,j);
swap(QD[i],QD[j]);
}
~ONE_CLASS_L2_Q()
{
delete cache;
delete[] QD;
}
private:
Cache *cache;
Qfloat *QD;
double C;
};
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;
cache = new Cache(l,(long int)(param.cache_size*(1<<20)));
QD = new Qfloat[2*l];
sign = new schar[2*l];
index = new int[2*l];
for(int k=0;k<l;k++)
{
sign[k] = 1;
sign[k+l] = -1;
index[k] = k;
index[k+l] = k;
QD[k]= (Qfloat)(this->*kernel_function)(k,k);
QD[k+l]=QD[k];
}
buffer[0] = new Qfloat[2*l];
buffer[1] = new Qfloat[2*l];
next_buffer = 0;
}
void swap_index(int i, int j) const
{
swap(sign[i],sign[j]);
swap(index[i],index[j]);
swap(QD[i],QD[j]);
}
Qfloat *get_Q(int i, int len) const
{
Qfloat *data;
int j, real_i = index[i];
if(cache->get_data(real_i,&data,l) < l)
{
for(j=0;j<l;j++)
data[j] = (Qfloat)(this->*kernel_function)(real_i,j);
}
// reorder and copy
Qfloat *buf = buffer[next_buffer];
next_buffer = 1 - next_buffer;
schar si = sign[i];
for(j=0;j<len;j++)
buf[j] = (Qfloat) si * (Qfloat) sign[j] * data[index[j]];
return buf;
}
Qfloat *get_QD() const
{
return QD;
}
~SVR_Q()
{
delete cache;
delete[] sign;
delete[] index;
delete[] buffer[0];
delete[] buffer[1];
delete[] QD;
}
private:
int l;
Cache *cache;
schar *sign;
int *index;
mutable int next_buffer;
Qfloat *buffer[2];
Qfloat *QD;
};
//
// construct and solve various formulations
//
static void solve_c_svc(
const svm_problem *prob, const svm_parameter* param,
double *alpha, Solver::SolutionInfo* si, double Cp, double Cn)
{
int l = prob->l;
double *minus_ones = new double[l];
schar *y = new schar[l];
int i;
for(i=0;i<l;i++)
{
alpha[i] = 0;
minus_ones[i] = -1;
if(prob->y[i] > 0) y[i] = +1; else y[i]=-1;
}
Solver s;
s.Solve(l, SVC_Q(*prob,*param,y), minus_ones, y,
alpha, Cp, Cn, param->eps, si, param->shrinking);
double sum_alpha=0;
for(i=0;i<l;i++)
sum_alpha += alpha[i];
if (Cp==Cn)
info("nu = %f\n", sum_alpha/(Cp*prob->l));
for(i=0;i<l;i++)
alpha[i] *= y[i];
delete[] minus_ones;
delete[] y;
}
static void solve_c_svc_l2(
const svm_problem *prob, const svm_parameter* param,
double *alpha, Solver::SolutionInfo* si, double Cp, double Cn)
{
int l = prob->l;
double *minus_ones = new double[l];
schar *y = new schar[l];
int i;
for(i=0;i<l;i++)
{
alpha[i] = 0;
minus_ones[i] = -1;
if(prob->y[i] > 0) y[i] = +1; else y[i]=-1;
}
Solver s;
s.Solve(l, SVC_L2_Q(*prob,*param,y), minus_ones, y,
alpha, Cp, Cn, param->eps, si, param->shrinking);
double sum_alpha=0;
for(i=0;i<l;i++)
sum_alpha += alpha[i];
if (Cp==Cn)
info("nu = %f\n", sum_alpha/(Cp*prob->l));
for(i=0;i<l;i++)
alpha[i] *= y[i];
delete[] minus_ones;
delete[] y;
}
static void solve_nu_svc(
const svm_problem *prob, const svm_parameter *param,
double *alpha, Solver::SolutionInfo* si)
{
int i;
int l = prob->l;
double nu = param->nu;
schar *y = new schar[l];
for(i=0;i<l;i++)
if(prob->y[i]>0)
y[i] = +1;
else
y[i] = -1;
double sum_pos = nu*l/2;
double sum_neg = nu*l/2;
for(i=0;i<l;i++)
if(y[i] == +1)
{
alpha[i] = min(1.0,sum_pos);
sum_pos -= alpha[i];
}
else
{
alpha[i] = min(1.0,sum_neg);
sum_neg -= alpha[i];
}
double *zeros = new double[l];
for(i=0;i<l;i++)
zeros[i] = 0;
Solver_NU s;
s.Solve(l, SVC_Q(*prob,*param,y), zeros, y,
alpha, 1.0, 1.0, param->eps, si, param->shrinking);
double r = si->r;
info("C = %f\n",1/r);
for(i=0;i<l;i++)
alpha[i] *= y[i]/r;
si->rho /= r;
si->obj /= (r*r);
si->upper_bound_p = 1/r;
si->upper_bound_n = 1/r;
delete[] y;
delete[] zeros;
}
static void solve_one_class(
const svm_problem *prob, const svm_parameter *param,
double *alpha, Solver::SolutionInfo* si)
{
int l = prob->l;
double *zeros = new double[l];
schar *ones = new schar[l];
int i;
int n = (int)(param->nu*prob->l); // # of alpha's at upper bound
for(i=0;i<n;i++)
alpha[i] = 1;
if(n<prob->l)
alpha[n] = param->nu * prob->l - n;
for(i=n+1;i<l;i++)
alpha[i] = 0;
for(i=0;i<l;i++)
{
zeros[i] = 0;
ones[i] = 1;
}
Solver s;
s.Solve(l, ONE_CLASS_Q(*prob,*param), zeros, ones,
alpha, 1.0, 1.0, param->eps, si, param->shrinking);
delete[] zeros;
delete[] ones;
}
static void solve_svdd(
const svm_problem *prob, const svm_parameter *param,
double *alpha, Solver::SolutionInfo* si)
{
int l = prob->l;
double *diag = new double[l];
schar *ones = new schar[l];
int i;
int n = (int)(param->nu*prob->l); // # of alpha's at upper bound
for(i=0;i<n;i++)
alpha[i] = 1;
if(n<prob->l)
alpha[n] = param->nu * prob->l - n;
for(i=n+1;i<l;i++)
alpha[i] = 0;
for(i=0;i<l;i++)
{
if ((param->kernel_type != GAUSSIAN) && (param->kernel_type != EXPO) && (param->kernel_type != LAPLACE))
diag[i]=-0.5 * Kernel::k_function(prob->x[i],prob->x[i],*param);
else
diag[i]=-0.5;
ones[i] = 1;
}
Solver s;
s.Solve(l, ONE_CLASS_Q(*prob,*param), diag, ones,
alpha, 1.0, 1.0, param->eps, si, param->shrinking);
delete[] diag;
delete[] ones;
}
static void solve_svdd_l2(
const svm_problem *prob, const svm_parameter *param,
double *alpha, Solver::SolutionInfo* si)
{
int l = prob->l;
double *diag = new double[l];
schar *ones = new schar[l];
int i;
int n = (int)(param->nu*prob->l); // # of alpha's at upper bound
for(i=0;i<n;i++)
alpha[i] = 1;
if(n<prob->l)
alpha[n] = param->nu * prob->l - n;
for(i=n+1;i<l;i++)
alpha[i] = 0;
for(i=0;i<l;i++)
{
if ((param->kernel_type != GAUSSIAN) && (param->kernel_type != EXPO) && (param->kernel_type != LAPLACE))
diag[i]=-0.5*(Kernel::k_function(prob->x[i],prob->x[i],*param) + 1.0/param->C);
else
diag[i]=-0.5*(1.0 + 1.0/param->C);
ones[i] = 1;
}
Solver s;
s.Solve(l, ONE_CLASS_L2_Q(*prob,*param), diag, ones,
alpha, 1.0, 1.0, param->eps, si, param->shrinking);
delete[] diag;
delete[] ones;
}
static void solve_epsilon_svr(
const svm_problem *prob, const svm_parameter *param,
double *alpha, Solver::SolutionInfo* si)
{
int l = prob->l;
double *alpha2 = new double[2*l];
double *linear_term = new double[2*l];
schar *y = new schar[2*l];
int i;
for(i=0;i<l;i++)
{
alpha2[i] = 0;
linear_term[i] = param->p - prob->y[i];
y[i] = 1;
alpha2[i+l] = 0;
linear_term[i+l] = param->p + prob->y[i];
y[i+l] = -1;
}
Solver s;
s.Solve(2*l, SVR_Q(*prob,*param), linear_term, y,
alpha2, param->C, param->C, param->eps, si, param->shrinking);
double sum_alpha = 0;
for(i=0;i<l;i++)
{
alpha[i] = alpha2[i] - alpha2[i+l];
sum_alpha += fabs(alpha[i]);
}
info("nu = %f\n",sum_alpha/(param->C*l));
delete[] alpha2;
delete[] linear_term;
delete[] y;
}
static void solve_nu_svr(
const svm_problem *prob, const svm_parameter *param,
double *alpha, Solver::SolutionInfo* si)
{
int l = prob->l;
double C = param->C;
double *alpha2 = new double[2*l];
double *linear_term = new double[2*l];
schar *y = new schar[2*l];
int i;
double sum = C * param->nu * l / 2;
for(i=0;i<l;i++)
{
alpha2[i] = alpha2[i+l] = min(sum,C);
sum -= alpha2[i];
linear_term[i] = - prob->y[i];
y[i] = 1;
linear_term[i+l] = prob->y[i];
y[i+l] = -1;
}
Solver_NU s;
s.Solve(2*l, SVR_Q(*prob,*param), linear_term, y,
alpha2, C, C, param->eps, si, param->shrinking);
info("epsilon = %f\n",-si->r);
for(i=0;i<l;i++)
alpha[i] = alpha2[i] - alpha2[i+l];
delete[] alpha2;
delete[] linear_term;
delete[] y;
}
static decision_function svm_train_one(
const svm_problem *prob, const svm_parameter *param,
double Cp, double Cn)
{
double *alpha = Malloc(double,prob->l);
Solver::SolutionInfo si;
switch(param->svm_type)
{
case C_SVC:
solve_c_svc(prob,param,alpha,&si,Cp,Cn);
break;
case C_SVC_L2:
solve_c_svc_l2(prob,param,alpha,&si,Cp,Cn);
break;
case NU_SVC:
solve_nu_svc(prob,param,alpha,&si);
break;
case ONE_CLASS:
solve_one_class(prob,param,alpha,&si);
break;
case SVDD:
solve_svdd(prob,param,alpha,&si);
break;
case SVDD_L2:
solve_svdd_l2(prob,param,alpha,&si);
break;
case EPSILON_SVR:
solve_epsilon_svr(prob,param,alpha,&si);
break;
case NU_SVR:
solve_nu_svr(prob,param,alpha,&si);
break;
}
info("obj = %f, rho = %f\n",si.obj,si.rho);
// output SVs
int nSV = 0;
int nBSV = 0;
for(int i=0;i<prob->l;i++)
{
if(fabs(alpha[i]) > 0)
{
++nSV;
// TODO check if the control "if (param->svm_type != C_SVC_L2 && param->svm_type != SVDD_L2) {"
// is really useful
//if (param->svm_type != C_SVC_L2 && param->svm_type != SVDD_L2) {
if(prob->y[i] > 0)
{
if(fabs(alpha[i]) >= si.upper_bound_p)
++nBSV;
}
else
{
if(fabs(alpha[i]) >= si.upper_bound_n)
++nBSV;
}
//}
}
}
info("nSV = %d, nBSV = %d\n",nSV,nBSV);
decision_function f;
f.alpha = alpha;
f.rho = si.rho;
f.l = nSV;
f.lbsv = nBSV;
f.BSV_idx = Malloc(int, nBSV);
f.SV_idx = Malloc(int, nSV - nBSV);
// TODO check if the control "if (param->svm_type != C_SVC_L2 && param->svm_type != SVDD_L2) {"
// is needed also below
int b = 0, s = 0;
for(int i=0;i<prob->l;i++)
{
if(fabs(alpha[i]) > 0)
{
if(prob->y[i] > 0)
{
if(fabs(alpha[i]) >= si.upper_bound_p) {
f.BSV_idx[b] = i;
++b;
}
else {
f.SV_idx[s] = i;
++s;
}
}
else
{
if(fabs(alpha[i]) >= si.upper_bound_n) {
f.BSV_idx[b] = i;
++b;
}
else {
f.SV_idx[s] = i;
++s;
}
}
}
}
return f;
}
// Platt's binary SVM Probablistic Output: an improvement from Lin et al.
static void sigmoid_train(
int l, const double *dec_values, const double *labels,
double& A, double& B)
{
double prior1=0, prior0 = 0;
int i;
for (i=0;i<l;i++)
if (labels[i] > 0) prior1+=1;
else prior0+=1;
int max_iter=100; // Maximal number of iterations
double min_step=1e-10; // Minimal step taken in line search
double sigma=1e-12; // For numerically strict PD of Hessian
double eps=1e-5;
double hiTarget=(prior1+1.0)/(prior1+2.0);
double loTarget=1/(prior0+2.0);
double *t=Malloc(double,l);
double fApB,p,q,h11,h22,h21,g1,g2,det,dA,dB,gd,stepsize;
double newA,newB,newf,d1,d2;
int iter;
// Initial Point and Initial Fun Value
A=0.0; B=log((prior0+1.0)/(prior1+1.0));
double fval = 0.0;
for (i=0;i<l;i++)
{
if (labels[i]>0) t[i]=hiTarget;
else t[i]=loTarget;
fApB = dec_values[i]*A+B;
if (fApB>=0)
fval += t[i]*fApB + log(1+exp(-fApB));
else
fval += (t[i] - 1)*fApB +log(1+exp(fApB));
}
for (iter=0;iter<max_iter;iter++)
{
// Update Gradient and Hessian (use H' = H + sigma I)
h11=sigma; // numerically ensures strict PD
h22=sigma;
h21=0.0;g1=0.0;g2=0.0;
for (i=0;i<l;i++)
{
fApB = dec_values[i]*A+B;
if (fApB >= 0)
{
p=exp(-fApB)/(1.0+exp(-fApB));
q=1.0/(1.0+exp(-fApB));
}
else
{
p=1.0/(1.0+exp(fApB));
q=exp(fApB)/(1.0+exp(fApB));
}
d2=p*q;
h11+=dec_values[i]*dec_values[i]*d2;
h22+=d2;
h21+=dec_values[i]*d2;
d1=t[i]-p;
g1+=dec_values[i]*d1;
g2+=d1;
}
// Stopping Criteria
if (fabs(g1)<eps && fabs(g2)<eps)
break;
// Finding Newton direction: -inv(H') * g
det=h11*h22-h21*h21;
dA=-(h22*g1 - h21 * g2) / det;
dB=-(-h21*g1+ h11 * g2) / det;
gd=g1*dA+g2*dB;
stepsize = 1; // Line Search
while (stepsize >= min_step)
{
newA = A + stepsize * dA;
newB = B + stepsize * dB;
// New function value
newf = 0.0;
for (i=0;i<l;i++)
{
fApB = dec_values[i]*newA+newB;
if (fApB >= 0)
newf += t[i]*fApB + log(1+exp(-fApB));
else
newf += (t[i] - 1)*fApB +log(1+exp(fApB));
}
// Check sufficient decrease
if (newf<fval+0.0001*stepsize*gd)
{
A=newA;B=newB;fval=newf;
break;
}
else
stepsize = stepsize / 2.0;
}
if (stepsize < min_step)
{
info("Line search fails in two-class probability estimates\n");
break;
}
}
if (iter>=max_iter)
info("Reaching maximal iterations in two-class probability estimates\n");
free(t);
}
static double sigmoid_predict(double decision_value, double A, double B)
{
double fApB = decision_value*A+B;
if (fApB >= 0)
return exp(-fApB)/(1.0+exp(-fApB));
else
return 1.0/(1+exp(fApB)) ;
}
// Method 2 from the multiclass_prob paper by Wu, Lin, and Weng
static void multiclass_probability(int k, double **r, double *p)
{
int t,j;
int iter = 0, max_iter=max(100,k);
double **Q=Malloc(double *,k);
double *Qp=Malloc(double,k);
double pQp, eps=0.005/k;
for (t=0;t<k;t++)
{
p[t]=1.0/k; // Valid if k = 1
Q[t]=Malloc(double,k);
Q[t][t]=0;
for (j=0;j<t;j++)
{
Q[t][t]+=r[j][t]*r[j][t];
Q[t][j]=Q[j][t];
}
for (j=t+1;j<k;j++)
{
Q[t][t]+=r[j][t]*r[j][t];
Q[t][j]=-r[j][t]*r[t][j];
}
}
for (iter=0;iter<max_iter;iter++)
{
// stopping condition, recalculate QP,pQP for numerical accuracy
pQp=0;
for (t=0;t<k;t++)
{
Qp[t]=0;
for (j=0;j<k;j++)
Qp[t]+=Q[t][j]*p[j];
pQp+=p[t]*Qp[t];
}
double max_error=0;
for (t=0;t<k;t++)
{
double error=fabs(Qp[t]-pQp);
if (error>max_error)
max_error=error;
}
if (max_error<eps) break;
for (t=0;t<k;t++)
{
double diff=(-Qp[t]+pQp)/Q[t][t];
p[t]+=diff;
pQp=(pQp+diff*(diff*Q[t][t]+2*Qp[t]))/(1+diff)/(1+diff);
for (j=0;j<k;j++)
{
Qp[j]=(Qp[j]+diff*Q[t][j])/(1+diff);
p[j]/=(1+diff);
}
}
}
if (iter>=max_iter)
info("Exceeds max_iter in multiclass_prob\n");
for(t=0;t<k;t++) free(Q[t]);
free(Q);
free(Qp);
}
// Cross-validation decision values for probability estimates
static void svm_binary_svc_probability(
const svm_problem *prob, const svm_parameter *param,
double Cp, double Cn, double& probA, double& probB)
{
int i;
int nr_fold = 5;
int *perm = Malloc(int,prob->l);
double *dec_values = Malloc(double,prob->l);
// random shuffle
for(i=0;i<prob->l;i++) perm[i]=i;
for(i=0;i<prob->l;i++)
{
int j = i+rand()%(prob->l-i);
swap(perm[i],perm[j]);
}
for(i=0;i<nr_fold;i++)
{
int begin = i*prob->l/nr_fold;
int end = (i+1)*prob->l/nr_fold;
int j,k;
struct svm_problem subprob;
subprob.l = prob->l-(end-begin);
subprob.x = Malloc(struct svm_node*,subprob.l);
subprob.y = Malloc(double,subprob.l);
k=0;
for(j=0;j<begin;j++)
{
subprob.x[k] = prob->x[perm[j]];
subprob.y[k] = prob->y[perm[j]];
++k;
}
for(j=end;j<prob->l;j++)
{
subprob.x[k] = prob->x[perm[j]];
subprob.y[k] = prob->y[perm[j]];
++k;
}
int p_count=0,n_count=0;
for(j=0;j<k;j++)
if(subprob.y[j]>0)
p_count++;
else
n_count++;
if(p_count==0 && n_count==0)
for(j=begin;j<end;j++)
dec_values[perm[j]] = 0;
else if(p_count > 0 && n_count == 0)
for(j=begin;j<end;j++)
dec_values[perm[j]] = 1;
else if(p_count == 0 && n_count > 0)
for(j=begin;j<end;j++)
dec_values[perm[j]] = -1;
else
{
svm_parameter subparam = *param;
subparam.probability=0;
subparam.C=1.0;
subparam.nr_weight=2;
subparam.weight_label = Malloc(int,2);
subparam.weight = Malloc(double,2);
subparam.weight_label[0]=+1;
subparam.weight_label[1]=-1;
subparam.weight[0]=Cp;
subparam.weight[1]=Cn;
struct svm_model *submodel = svm_train(&subprob,&subparam);
for(j=begin;j<end;j++)
{
svm_predict_values(submodel,prob->x[perm[j]],&(dec_values[perm[j]]));
// ensure +1 -1 order; reason not using CV subroutine
dec_values[perm[j]] *= submodel->label[0];
}
svm_destroy_model(submodel);
svm_destroy_param(&subparam);
}
free(subprob.x);
free(subprob.y);
}
sigmoid_train(prob->l,dec_values,prob->y,probA,probB);
free(dec_values);
free(perm);
}
// Return parameter of a Laplace distribution
static double svm_svr_probability(
const svm_problem *prob, const svm_parameter *param)
{
int i;
int nr_fold = 5;
double *ymv = Malloc(double,prob->l);
double mae = 0;
svm_parameter newparam = *param;
newparam.probability = 0;
svm_cross_validation(prob,&newparam,nr_fold,ymv);
for(i=0;i<prob->l;i++)
{
ymv[i]=prob->y[i]-ymv[i];
mae += fabs(ymv[i]);
}
mae /= prob->l;
double std=sqrt(2*mae*mae);
int count=0;
mae=0;
for(i=0;i<prob->l;i++)
if (fabs(ymv[i]) > 5*std)
count=count+1;
else
mae+=fabs(ymv[i]);
mae /= (prob->l-count);
info("Prob. model for test data: target value = predicted value + z,\nz: Laplace distribution e^(-|z|/sigma)/(2sigma),sigma= %g\n",mae);
free(ymv);
return mae;
}
// label: label name, start: begin of each class, count: #data of classes, perm: indices to the original data
// perm, length l, must be allocated before calling this subroutine
static void svm_group_classes(const svm_problem *prob, int *nr_class_ret, int **label_ret, int **start_ret, int **count_ret, int *perm)
{
int l = prob->l;
int max_nr_class = 16;
int nr_class = 0;
int *label = Malloc(int,max_nr_class);
int *count = Malloc(int,max_nr_class);
int *data_label = Malloc(int,l);
int i;
for(i=0;i<l;i++)
{
int this_label = (int)prob->y[i];
int j;
for(j=0;j<nr_class;j++)
{
if(this_label == label[j])
{
++count[j];
break;
}
}
data_label[i] = j;
if(j == nr_class)
{
if(nr_class == max_nr_class)
{
max_nr_class *= 2;
label = (int *)realloc(label,max_nr_class*sizeof(int));
count = (int *)realloc(count,max_nr_class*sizeof(int));
}
label[nr_class] = this_label;
count[nr_class] = 1;
++nr_class;
}
}
int *start = Malloc(int,nr_class);
start[0] = 0;
for(i=1;i<nr_class;i++)
start[i] = start[i-1]+count[i-1];
for(i=0;i<l;i++)
{
perm[start[data_label[i]]] = i;
++start[data_label[i]];
}
start[0] = 0;
for(i=1;i<nr_class;i++)
start[i] = start[i-1]+count[i-1];
*nr_class_ret = nr_class;
*label_ret = label;
*start_ret = start;
*count_ret = count;
free(data_label);
}
//
// Interface functions
//
svm_model *svm_train(const svm_problem *prob, const svm_parameter *param)
{
svm_model *model = Malloc(svm_model,1);
model->param = *param;
model->free_sv = 0; // XXX
if(param->svm_type == ONE_CLASS ||
param->svm_type == SVDD ||
param->svm_type == SVDD_L2 ||
param->svm_type == EPSILON_SVR ||
param->svm_type == NU_SVR)
{
// regression or one-class-svm or SVDD
model->nr_class = 2;
model->label = NULL;
model->nSV = NULL;
model->probA = NULL; model->probB = NULL;
model->sv_coef = Malloc(double *,1);
if(param->probability &&
(param->svm_type == EPSILON_SVR ||
param->svm_type == NU_SVR))
{
model->probA = Malloc(double,1);
model->probA[0] = svm_svr_probability(prob,param);
}
decision_function f = svm_train_one(prob,param,0,0);
model->rho = Malloc(double,1);
model->rho[0] = f.rho;
model->l = f.l; //nSV
model->lbsv = f.lbsv; //nBSV
model->SV_idx = f.SV_idx;
model->BSV_idx = f.BSV_idx;
model->SV = Malloc(svm_node *,f.l);
model->sv_coef[0] = Malloc(double,f.l);
int j = 0;
int i;
for(i=0;i<prob->l;i++) {
if(fabs(f.alpha[i]) > 0) {
model->SV[j] = prob->x[i];
model->sv_coef[0][j] = f.alpha[i];
++j;
}
}
free(f.alpha);
}
else
{
// classification
int l = prob->l;
int nr_class;
int *label = NULL;
int *start = NULL;
int *count = NULL;
int *perm = Malloc(int,l);
// group training data of the same class
svm_group_classes(prob,&nr_class,&label,&start,&count,perm);
svm_node **x = Malloc(svm_node *,l);
int i;
for(i=0;i<l;i++)
x[i] = prob->x[perm[i]];
// calculate weighted C
double *weighted_C = Malloc(double, nr_class);
for(i=0;i<nr_class;i++)
weighted_C[i] = param->C;
for(i=0;i<param->nr_weight;i++)
{
int j;
for(j=0;j<nr_class;j++)
if(param->weight_label[i] == label[j])
break;
if(j == nr_class)
fprintf(stderr,"warning: class label %d specified in weight is not found\n", param->weight_label[i]);
else
weighted_C[j] *= param->weight[i];
}
// train k*(k-1)/2 models
bool *nonzero = Malloc(bool,l);
for(i=0;i<l;i++)
nonzero[i] = false;
decision_function *f = Malloc(decision_function,nr_class*(nr_class-1)/2);
double *probA=NULL,*probB=NULL;
if (param->probability)
{
probA=Malloc(double,nr_class*(nr_class-1)/2);
probB=Malloc(double,nr_class*(nr_class-1)/2);
}
int p = 0;
for(i=0;i<nr_class;i++)
for(int j=i+1;j<nr_class;j++)
{
svm_problem sub_prob;
int si = start[i], sj = start[j];
int ci = count[i], cj = count[j];
sub_prob.l = ci+cj;
sub_prob.x = Malloc(svm_node *,sub_prob.l);
sub_prob.y = Malloc(double,sub_prob.l);
int k;
for(k=0;k<ci;k++)
{
sub_prob.x[k] = x[si+k];
sub_prob.y[k] = +1;
}
for(k=0;k<cj;k++)
{
sub_prob.x[ci+k] = x[sj+k];
sub_prob.y[ci+k] = -1;
}
if(param->probability)
svm_binary_svc_probability(&sub_prob,param,weighted_C[i],weighted_C[j],probA[p],probB[p]);
f[p] = svm_train_one(&sub_prob,param,weighted_C[i],weighted_C[j]);
for(k=0;k<ci;k++)
if(!nonzero[si+k] && fabs(f[p].alpha[k]) > 0)
nonzero[si+k] = true;
for(k=0;k<cj;k++)
if(!nonzero[sj+k] && fabs(f[p].alpha[ci+k]) > 0)
nonzero[sj+k] = true;
free(sub_prob.x);
free(sub_prob.y);
++p;
}
// build output
model->nr_class = nr_class;
model->label = Malloc(int,nr_class);
for(i=0;i<nr_class;i++)
model->label[i] = label[i];
model->rho = Malloc(double,nr_class*(nr_class-1)/2);
for(i=0;i<nr_class*(nr_class-1)/2;i++)
model->rho[i] = f[i].rho;
if(param->probability)
{
model->probA = Malloc(double,nr_class*(nr_class-1)/2);
model->probB = Malloc(double,nr_class*(nr_class-1)/2);
for(i=0;i<nr_class*(nr_class-1)/2;i++)
{
model->probA[i] = probA[i];
model->probB[i] = probB[i];
}
}
else
{
model->probA=NULL;
model->probB=NULL;
}
int total_sv = 0;
int *nz_count = Malloc(int,nr_class);
model->nSV = Malloc(int,nr_class);
for(i=0;i<nr_class;i++)
{
int nSV = 0;
for(int j=0;j<count[i];j++)
if(nonzero[start[i]+j])
{
++nSV;
++total_sv;
}
model->nSV[i] = nSV;
nz_count[i] = nSV;
}
info("Total nSV = %d\n",total_sv);
model->l = total_sv;
model->SV = Malloc(svm_node *,total_sv);
p = 0;
for(i=0;i<l;i++)
if(nonzero[i]) model->SV[p++] = x[i];
int *nz_start = Malloc(int,nr_class);
nz_start[0] = 0;
for(i=1;i<nr_class;i++)
nz_start[i] = nz_start[i-1]+nz_count[i-1];
model->sv_coef = Malloc(double *,nr_class-1);
for(i=0;i<nr_class-1;i++)
model->sv_coef[i] = Malloc(double,total_sv);
p = 0;
for(i=0;i<nr_class;i++)
for(int j=i+1;j<nr_class;j++)
{
// classifier (i,j): coefficients with
// i are in sv_coef[j-1][nz_start[i]...],
// j are in sv_coef[i][nz_start[j]...]
int si = start[i];
int sj = start[j];
int ci = count[i];
int cj = count[j];
int q = nz_start[i];
int k;
for(k=0;k<ci;k++)
if(nonzero[si+k])
model->sv_coef[j-1][q++] = f[p].alpha[k];
q = nz_start[j];
for(k=0;k<cj;k++)
if(nonzero[sj+k])
model->sv_coef[i][q++] = f[p].alpha[ci+k];
++p;
}
free(label);
free(probA);
free(probB);
free(count);
free(perm);
free(start);
free(x);
free(weighted_C);
free(nonzero);
for(i=0;i<nr_class*(nr_class-1)/2;i++)
free(f[i].alpha);
free(f);
free(nz_count);
free(nz_start);
}
return model;
}
// Stratified cross validation
void svm_cross_validation(const svm_problem *prob, const svm_parameter *param, int nr_fold, double *target)
{
int i;
int *fold_start = Malloc(int,nr_fold+1);
int l = prob->l;
int *perm = Malloc(int,l);
int nr_class;
// stratified cv may not give leave-one-out rate
// Each class to l folds -> some folds may have zero elements
if((param->svm_type == C_SVC ||
param->svm_type == NU_SVC) && nr_fold < l)
{
int *start = NULL;
int *label = NULL;
int *count = NULL;
svm_group_classes(prob,&nr_class,&label,&start,&count,perm);
// random shuffle and then data grouped by fold using the array perm
int *fold_count = Malloc(int,nr_fold);
int c;
int *index = Malloc(int,l);
for(i=0;i<l;i++)
index[i]=perm[i];
for (c=0; c<nr_class; c++)
for(i=0;i<count[c];i++)
{
int j = i+rand()%(count[c]-i);
swap(index[start[c]+j],index[start[c]+i]);
}
for(i=0;i<nr_fold;i++)
{
fold_count[i] = 0;
for (c=0; c<nr_class;c++)
fold_count[i]+=(i+1)*count[c]/nr_fold-i*count[c]/nr_fold;
}
fold_start[0]=0;
for (i=1;i<=nr_fold;i++)
fold_start[i] = fold_start[i-1]+fold_count[i-1];
for (c=0; c<nr_class;c++)
for(i=0;i<nr_fold;i++)
{
int begin = start[c]+i*count[c]/nr_fold;
int end = start[c]+(i+1)*count[c]/nr_fold;
for(int j=begin;j<end;j++)
{
perm[fold_start[i]] = index[j];
fold_start[i]++;
}
}
fold_start[0]=0;
for (i=1;i<=nr_fold;i++)
fold_start[i] = fold_start[i-1]+fold_count[i-1];
free(start);
free(label);
free(count);
free(index);
free(fold_count);
}
else
{
for(i=0;i<l;i++) perm[i]=i;
for(i=0;i<l;i++)
{
int j = i+rand()%(l-i);
swap(perm[i],perm[j]);
}
for(i=0;i<=nr_fold;i++)
fold_start[i]=i*l/nr_fold;
}
for(i=0;i<nr_fold;i++)
{
int begin = fold_start[i];
int end = fold_start[i+1];
int j,k;
struct svm_problem subprob;
subprob.l = l-(end-begin);
subprob.x = Malloc(struct svm_node*,subprob.l);
subprob.y = Malloc(double,subprob.l);
k=0;
for(j=0;j<begin;j++)
{
subprob.x[k] = prob->x[perm[j]];
subprob.y[k] = prob->y[perm[j]];
++k;
}
for(j=end;j<l;j++)
{
subprob.x[k] = prob->x[perm[j]];
subprob.y[k] = prob->y[perm[j]];
++k;
}
struct svm_model *submodel = svm_train(&subprob,param);
if(param->probability &&
(param->svm_type == C_SVC || param->svm_type == NU_SVC))
{
double *prob_estimates=Malloc(double,svm_get_nr_class(submodel));
for(j=begin;j<end;j++)
target[perm[j]] = svm_predict_probability(submodel,prob->x[perm[j]],prob_estimates);
free(prob_estimates);
}
else
for(j=begin;j<end;j++)
target[perm[j]] = svm_predict(submodel,prob->x[perm[j]]);
svm_destroy_model(submodel);
free(subprob.x);
free(subprob.y);
}
free(fold_start);
free(perm);
}
int svm_get_svm_type(const svm_model *model)
{
return model->param.svm_type;
}
int svm_get_nr_class(const svm_model *model)
{
return model->nr_class;
}
void svm_get_labels(const svm_model *model, int* label)
{
if (model->label != NULL)
for(int i=0;i<model->nr_class;i++)
label[i] = model->label[i];
}
double svm_get_svr_probability(const svm_model *model)
{
if ((model->param.svm_type == EPSILON_SVR || model->param.svm_type == NU_SVR) &&
model->probA!=NULL)
return model->probA[0];
else
{
fprintf(stderr,"Model doesn't contain information for SVR probability inference\n");
return 0;
}
}
void svm_predict_values(const svm_model *model, const svm_node *x, double* dec_values)
{
if(model->param.svm_type == ONE_CLASS ||
model->param.svm_type == SVDD ||
model->param.svm_type == SVDD_L2 ||
model->param.svm_type == EPSILON_SVR ||
model->param.svm_type == NU_SVR)
{
double *sv_coef = model->sv_coef[0];
double sum = 0;
for(int i=0;i<model->l;i++)
sum += sv_coef[i] * Kernel::k_function(x,model->SV[i],model->param);
sum -= model->rho[0];
*dec_values = sum;
}
else
{
int i;
int nr_class = model->nr_class;
int l = model->l;
double *kvalue = Malloc(double,l);
for(i=0;i<l;i++)
kvalue[i] = Kernel::k_function(x,model->SV[i],model->param);
int *start = Malloc(int,nr_class);
start[0] = 0;
for(i=1;i<nr_class;i++)
start[i] = start[i-1]+model->nSV[i-1];
int p=0;
for(i=0;i<nr_class;i++)
for(int j=i+1;j<nr_class;j++)
{
double sum = 0;
int si = start[i];
int sj = start[j];
int ci = model->nSV[i];
int cj = model->nSV[j];
int k;
double *coef1 = model->sv_coef[j-1];
double *coef2 = model->sv_coef[i];
for(k=0;k<ci;k++)
sum += coef1[si+k] * kvalue[si+k];
for(k=0;k<cj;k++)
sum += coef2[sj+k] * kvalue[sj+k];
sum -= model->rho[p];
dec_values[p] = sum;
p++;
}
free(kvalue);
free(start);
}
}
double svm_predict(const svm_model *model, const svm_node *x)
{
if(model->param.svm_type == ONE_CLASS ||
model->param.svm_type == SVDD ||
model->param.svm_type == SVDD_L2 ||
model->param.svm_type == EPSILON_SVR ||
model->param.svm_type == NU_SVR)
{
double res;
svm_predict_values(model, x, &res);
if (model->param.svm_type == ONE_CLASS || model->param.svm_type == SVDD || model->param.svm_type == SVDD_L2)
return (res>0)?1:-1;
else
return res;
}
else
{
int i;
int nr_class = model->nr_class;
double *dec_values = Malloc(double, nr_class*(nr_class-1)/2);
svm_predict_values(model, x, dec_values);
int *vote = Malloc(int,nr_class);
for(i=0;i<nr_class;i++)
vote[i] = 0;
int pos=0;
for(i=0;i<nr_class;i++)
for(int j=i+1;j<nr_class;j++)
{
if(dec_values[pos++] > 0)
++vote[i];
else
++vote[j];
}
int vote_max_idx = 0;
for(i=1;i<nr_class;i++)
if(vote[i] > vote[vote_max_idx])
vote_max_idx = i;
free(vote);
free(dec_values);
return model->label[vote_max_idx];
}
}
double svm_predict_probability(
const svm_model *model, const svm_node *x, double *prob_estimates)
{
if ((model->param.svm_type == C_SVC || model->param.svm_type == NU_SVC) &&
model->probA!=NULL && model->probB!=NULL)
{
int i;
int nr_class = model->nr_class;
double *dec_values = Malloc(double, nr_class*(nr_class-1)/2);
svm_predict_values(model, x, dec_values);
double min_prob=1e-7;
double **pairwise_prob=Malloc(double *,nr_class);
for(i=0;i<nr_class;i++)
pairwise_prob[i]=Malloc(double,nr_class);
int k=0;
for(i=0;i<nr_class;i++)
for(int j=i+1;j<nr_class;j++)
{
pairwise_prob[i][j]=min(max(sigmoid_predict(dec_values[k],model->probA[k],model->probB[k]),min_prob),1-min_prob);
pairwise_prob[j][i]=1-pairwise_prob[i][j];
k++;
}
multiclass_probability(nr_class,pairwise_prob,prob_estimates);
int prob_max_idx = 0;
for(i=1;i<nr_class;i++)
if(prob_estimates[i] > prob_estimates[prob_max_idx])
prob_max_idx = i;
for(i=0;i<nr_class;i++)
free(pairwise_prob[i]);
free(dec_values);
free(pairwise_prob);
return model->label[prob_max_idx];
}
else
return svm_predict(model, x);
}
static const char *svm_type_table[] =
{
"c_svc","c_svc_l2","nu_svc","one_class","epsilon_svr","nu_svr","svdd","svdd_l2",NULL
};
static const char *kernel_type_table[]=
{
"linear","polynomial","gaussian","sigmoid","stump","perc","laplace","expo","precomputed",NULL
};
int svm_save_model(const char *model_file_name, const svm_model *model)
{
FILE *fp = fopen(model_file_name,"w");
if(fp==NULL) return -1;
const svm_parameter& param = model->param;
fprintf(fp,"svm_type %s\n", svm_type_table[param.svm_type]);
fprintf(fp,"kernel_type %s\n", kernel_type_table[param.kernel_type]);
if(param.kernel_type == POLY)
fprintf(fp,"degree %d\n", param.degree);
if(param.kernel_type == POLY || param.kernel_type == GAUSSIAN || param.kernel_type == SIGMOID
|| param.kernel_type == LAPLACE || param.kernel_type == EXPO)
fprintf(fp,"gamma %g\n", param.gamma);
if(param.kernel_type == POLY || param.kernel_type == SIGMOID
|| param.kernel_type == STUMP || param.kernel_type == PERC)
fprintf(fp,"coef0 %g\n", param.coef0);
int nr_class = model->nr_class;
int l = model->l;
fprintf(fp, "nr_class %d\n", nr_class);
fprintf(fp, "total_sv %d\n",l);
{
fprintf(fp, "rho");
for(int i=0;i<nr_class*(nr_class-1)/2;i++)
fprintf(fp," %g",model->rho[i]);
fprintf(fp, "\n");
}
if(model->label)
{
fprintf(fp, "label");
for(int i=0;i<nr_class;i++)
fprintf(fp," %d",model->label[i]);
fprintf(fp, "\n");
}
if(model->probA) // regression has probA only
{
fprintf(fp, "probA");
for(int i=0;i<nr_class*(nr_class-1)/2;i++)
fprintf(fp," %g",model->probA[i]);
fprintf(fp, "\n");
}
if(model->probB)
{
fprintf(fp, "probB");
for(int i=0;i<nr_class*(nr_class-1)/2;i++)
fprintf(fp," %g",model->probB[i]);
fprintf(fp, "\n");
}
if(model->nSV)
{
fprintf(fp, "nr_sv");
for(int i=0;i<nr_class;i++)
fprintf(fp," %d",model->nSV[i]);
fprintf(fp, "\n");
}
fprintf(fp, "SV\n");
const double * const *sv_coef = model->sv_coef;
const svm_node * const *SV = model->SV;
for(int i=0;i<l;i++)
{
for(int j=0;j<nr_class-1;j++)
fprintf(fp, "%.16g ",sv_coef[j][i]);
const svm_node *p = SV[i];
if(param.kernel_type == PRECOMPUTED)
fprintf(fp,"0:%d ",(int)(p->value));
else
while(p->index != -1)
{
fprintf(fp,"%d:%.8g ",p->index,p->value);
p++;
}
fprintf(fp, "\n");
}
if (ferror(fp) != 0 || fclose(fp) != 0) return -1;
else return 0;
}
static char *line = NULL;
static int max_line_len;
static char* readline(FILE *input)
{
int len;
if(fgets(line,max_line_len,input) == NULL)
return NULL;
while(strrchr(line,'\n') == NULL)
{
max_line_len *= 2;
line = (char *) realloc(line,max_line_len);
len = (int) strlen(line);
if(fgets(line+len,max_line_len-len,input) == NULL)
break;
}
return line;
}
svm_model *svm_load_model(const char *model_file_name)
{
FILE *fp = fopen(model_file_name,"rb");
if(fp==NULL) return NULL;
// read parameters
svm_model *model = Malloc(svm_model,1);
svm_parameter& param = model->param;
model->rho = NULL;
model->probA = NULL;
model->probB = NULL;
model->label = NULL;
model->nSV = NULL;
char cmd[81];
while(1)
{
fscanf(fp,"%80s",cmd);
if(strcmp(cmd,"svm_type")==0)
{
fscanf(fp,"%80s",cmd);
int i;
for(i=0;svm_type_table[i];i++)
{
if(strcmp(svm_type_table[i],cmd)==0)
{
param.svm_type=i;
break;
}
}
if(svm_type_table[i] == NULL)
{
fprintf(stderr,"unknown svm type.\n");
free(model->rho);
free(model->label);
free(model->nSV);
free(model);
return NULL;
}
}
else if(strcmp(cmd,"kernel_type")==0)
{
fscanf(fp,"%80s",cmd);
int i;
for(i=0;kernel_type_table[i];i++)
{
if(strcmp(kernel_type_table[i],cmd)==0)
{
param.kernel_type=i;
break;
}
}
if(kernel_type_table[i] == NULL)
{
fprintf(stderr,"unknown kernel function.\n");
free(model->rho);
free(model->label);
free(model->nSV);
free(model);
return NULL;
}
}
else if(strcmp(cmd,"degree")==0)
fscanf(fp,"%d",&param.degree);
else if(strcmp(cmd,"gamma")==0)
fscanf(fp,"%lf",&param.gamma);
else if(strcmp(cmd,"coef0")==0)
fscanf(fp,"%lf",&param.coef0);
else if(strcmp(cmd,"nr_class")==0)
fscanf(fp,"%d",&model->nr_class);
else if(strcmp(cmd,"total_sv")==0)
fscanf(fp,"%d",&model->l);
else if(strcmp(cmd,"rho")==0)
{
int n = model->nr_class * (model->nr_class-1)/2;
model->rho = Malloc(double,n);
for(int i=0;i<n;i++)
fscanf(fp,"%lf",&model->rho[i]);
}
else if(strcmp(cmd,"label")==0)
{
int n = model->nr_class;
model->label = Malloc(int,n);
for(int i=0;i<n;i++)
fscanf(fp,"%d",&model->label[i]);
}
else if(strcmp(cmd,"probA")==0)
{
int n = model->nr_class * (model->nr_class-1)/2;
model->probA = Malloc(double,n);
for(int i=0;i<n;i++)
fscanf(fp,"%lf",&model->probA[i]);
}
else if(strcmp(cmd,"probB")==0)
{
int n = model->nr_class * (model->nr_class-1)/2;
model->probB = Malloc(double,n);
for(int i=0;i<n;i++)
fscanf(fp,"%lf",&model->probB[i]);
}
else if(strcmp(cmd,"nr_sv")==0)
{
int n = model->nr_class;
model->nSV = Malloc(int,n);
for(int i=0;i<n;i++)
fscanf(fp,"%d",&model->nSV[i]);
}
else if(strcmp(cmd,"SV")==0)
{
while(1)
{
int c = getc(fp);
if(c==EOF || c=='\n') break;
}
break;
}
else
{
fprintf(stderr,"unknown text in model file: [%s]\n",cmd);
free(model->rho);
free(model->label);
free(model->nSV);
free(model);
return NULL;
}
}
// read sv_coef and SV
int elements = 0;
long pos = ftell(fp);
max_line_len = 1024;
line = Malloc(char,max_line_len);
char *p,*endptr,*idx,*val;
while(readline(fp)!=NULL)
{
p = strtok(line,":");
while(1)
{
p = strtok(NULL,":");
if(p == NULL)
break;
++elements;
}
}
elements += model->l;
fseek(fp,pos,SEEK_SET);
int m = model->nr_class - 1;
int l = model->l;
model->sv_coef = Malloc(double *,m);
int i;
for(i=0;i<m;i++)
model->sv_coef[i] = Malloc(double,l);
model->SV = Malloc(svm_node*,l);
svm_node *x_space=NULL;
if(l>0) x_space = Malloc(svm_node,elements);
int j=0;
for(i=0;i<l;i++)
{
readline(fp);
model->SV[i] = &x_space[j];
p = strtok(line, " \t");
model->sv_coef[0][i] = strtod(p,&endptr);
for(int k=1;k<m;k++)
{
p = strtok(NULL, " \t");
model->sv_coef[k][i] = strtod(p,&endptr);
}
while(1)
{
idx = strtok(NULL, ":");
val = strtok(NULL, " \t");
if(val == NULL)
break;
x_space[j].index = (int) strtol(idx,&endptr,10);
x_space[j].value = strtod(val,&endptr);
++j;
}
x_space[j++].index = -1;
}
free(line);
if (ferror(fp) != 0 || fclose(fp) != 0)
return NULL;
model->free_sv = 1; // XXX
return model;
}
void svm_destroy_model(svm_model* model)
{
if(model->free_sv && model->l > 0)
free((void *)(model->SV[0]));
for(int i=0;i<model->nr_class-1;i++)
free(model->sv_coef[i]);
free(model->SV);
free(model->sv_coef);
free(model->rho);
free(model->label);
free(model->probA);
free(model->probB);
free(model->nSV);
free(model);
}
void svm_destroy_param(svm_parameter* param)
{
free(param->weight_label);
free(param->weight);
}
const char *svm_check_parameter(const svm_problem *prob, const svm_parameter *param)
{
// svm_type
int svm_type = param->svm_type;
if(svm_type != C_SVC &&
svm_type != C_SVC_L2 &&
svm_type != NU_SVC &&
svm_type != ONE_CLASS &&
svm_type != EPSILON_SVR &&
svm_type != NU_SVR &&
svm_type != SVDD &&
svm_type != SVDD_L2)
return "unknown svm type";
// kernel_type, degree
int kernel_type = param->kernel_type;
if(kernel_type != LINEAR &&
kernel_type != POLY &&
kernel_type != GAUSSIAN &&
kernel_type != SIGMOID &&
kernel_type != STUMP &&
kernel_type != PERC &&
kernel_type != LAPLACE &&
kernel_type != EXPO &&
kernel_type != PRECOMPUTED)
return "unknown kernel type";
if(param->gamma < 0)
return "gamma < 0";
if(param->degree < 0)
return "degree of polynomial kernel < 0";
// cache_size,eps,C,nu,p,shrinking
if(param->cache_size <= 0)
return "cache_size <= 0";
if(param->eps <= 0)
return "eps <= 0";
if(svm_type == C_SVC ||
svm_type == EPSILON_SVR ||
svm_type == NU_SVR)
if(param->C <= 0)
return "C <= 0";
if(svm_type == NU_SVC ||
svm_type == ONE_CLASS ||
svm_type == NU_SVR)
if(param->nu <= 0 || param->nu > 1)
return "nu <= 0 or nu > 1";
if(svm_type == EPSILON_SVR)
if(param->p < 0)
return "p < 0";
if(param->shrinking != 0 &&
param->shrinking != 1)
return "shrinking != 0 and shrinking != 1";
if(param->probability != 0 &&
param->probability != 1)
return "probability != 0 and probability != 1";
if(param->probability == 1 &&
(svm_type == ONE_CLASS || svm_type == SVDD || svm_type == SVDD_L2))
return "one-class SVM probability output not supported yet";
// check whether nu-svc is feasible
if(svm_type == NU_SVC)
{
int l = prob->l;
int max_nr_class = 16;
int nr_class = 0;
int *label = Malloc(int,max_nr_class);
int *count = Malloc(int,max_nr_class);
int i;
for(i=0;i<l;i++)
{
int this_label = (int)prob->y[i];
int j;
for(j=0;j<nr_class;j++)
if(this_label == label[j])
{
++count[j];
break;
}
if(j == nr_class)
{
if(nr_class == max_nr_class)
{
max_nr_class *= 2;
label = (int *)realloc(label,max_nr_class*sizeof(int));
count = (int *)realloc(count,max_nr_class*sizeof(int));
}
label[nr_class] = this_label;
count[nr_class] = 1;
++nr_class;
}
}
for(i=0;i<nr_class;i++)
{
int n1 = count[i];
for(int j=i+1;j<nr_class;j++)
{
int n2 = count[j];
if(param->nu*(n1+n2)/2 > min(n1,n2))
{
free(label);
free(count);
return "specified nu is infeasible";
}
}
}
free(label);
free(count);
}
return NULL;
}
int svm_check_probability_model(const svm_model *model)
{
return ((model->param.svm_type == C_SVC || model->param.svm_type == NU_SVC) &&
model->probA!=NULL && model->probB!=NULL) ||
((model->param.svm_type == EPSILON_SVR || model->param.svm_type == NU_SVR) &&
model->probA!=NULL);
}