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svm.cpp
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svm.cpp
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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 <limits.h>
#include <locale.h>
#include "svm.h"
int libsvm_version = LIBSVM_VERSION;
typedef float 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);
}
static 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 double *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 double *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);
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*(x_square[i]+x_square[j]-2*dot(x[i],x[j])));
}
double kernel_sigmoid(int i, int j) const
{
return tanh(gamma*dot(x[i],x[j])+coef0);
}
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 RBF:
kernel_function = &Kernel::kernel_rbf;
break;
case SIGMOID:
kernel_function = &Kernel::kernel_sigmoid;
break;
case PRECOMPUTED:
kernel_function = &Kernel::kernel_precomputed;
break;
}
clone(x,x_,l);
if(kernel_type == RBF)
{
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::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 RBF:
{
double sum = 0;
while(x->index != -1 && y->index !=-1)
{
if(x->index == y->index)
{
double d = x->value - y->value;
sum += d*d;
++x;
++y;
}
else
{
if(x->index > y->index)
{
sum += y->value * y->value;
++y;
}
else
{
sum += x->value * x->value;
++x;
}
}
}
while(x->index != -1)
{
sum += x->value * x->value;
++x;
}
while(y->index != -1)
{
sum += y->value * y->value;
++y;
}
return exp(-param.gamma*sum);
}
case SIGMOID:
return tanh(param.gamma*dot(x,y)+param.coef0);
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 double *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 max_iter = max(10000000, l>INT_MAX/100 ? INT_MAX : 100*l);
int counter = min(l,1000)+1;
while(iter < max_iter)
{
// 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 = QD[i]+QD[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 = QD[i]+QD[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];
}
}
}
if(iter >= max_iter)
{
if(active_size < l)
{
// reconstruct the whole gradient to calculate objective value
reconstruct_gradient();
active_size = l;
info("*");
}
fprintf(stderr,"\nWARNING: reaching max number of iterations\n");
}
// 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 = QD[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 = QD[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 || Gmin_idx == -1)
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;