svm_hideo.c

svm(支持向量机)分类算法本质上是二类分类器

/***********************************************************************/
/*                                                                     */
/*   svm_hideo.c                                                       */
/*                                                                     */
/*   The Hildreth and D'Espo solver specialized for SVMs.              */
/*                                                                     */
/*   Author: Thorsten Joachims                                         */
/*   Date: 02.07.02                                                    */
/*                                                                     */
/*   Copyright (c) 2002  Thorsten Joachims - All rights reserved       */
/*                                                                     */
/*   This software is available for non-commercial use only. It must   */
/*   not be modified and distributed without prior permission of the   */
/*   author. The author is not responsible for implications from the   */
/*   use of this software.                                             */
/*                                                                     */
/***********************************************************************/

# include <math.h>
# include "svm_common.h"

/* 
  solve the quadratic programming problem
 
  minimize   g0 * x + 1/2 x' * G * x
  subject to ce*x = ce0
             l <= x <= u
 
  The linear constraint vector ce can only have -1/+1 as entries 
*/

/* Common Block Declarations */

long verbosity;

# define PRIMAL_OPTIMAL      1
# define DUAL_OPTIMAL        2
# define MAXITER_EXCEEDED    3
# define NAN_SOLUTION        4
# define ONLY_ONE_VARIABLE   5

# define LARGEROUND          0
# define SMALLROUND          1

/* /////////////////////////////////////////////////////////////// */

# define DEF_PRECISION          1E-5
# define DEF_MAX_ITERATIONS     200
# define DEF_LINDEP_SENSITIVITY 1E-8
# define EPSILON_HIDEO          1E-20
# define EPSILON_EQ             1E-5

double *optimize_qp(QP *, double *, long, double *, LEARN_PARM *);
double *primal=0,*dual=0;
long   precision_violations=0;
double opt_precision=DEF_PRECISION;
long   maxiter=DEF_MAX_ITERATIONS;
double lindep_sensitivity=DEF_LINDEP_SENSITIVITY;
double *buffer;
long   *nonoptimal;

long  smallroundcount=0;
long  roundnumber=0;

/* /////////////////////////////////////////////////////////////// */

void *my_malloc();

int optimize_hildreth_despo(long,long,double,double,double,long,long,long,double,double *,
			    double *,double *,double *,double *,double *,
			    double *,double *,double *,long *,double *,double *);
int solve_dual(long,long,double,double,long,double *,double *,double *,
	       double *,double *,double *,double *,double *,double *,
	       double *,double *,double *,double *,long);

void linvert_matrix(double *, long, double *, double, long *);
void lprint_matrix(double *, long);
void ladd_matrix(double *, long, double);
void lcopy_matrix(double *, long, double *);
void lswitch_rows_matrix(double *, long, long, long);
void lswitchrk_matrix(double *, long, long, long);

double calculate_qp_objective(long, double *, double *, double *);



double *optimize_qp(qp,epsilon_crit,nx,threshold,learn_parm)
QP *qp;
double *epsilon_crit;
long nx; /* Maximum number of variables in QP */
double *threshold; 
LEARN_PARM *learn_parm;
/* start the optimizer and return the optimal values */
/* The HIDEO optimizer does not necessarily fully solve the problem. */
/* Since it requires a strictly positive definite hessian, the solution */
/* is restricted to a linear independent subset in case the matrix is */
/* only semi-definite. */
{
  long i,j;
  int result;
  double eq,progress;

  roundnumber++;

  if(!primal) { /* allocate memory at first call */
    primal=(double *)my_malloc(sizeof(double)*nx);
    dual=(double *)my_malloc(sizeof(double)*((nx+1)*2));
    nonoptimal=(long *)my_malloc(sizeof(long)*(nx));
    buffer=(double *)my_malloc(sizeof(double)*((nx+1)*2*(nx+1)*2+
					       nx*nx+2*(nx+1)*2+2*nx+1+2*nx+
					       nx+nx+nx*nx));
    (*threshold)=0;
    for(i=0;i<nx;i++) {
      primal[i]=0;
    }
  }

  if(verbosity>=4) { /* really verbose */
    printf("\n\n");
    eq=qp->opt_ce0[0];
    for(i=0;i<qp->opt_n;i++) {
      eq+=qp->opt_xinit[i]*qp->opt_ce[i];
      printf("%f: ",qp->opt_g0[i]);
      for(j=0;j<qp->opt_n;j++) {
	printf("%f ",qp->opt_g[i*qp->opt_n+j]);
      }
      printf(": a=%.10f < %f",qp->opt_xinit[i],qp->opt_up[i]);
      printf(": y=%f\n",qp->opt_ce[i]);
    }
    if(qp->opt_m) {
      printf("EQ: %f*x0",qp->opt_ce[0]);
      for(i=1;i<qp->opt_n;i++) {
	printf(" + %f*x%ld",qp->opt_ce[i],i);
      }
      printf(" = %f\n\n",-qp->opt_ce0[0]);
    }
  }

  result=optimize_hildreth_despo(qp->opt_n,qp->opt_m,
				 opt_precision,(*epsilon_crit),
				 learn_parm->epsilon_a,maxiter,
				 /* (long)PRIMAL_OPTIMAL, */
				 (long)0, (long)0,
				 lindep_sensitivity,
				 qp->opt_g,qp->opt_g0,qp->opt_ce,qp->opt_ce0,
				 qp->opt_low,qp->opt_up,primal,qp->opt_xinit,
				 dual,nonoptimal,buffer,&progress);
  if(verbosity>=3) { 
    printf("return(%d)...",result);
  }

  if(learn_parm->totwords < learn_parm->svm_maxqpsize) { 
    /* larger working sets will be linear dependent anyway */
    learn_parm->svm_maxqpsize=maxl(learn_parm->totwords,(long)2);
  }

  if(result == NAN_SOLUTION) {
    lindep_sensitivity*=2;  /* throw out linear dependent examples more */
                            /* generously */
    if(learn_parm->svm_maxqpsize>2) {
      learn_parm->svm_maxqpsize--;  /* decrease size of qp-subproblems */
    }
    precision_violations++;
  }

  /* take one round of only two variable to get unstuck */
  if((result != PRIMAL_OPTIMAL) || (!(roundnumber % 31)) || (progress <= 0)) {

    smallroundcount++;

    result=optimize_hildreth_despo(qp->opt_n,qp->opt_m,
				   opt_precision,(*epsilon_crit),
				   learn_parm->epsilon_a,(long)maxiter,
				   (long)PRIMAL_OPTIMAL,(long)SMALLROUND,
				   lindep_sensitivity,
				   qp->opt_g,qp->opt_g0,qp->opt_ce,qp->opt_ce0,
				   qp->opt_low,qp->opt_up,primal,qp->opt_xinit,
				   dual,nonoptimal,buffer,&progress);
    if(verbosity>=3) { 
      printf("return_srd(%d)...",result);
    }

    if(result != PRIMAL_OPTIMAL) {
      if(result != ONLY_ONE_VARIABLE) 
	precision_violations++;
      if(result == MAXITER_EXCEEDED) 
	maxiter+=100;
      if(result == NAN_SOLUTION) {
	lindep_sensitivity*=2;  /* throw out linear dependent examples more */
	                        /* generously */
	/* results not valid, so return inital values */
	for(i=0;i<qp->opt_n;i++) {
	  primal[i]=qp->opt_xinit[i];
	}
      }
    }
  }


  if(precision_violations > 50) {
    precision_violations=0;
    (*epsilon_crit)*=10.0; 
    if(verbosity>=1) {
      printf("\nWARNING: Relaxing epsilon on KT-Conditions (%f).\n",
	     (*epsilon_crit));
    }
  }	  

  if((qp->opt_m>0) && (result != NAN_SOLUTION) && (!isnan(dual[1]-dual[0])))
    (*threshold)=dual[1]-dual[0];
  else
    (*threshold)=0;

  if(verbosity>=4) { /* really verbose */
    printf("\n\n");
    eq=qp->opt_ce0[0];
    for(i=0;i<qp->opt_n;i++) {
      eq+=primal[i]*qp->opt_ce[i];
      printf("%f: ",qp->opt_g0[i]);
      for(j=0;j<qp->opt_n;j++) {
	printf("%f ",qp->opt_g[i*qp->opt_n+j]);
      }
      printf(": a=%.30f",primal[i]);
      printf(": nonopti=%ld",nonoptimal[i]);
      printf(": y=%f\n",qp->opt_ce[i]);
    }
    printf("eq-constraint=%.30f\n",eq);
    printf("b=%f\n",(*threshold));
    printf(" smallroundcount=%ld ",smallroundcount);
  }

  return(primal);
}



int optimize_hildreth_despo(n,m,precision,epsilon_crit,epsilon_a,maxiter,goal,
			    smallround,lindep_sensitivity,g,g0,ce,ce0,low,up,
			    primal,init,dual,lin_dependent,buffer,progress)
     long   n;            /* number of variables */
     long   m;            /* number of linear equality constraints [0,1] */
     double precision;    /* solve at least to this dual precision */
     double epsilon_crit; /* stop, if KT-Conditions approx fulfilled */
     double epsilon_a;    /* precision of alphas at bounds */
     long   maxiter;      /* stop after this many iterations */
     long   goal;         /* keep going until goal fulfilled */
     long   smallround;   /* use only two variables of steepest descent */
     double lindep_sensitivity; /* epsilon for detecting linear dependent ex */
     double *g;           /* hessian of objective */
     double *g0;          /* linear part of objective */
     double *ce,*ce0;     /* linear equality constraints */
     double *low,*up;     /* box constraints */
     double *primal;      /* primal variables */
     double *init;        /* initial values of primal */
     double *dual;        /* dual variables */
     long   *lin_dependent;
     double *buffer;
     double *progress;    /* delta in the objective function between
                             before and after */
{
  long i,j,k,from,to,n_indep,changed;
  double sum,bmin=0,bmax=0;
  double *d,*d0,*ig,*dual_old,*temp,*start;       
  double *g0_new,*g_new,*ce_new,*ce0_new,*low_new,*up_new;
  double add,t;
  int result;
  double obj_before,obj_after; 
  long b1,b2;
  double g0_b1,g0_b2,ce0_b;

  g0_new=&(buffer[0]);    /* claim regions of buffer */
  d=&(buffer[n]);
  d0=&(buffer[n+(n+m)*2*(n+m)*2]);
  ce_new=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2]);
  ce0_new=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2+n]);
  ig=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2+n+m]);
  dual_old=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2+n+m+n*n]);
  low_new=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2+n+m+n*n+(n+m)*2]);
  up_new=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2+n+m+n*n+(n+m)*2+n]);
  start=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2+n+m+n*n+(n+m)*2+n+n]);
  g_new=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2+n+m+n*n+(n+m)*2+n+n+n]);
  temp=&(buffer[n+(n+m)*2*(n+m)*2+(n+m)*2+n+m+n*n+(n+m)*2+n+n+n+n*n]);

  b1=-1;
  b2=-1;
  for(i=0;i<n;i++) {   /* get variables with steepest feasible descent */
    sum=g0[i];         
    for(j=0;j<n;j++) 
      sum+=init[j]*g[i*n+j];
    sum=sum*ce[i];
    if(((b1==-1) || (sum<bmin)) 
       && (!((init[i]<=(low[i]+epsilon_a)) && (ce[i]<0.0)))
       && (!((init[i]>=( up[i]-epsilon_a)) && (ce[i]>0.0)))
       ) {
      bmin=sum;
      b1=i;
    }
    if(((b2==-1) || (sum>=bmax)) 
       && (!((init[i]<=(low[i]+epsilon_a)) && (ce[i]>0.0)))
       && (!((init[i]>=( up[i]-epsilon_a)) && (ce[i]<0.0)))
       ) {
      bmax=sum;
      b2=i;
    }
  }
  /* in case of unbiased hyperplane, the previous projection on */
  /* equality constraint can lead to b1 or b2 being -1. */
  if((b1 == -1) || (b2 == -1)) {
    b1=maxl(b1,b2);
    b2=maxl(b1,b2);
  }

  for(i=0;i<n;i++) {
    start[i]=init[i];
  }

  /* in case both example vectors are linearly dependent */
  /* WARNING: Assumes that ce[] in {-1,1} */
  add=0;
  changed=0;
  if((b1 != b2) && (m==1)) {
    for(i=0;i<n;i++) {  /* fix other vectors */
      if(i==b1) 
	g0_b1=g0[i];
      if(i==b2) 
	g0_b2=g0[i];
    }
    ce0_b=ce0[0];
    for(i=0;i<n;i++) {  
      if((i!=b1) && (i!=b2)) {
	for(j=0;j<n;j++) {
	  if(j==b1) 
	    g0_b1+=start[i]*g[i*n+j];
	  if(j==b2) 
	    g0_b2+=start[i]*g[i*n+j];
	}
	ce0_b-=(start[i]*ce[i]);
      }
    }
    if((g[b1*n+b2] == g[b1*n+b1]) && (g[b1*n+b2] == g[b2*n+b2])) {
      /* printf("euqal\n"); */
      if(ce[b1] == ce[b2]) { 
	if(g0_b1 <= g0_b2) { /* set b1 to upper bound */
	  /* printf("case +=<\n"); */
	  changed=1;
	  t=up[b1]-init[b1];
	  if((init[b2]-low[b2]) < t) {
	    t=init[b2]-low[b2];
	  }
	  start[b1]=init[b1]+t;
	  start[b2]=init[b2]-t;
	}
	else if(g0_b1 > g0_b2) { /* set b2 to upper bound */
	  /* printf("case +=>\n"); */
	  changed=1;
	  t=up[b2]-init[b2];
	  if((init[b1]-low[b1]) < t) {
	    t=init[b1]-low[b1];
	  }
	  start[b1]=init[b1]-t;
	  start[b2]=init[b2]+t;
	}
      }
      else if(((g[b1*n+b1]>0) || (g[b2*n+b2]>0))) { /* (ce[b1] != ce[b2]) */ 
	/* printf("case +!\n"); */
	t=((ce[b2]/ce[b1])*g0[b1]-g0[b2]+ce0[0]*(g[b1*n+b1]*ce[b2]/ce[b1]-g[b1*n+b2]/ce[b1]))/((ce[b2]*ce[b2]/(ce[b1]*ce[b1]))*g[b1*n+b1]+g[b2*n+b2]-2*(g[b1*n+b2]*ce[b2]/ce[b1]))-init[b2];
	changed=1;
	if((up[b2]-init[b2]) < t) {
	  t=up[b2]-init[b2];
	}
	if((init[b2]-low[b2]) < -t) {
	  t=-(init[b2]-low[b2]);
	}
	if((up[b1]-init[b1]) < t) {
	  t=(up[b1]-init[b1]);
	}
	if((init[b1]-low[b1]) < -t) {
	  t=-(init[b1]-low[b1]);
	}
	start[b1]=init[b1]+t;
	start[b2]=init[b2]+t;
      }
    }
    if((-g[b1*n+b2] == g[b1*n+b1]) && (-g[b1*n+b2] == g[b2*n+b2])) {
      /* printf("diffeuqal\n"); */
      if(ce[b1] != ce[b2]) {
	if((g0_b1+g0_b2) < 0) { /* set b1 and b2 to upper bound */
	  /* printf("case -!<\n"); */
	  changed=1;
	  t=up[b1]-init[b1];
	  if((up[b2]-init[b2]) < t) {
	    t=up[b2]-init[b2];
	  }
	  start[b1]=init[b1]+t;
	  start[b2]=init[b2]+t;
	}     
	else if((g0_b1+g0_b2) >= 0) { /* set b1 and b2 to lower bound */
	  /* printf("case -!>\n"); */
	  changed=1;
	  t=init[b1]-low[b1];
	  if((init[b2]-low[b2]) < t) {
	    t=init[b2]-low[b2];
	  }
	  start[b1]=init[b1]-t;
	  start[b2]=init[b2]-t;
	}
      }
      else if(((g[b1*n+b1]>0) || (g[b2*n+b2]>0))) { /* (ce[b1]==ce[b2]) */
	/*  printf("case -=\n"); */
	t=((ce[b2]/ce[b1])*g0[b1]-g0[b2]+ce0[0]*(g[b1*n+b1]*ce[b2]/ce[b1]-g[b1*n+b2]/ce[b1]))/((ce[b2]*ce[b2]/(ce[b1]*ce[b1]))*g[b1*n+b1]+g[b2*n+b2]-2*(g[b1*n+b2]*ce[b2]/ce[b1]))-init[b2];
	changed=1;
	if((up[b2]-init[b2]) < t) {
	  t=up[b2]-init[b2];
	}
	if((init[b2]-low[b2]) < -t) {
	  t=-(init[b2]-low[b2]);
	}
	if((up[b1]-init[b1]) < -t) {
	  t=-(up[b1]-init[b1]);
	}
	if((init[b1]-low[b1]) < t) {
	  t=init[b1]-low[b1];
	}
	start[b1]=init[b1]-t;
	start[b2]=init[b2]+t;
      }	
    }
  }
  /* if we have a biased hyperplane, then adding a constant to the */
  /* hessian does not change the solution. So that is done for examples */
  /* with zero diagonal entry, since HIDEO cannot handle them. */
  if((m>0) 
     && ((fabs(g[b1*n+b1]) < lindep_sensitivity) 
	 || (fabs(g[b2*n+b2]) < lindep_sensitivity))) {
    /* printf("Case 0\n"); */
    add+=0.093274;
  }    
  /* in case both examples are linear dependent */
  else if((m>0) 
	  && (g[b1*n+b2] != 0 && g[b2*n+b2] != 0)
	  && (fabs(g[b1*n+b1]/g[b1*n+b2] - g[b1*n+b2]/g[b2*n+b2])
	      < lindep_sensitivity)) { 
    /* printf("Case lindep\n"); */
    add+=0.078274;
  }

  /* special case for zero diagonal entry on unbiased hyperplane */
  if((m==0) && (b1>=0))  {
    if(fabs(g[b1*n+b1]) < lindep_sensitivity) { 
      /* printf("Case 0b1\n"); */
      for(i=0;i<n;i++) {  /* fix other vectors */
	if(i==b1) 
	  g0_b1=g0[i];
      }
      for(i=0;i<n;i++) {  
	if(i!=b1) {
	  for(j=0;j<n;j++) {
	    if(j==b1) 
	      g0_b1+=start[i]*g[i*n+j];
	  }
	}
      }
      if(g0_b1<0)
	start[b1]=up[b1];
      if(g0_b1>=0)
	start[b1]=low[b1];
    }
  }
  if((m==0) && (b2>=0))  {
    if(fabs(g[b2*n+b2]) < lindep_sensitivity) { 
      /* printf("Case 0b2\n"); */
      for(i=0;i<n;i++) {  /* fix other vectors */
	if(i==b2) 
	  g0_b2=g0[i];
      }
      for(i=0;i<n;i++) {  
	if(i!=b2) {
	  for(j=0;j<n;j++) {
	    if(j==b2) 
	      g0_b2+=start[i]*g[i*n+j];
	  }
	}
      }
      if(g0_b2<0)
	start[b2]=up[b2];
      if(g0_b2>=0)
	start[b2]=low[b2];
    }
  }

  /* printf("b1=%ld,b2=%ld\n",b1,b2); */

  lcopy_matrix(g,n,d);
  if((m==1) && (add>0.0)) {
    for(j=0;j<n;j++) {
      for(k=0;k<n;k++) {
	d[j*n+k]+=add*ce[j]*ce[k];
      }
    }
  }
  else {
    add=0.0;
  }

  if(n>2) {                    /* switch, so that variables are better mixed */
    lswitchrk_matrix(d,n,b1,(long)0); 
    if(b2 == 0) 
      lswitchrk_matrix(d,n,b1,(long)1); 
    else
      lswitchrk_matrix(d,n,b2,(long)1); 
  }
  if(smallround == SMALLROUND) {
    for(i=2;i<n;i++) {
      lin_dependent[i]=1;
    }
    if(m>0) { /* for biased hyperplane, pick two variables */
      lin_dependent[0]=0;
      lin_dependent[1]=0;
    }
    else {    /* for unbiased hyperplane, pick only one variable */
      lin_dependent[0]=smallroundcount % 2;
      lin_dependent[1]=(smallroundcount+1) % 2;
    }
  }
  else {
    for(i=0;i<n;i++) {
      lin_dependent[i]=0;
    }
  }
  linvert_matrix(d,n,ig,lindep_sensitivity,lin_dependent);
  if(n>2) {                    /* now switch back */
    if(b2 == 0) {