Results* join_clusters2_restart
(double *x,//array/matrix of data
SymNoDiag *W,//lower triangle of weight matrix
unsigned int Px,//problem size
double lambda,//starting point in regularization path
double join_thresh, //tolerance for equality of points
double opt_thresh, //tolerance for optimality
double lambda_factor,//increase of lambda after optimality
double smooth,//smoothing parameter
int maxit,
int linesearch_freq,//how often to do a linesearch? if 0, never. if
//n>0, do n-1 linesearch steps for every
//decreasing step size step. set this to 2 if
//unsure.
int linesearch_points,//how many points to check along the gradient
//direction. set to 10 if unsure.
int check_splits,
int target_cluster,
int verbose
){
unsigned int N = W->N;
//W->print();
double old_lambda=0;
std::vector<int> rows,rowsj;
std::vector<int>::iterator rowit,ri,rj;
std::list< std::vector<int> > clusters,tocheck;
std::list< std::vector<int> >::iterator it,cj;
unsigned int i,k,j;
int tried_restart;
for(i=0;i<N;i++){
rows.assign(1,i);
clusters.push_back(rows);
}
double *old_alpha = new double[N*Px];
double *alpha = new double[N*Px];
double *xbar = new double[N*Px];
double *dir = new double[N*Px];
for(i=0;i<N*Px;i++){
alpha[i]=xbar[i]=x[i];
}
Matrix amat(alpha,N,Px),xmat(x,N,Px);
SymNoDiag diffs(N);
diffs.calc_diffs(clusters,amat,nrm2);
//store initial trivial solution
Results *results = new Results(N,Px,opt_thresh);
if(target_cluster==0)results->add(alpha,0,0);
double weight,diff,step;
while(clusters.size()>1){
double grad=opt_thresh;
int iteration=1;
tried_restart=0;
//if we use the general (slower) algorithm for any weights, then
//split the clusters to individual points
if(check_splits){
clusters.clear();
//reassign original clusters
for(i=0;i<N;i++){
rows.assign(1,i);
clusters.push_back(rows);
}
//recopy original xbar
for(i=0;i<N*Px;i++){
xbar[i]=x[i];
}
}
while(grad>=opt_thresh){
//first calc gradients
grad = 0;
for(it=clusters.begin();it!=clusters.end();it++){
rows = *it;
i = rows[0];
for(k=0;k<Px;k++){
dir[i+k*N] = xbar[i+k*N] - alpha[i+k*N];
}
for(cj=clusters.begin();cj!=clusters.end();cj++){
if(it!=cj){
rowsj = *cj;
j=rowsj[0];
weight=0;
diff = *diffs(i,j);
if(diff!=0){
if(smooth!=0){
diff *= diff; //now squared l2 norm
diff += smooth; //add smoothing parameter under sqrt
diff = sqrt(diff);//put sqrt back
}
for(ri=rows.begin();ri!=rows.end();ri++){
for(rj=rowsj.begin();rj!=rowsj.end();rj++){
weight += W->getval(*ri,*rj);
}
}
//weight *= lambda / diff / ((double)(N-1)) / ((double)rows.size());
weight *= lambda / diff / ((double)rows.size());
for(k=0;k<Px;k++){
dir[i+k*N] += weight * (alpha[j+k*N]-alpha[i+k*N]);
}
}
}
}
grad += nrm2(Array(dir+i,N,Px));
}
//store this iteration
//results->add(alpha,lambda,grad);
//then take a step
if(linesearch_freq==0 || (iteration % linesearch_freq)==0 ){
//Decreasing step size
//TDH and pierre 18 jan 2011 try sqrt dec step size
step=1/((double)iteration);
//step=1/sqrt((double)iteration);
if(verbose>=2)printf("grad %f step %f it %d\n",grad,step,iteration);
take_step(clusters,alpha,dir,N,Px,step);
}else{
double cost_here,cost_step;
std::map<double,double> cost_steps;
std::map<double,double>::iterator step1,step2;
for(i=0;i<N*Px;i++)old_alpha[i]=alpha[i];//copy alpha
//compare current cost to cost after stepping in gradient direction
cost_here=cost_step=calc_cost(clusters,amat,xmat,W,diffs,lambda);
step = 0;
cost_steps.insert(std::pair<double,double>(cost_here,0));
while(cost_step<=cost_here){
take_step(clusters,alpha,dir,N,Px,1);
step += 1;
diffs.calc_diffs(clusters,amat,nrm2);
cost_step=calc_cost(clusters,amat,xmat,W,diffs,lambda);
if(verbose>=2)
printf("cost %.10f step %f cost_here %f\n",cost_step,step,cost_here);
cost_steps.insert(std::pair<double,double>(cost_step,step));
}
for(int cuts=0;cuts<linesearch_points;cuts++){
step1=step2=cost_steps.begin();
step2++;
step = (step1->second + step2->second)/2;
for(i=0;i<N*Px;i++){
alpha[i]=old_alpha[i];
}
take_step(clusters,alpha,dir,N,Px,step);
diffs.calc_diffs(clusters,amat,nrm2);
cost_step=calc_cost(clusters,amat,xmat,W,diffs,lambda);
if(verbose>=2)printf("cost %.10f step %f %d\n",cost_step,step,cuts);
cost_steps.insert(std::pair<double,double>(cost_step,step));
}
cost_steps.clear();
}
if(iteration++ > maxit){
if(tried_restart){
printf("max iteration %d exit\n",maxit);
delete old_alpha;
delete alpha;
delete xbar;
delete dir;
return results;
}else{
if(verbose>=1)printf("max iterations, trying restart from x\n");
tried_restart=1;
iteration=1;
for(i=0;i<N*Px;i++)alpha[i]=x[i];
}
}
//calculate differences
diffs.calc_diffs(clusters,amat,nrm2);
//check for joins
JoinPair tojoin;
while(dojoin(tojoin=check_clusters_thresh(&clusters,diffs,join_thresh))){
//if(verbose>=1)
// printf("join: %d %d\n",tojoin.first->front(),tojoin.second->front());
int ni=tojoin.first->size();
int nj=tojoin.second->size();
i=tojoin.first->front();
j=tojoin.second->front();
tojoin.first->insert(tojoin.first->end(),
tojoin.second->begin(),
tojoin.second->end());
for(k=0;k<Px;k++){
alpha[i+k*N] = (alpha[i+k*N]*ni + alpha[j+k*N]*nj)/(ni+nj);
xbar[i+k*N] = (xbar[i+k*N]*ni + xbar[j+k*N]*nj)/(ni+nj);
}
clusters.erase(tojoin.second);
iteration=1;
if(clusters.size()>1){
diffs.calc_diffs(clusters,amat,nrm2);//inefficient
}else{
grad=0;//so we can escape from the last optimization loop
}
}
}//while(grad>=opt_thresh)
if(verbose>=1)
printf("solution iteration %d lambda %f nclusters %d\n",
iteration,lambda,(int)clusters.size());
if(target_cluster == 0){
//for each cluster, there may be several points. we store the
//alpha value just in the row of the first point. thus here we
//copy this value to the other rows before copying the optimal
//alpha to results.
for(it=clusters.begin();it!=clusters.end();it++){
rows = *it;
if(rows.size()>1){
for(i=1;i<rows.size();i++){
for(k=0;k<Px;k++){
alpha[rows[i]+k*N] = alpha[rows[0]+k*N];
}
}
}
}
results->add(alpha,lambda,grad);
}
//haven't yet reached the target number of clusters, multiply
//lambda by lambda_factor and continue along the path
if((int)clusters.size()>target_cluster){
old_lambda=lambda;
lambda *= lambda_factor;
}
//if we have passed the target cluster number then decrease
//lambda and go look for it!
if((int)clusters.size()<target_cluster){
if(verbose>=1){
printf("missed target %d, going back for it\n",target_cluster);
}
lambda = (lambda+old_lambda)/2;
clusters.clear();
//reassign original clusters
for(i=0;i<N;i++){
rows.assign(1,i);
clusters.push_back(rows);
}
//recopy original xbar
for(i=0;i<N*Px;i++){
xbar[i]=x[i];
}
}
//this is the number of clusters that we were looking for,
//save and quit!
if((int)clusters.size()==target_cluster){
for(it=clusters.begin();it!=clusters.end();it++){
rows = *it;
if(rows.size()>1){
for(i=1;i<rows.size();i++){
for(k=0;k<Px;k++){
alpha[rows[i]+k*N] = alpha[rows[0]+k*N];
}
}
}
}
results->add(alpha,lambda,grad);
if(verbose>=1)printf("got target cluster %d exit\n",target_cluster);
delete old_alpha;
delete alpha;
delete xbar;
delete dir;
return results;
}
}
//TODO: consolidate cleanup... just use data structures that
//automatically clean themselves up when the function exits.
delete old_alpha;
delete alpha;
delete xbar;
delete dir;
return results;
}
Results *Recognizer::recognize(Character *ch, unsigned int n_results) {
unsigned int group_id, i, size, n_chars, char_id, n_group_chars;
unsigned int n_vectors, n_strokes;
float *cursor = strokedata;
float *input;
n_vectors = ch->get_n_vectors();
n_strokes = ch->get_n_strokes();
input = ch->get_points();
#if 0
assert_aligned16((char *) input);
#endif
for (group_id=0, n_chars=0, char_id=0; group_id < n_groups; group_id++) {
/* Only compare the input with templates which have
+- window_size the same number of strokes as the input */
if (n_strokes > window_size) {
if (groups[group_id].n_strokes > (n_strokes + window_size))
break;
if (groups[group_id].n_strokes < (n_strokes - window_size)) {
char_id += groups[group_id].n_chars;
continue;
}
}
cursor = (float *) (data + groups[group_id].offset);
#ifdef __SSE__
float *ref1, *ref2, *ref3, *ref4;
unsigned int size1, size2, size3, size4;
wg_v4sf dtwres4;
/* Process 4 reference characters at a time */
for (i=0; i < (groups[group_id].n_chars / 4); i++) {
distm[n_chars].unicode = characters[char_id].unicode;
ref1 = cursor;
size1 = characters[char_id].n_vectors;
ref2 = ref1 + characters[char_id].n_vectors * VEC_DIM_MAX;
char_id++;
distm[n_chars+1].unicode = characters[char_id].unicode;
size2 = characters[char_id].n_vectors;
ref3 = ref2 + characters[char_id].n_vectors * VEC_DIM_MAX;
char_id++;
distm[n_chars+2].unicode = characters[char_id].unicode;
size3 = characters[char_id].n_vectors;
ref4 = ref3 + characters[char_id].n_vectors * VEC_DIM_MAX;
char_id++;
distm[n_chars+3].unicode = characters[char_id].unicode;
size4 = characters[char_id].n_vectors;
cursor = ref4 + characters[char_id].n_vectors *
VEC_DIM_MAX;
char_id++;
dtwres4 = dtw4(input, n_vectors,
ref1, size1,
ref2, size2,
ref3, size3,
ref4, size4);
distm[n_chars++].dist = dtwres4.s[0];
distm[n_chars++].dist = dtwres4.s[1];
distm[n_chars++].dist = dtwres4.s[2];
distm[n_chars++].dist = dtwres4.s[3];
}
/* Process the remaining of references */
n_group_chars = (groups[group_id].n_chars % 4);
#else
/* SSE not available, we need to process references sequentially */
n_group_chars = groups[group_id].n_chars;
#endif
for (i=0; i < n_group_chars; i++) {
distm[n_chars].unicode = characters[char_id].unicode;
distm[n_chars].dist = dtw(input, n_vectors,
cursor, characters[char_id].n_vectors);
cursor += characters[char_id].n_vectors * VEC_DIM_MAX;
char_id++;
n_chars++;
}
}
/* sort the results with glibc's quicksort */
qsort ((void *) distm,
(size_t) n_chars,
sizeof (CharDist),
(int (*) (const void *, const void*)) char_dist_cmp);
size = MIN(n_chars, n_results);
Results *results = new Results(size);
for(i=0; i < size; i++)
results->add(i, distm[i].unicode, distm[i].dist);
return results;
}