LaRank.cpp

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// -*- C++ -*-
// Main functions of the LaRank algorithm for soving Multiclass SVM
// Copyright (C) 2008- Antoine Bordes
// Shogun specific adjustments (w) 2009 Soeren Sonnenburg

// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// 
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
// 
// You should have received a copy of the GNU General Public License
// aint64_t with this program; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111, USA
//
/***********************************************************************
 * 
 *  LUSH Lisp Universal Shell
 *    Copyright (C) 2002 Leon Bottou, Yann Le Cun, AT&T Corp, NECI.
 *  Includes parts of TL3:
 *    Copyright (C) 1987-1999 Leon Bottou and Neuristique.
 *  Includes selected parts of SN3.2:
 *    Copyright (C) 1991-2001 AT&T Corp.
 * 
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 * 
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 * 
 *  You should have received a copy of the GNU General Public License
 *  aint64_t with this program; if not, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111, USA
 * 
 ***********************************************************************/

/***********************************************************************
 * $Id: kcache.c,v 1.9 2007/01/25 22:42:09 leonb Exp $
 **********************************************************************/

#include <vector>
#include <algorithm>

#include <shogun/io/SGIO.h>
#include <shogun/lib/Signal.h>
#include <shogun/lib/Time.h>
#include <shogun/mathematics/Math.h>
#include <shogun/classifier/svm/LaRank.h>
#include <shogun/kernel/Kernel.h>

using namespace shogun;

namespace shogun
{
    static larank_kcache_t* larank_kcache_create (CKernel* kernelfunc)
    {
        larank_kcache_t *self;
        self = SG_CALLOC (larank_kcache_t, 1);
        self->l = 0;
        self->maxrowlen = 0;
        self->func = kernelfunc;
        self->prevbuddy = self;
        self->nextbuddy = self;
        self->cursize = sizeof (larank_kcache_t);
        self->maxsize = 256 * 1024 * 1024;
        self->qprev = SG_MALLOC(int32_t, 1);
        self->qnext = SG_MALLOC(int32_t, 1);
        self->rnext = self->qnext + 1;
        self->rprev = self->qprev + 1;
        self->rprev[-1] = -1;
        self->rnext[-1] = -1;
        return self;
    }

    static void xtruncate (larank_kcache_t * self, int32_t k, int32_t nlen)
    {
        int32_t olen = self->rsize[k];
        if (nlen < olen)
        {
            float32_t *ndata;
            float32_t *odata = self->rdata[k];
            if (nlen > 0)
            {
                ndata = SG_MALLOC(float32_t, nlen);
                memcpy (ndata, odata, nlen * sizeof (float32_t));
            }
            else
            {
                ndata = 0;
                self->rnext[self->rprev[k]] = self->rnext[k];
                self->rprev[self->rnext[k]] = self->rprev[k];
                self->rnext[k] = self->rprev[k] = k;
            }
            SG_FREE (odata);
            self->rdata[k] = ndata;
            self->rsize[k] = nlen;
            self->cursize += (int64_t) (nlen - olen) * sizeof (float32_t);
        }
    }

    static void xpurge (larank_kcache_t * self)
    {
        if (self->cursize > self->maxsize)
        {
            int32_t k = self->rprev[-1];
            while (self->cursize > self->maxsize && k != self->rnext[-1])
            {
                int32_t pk = self->rprev[k];
                xtruncate (self, k, 0);
                k = pk;
            }
        }
    }

    static void larank_kcache_set_maximum_size (larank_kcache_t * self, int64_t entries)
    {
        ASSERT (self);
        ASSERT (entries > 0);
        self->maxsize = entries;
        xpurge (self);
    }

    static void larank_kcache_destroy (larank_kcache_t * self)
    {
        if (self)
        {
            int32_t i;
            larank_kcache_t *nb = self->nextbuddy;
            larank_kcache_t *pb = self->prevbuddy;
            pb->nextbuddy = nb;
            nb->prevbuddy = pb;
            /* delete */
            if (self->i2r)
                SG_FREE (self->i2r);
            if (self->r2i)
                SG_FREE (self->r2i);
            if (self->rdata)
                for (i = 0; i < self->l; i++)
                    if (self->rdata[i])
                        SG_FREE (self->rdata[i]);
            if (self->rdata)
                SG_FREE (self->rdata);
            if (self->rsize)
                SG_FREE (self->rsize);
            if (self->rdiag)
                SG_FREE (self->rdiag);
            if (self->qnext)
                SG_FREE (self->qnext);
            if (self->qprev)
                SG_FREE (self->qprev);
            memset (self, 0, sizeof (larank_kcache_t));
            SG_FREE (self);
        }
    }

    static void xminsize (larank_kcache_t * self, int32_t n)
    {
        int32_t ol = self->l;
        if (n > ol)
        {
            int32_t i;
            int32_t nl = CMath::max (256, ol);
            while (nl < n)
                nl = nl + nl;
            self->i2r = SG_REALLOC (int32_t, self->i2r, nl);
            self->r2i = SG_REALLOC (int32_t, self->r2i, nl);
            self->rsize = SG_REALLOC (int32_t, self->rsize, nl);
            self->qnext = SG_REALLOC (int32_t, self->qnext, (1 + nl));
            self->qprev = SG_REALLOC (int32_t, self->qprev, (1 + nl));
            self->rdiag = SG_REALLOC (float32_t, self->rdiag, nl);
            self->rdata = SG_REALLOC (float32_t*, self->rdata, nl);
            self->rnext = self->qnext + 1;
            self->rprev = self->qprev + 1;
            for (i = ol; i < nl; i++)
            {
                self->i2r[i] = i;
                self->r2i[i] = i;
                self->rsize[i] = -1;
                self->rnext[i] = i;
                self->rprev[i] = i;
                self->rdata[i] = 0;
            }
            self->l = nl;
        }
    }

    static int32_t* larank_kcache_r2i (larank_kcache_t * self, int32_t n)
    {
        xminsize (self, n);
        return self->r2i;
    }

    static void xextend (larank_kcache_t * self, int32_t k, int32_t nlen)
    {
        int32_t olen = self->rsize[k];
        if (nlen > olen)
        {
            float32_t *ndata = SG_MALLOC(float32_t, nlen);
            if (olen > 0)
            {
                float32_t *odata = self->rdata[k];
                memcpy (ndata, odata, olen * sizeof (float32_t));
                SG_FREE (odata);
            }
            self->rdata[k] = ndata;
            self->rsize[k] = nlen;
            self->cursize += (int64_t) (nlen - olen) * sizeof (float32_t);
            self->maxrowlen = CMath::max (self->maxrowlen, nlen);
        }
    }

    static void xswap (larank_kcache_t * self, int32_t i1, int32_t i2, int32_t r1, int32_t r2)
    {
        /* swap row data */
        if (r1 < self->maxrowlen || r2 < self->maxrowlen)
        {
            int32_t mrl = 0;
            int32_t k = self->rnext[-1];
            while (k >= 0)
            {
                int32_t nk = self->rnext[k];
                int32_t n = self->rsize[k];
                int32_t rr = self->i2r[k];
                float32_t *d = self->rdata[k];
                if (r1 < n)
                {
                    if (r2 < n)
                    {
                        float32_t t1 = d[r1];
                        float32_t t2 = d[r2];
                        d[r1] = t2;
                        d[r2] = t1;
                    }
                    else if (rr == r2)
                    {
                        d[r1] = self->rdiag[k];
                    }
                    else
                    {
                        int32_t arsize = self->rsize[i2];
                        if (rr < arsize && rr != r1)
                            d[r1] = self->rdata[i2][rr];
                        else
                            xtruncate (self, k, r1);
                    }
                }
                else if (r2 < n)
                {
                    if (rr == r1)
                    {
                        d[r2] = self->rdiag[k];
                    }
                    else
                    {
                        int32_t arsize = self->rsize[i1];
                        if (rr < arsize && rr != r2)
                            d[r2] = self->rdata[i1][rr];
                        else
                            xtruncate (self, k, r2);
                    }
                }
                mrl = CMath::max (mrl, self->rsize[k]);
                k = nk;
            }
            self->maxrowlen = mrl;
        }
        /* swap r2i and i2r */
        self->r2i[r1] = i2;
        self->r2i[r2] = i1;
        self->i2r[i1] = r2;
        self->i2r[i2] = r1;
    }

    static void larank_kcache_swap_rr (larank_kcache_t * self, int32_t r1, int32_t r2)
    {
        xminsize (self, 1 + CMath::max(r1, r2));
        xswap (self, self->r2i[r1], self->r2i[r2], r1, r2);
    }

    static void larank_kcache_swap_ri (larank_kcache_t * self, int32_t r1, int32_t i2)
    {
        xminsize (self, 1 + CMath::max (r1, i2));
        xswap (self, self->r2i[r1], i2, r1, self->i2r[i2]);
    }

    static float64_t xquery (larank_kcache_t * self, int32_t i, int32_t j)
    {
        /* search buddies */
        larank_kcache_t *cache = self->nextbuddy;
        do
        {
            int32_t l = cache->l;
            if (i < l && j < l)
            {
                int32_t s = cache->rsize[i];
                int32_t p = cache->i2r[j];
                if (p < s)
                    return cache->rdata[i][p];
                if (i == j && s >= 0)
                    return cache->rdiag[i];
                p = cache->i2r[i];
                s = cache->rsize[j];
                if (p < s)
                    return cache->rdata[j][p];
            }
            cache = cache->nextbuddy;
        }
        while (cache != self);
        /* compute */
        return self->func->kernel(i, j);
    }


    static float64_t larank_kcache_query (larank_kcache_t * self, int32_t i, int32_t j)
    {
        ASSERT (self);
        ASSERT (i >= 0);
        ASSERT (j >= 0);
        return xquery (self, i, j);
    }


    static void larank_kcache_set_buddy (larank_kcache_t * self, larank_kcache_t * buddy)
    {
        larank_kcache_t *p = self;
        larank_kcache_t *selflast = self->prevbuddy;
        larank_kcache_t *buddylast = buddy->prevbuddy;
        /* check functions are identical */
        ASSERT (self->func == buddy->func);
        /* make sure we are not already buddies */
        do
        {
            if (p == buddy)
                return;
            p = p->nextbuddy;
        }
        while (p != self);
        /* link */
        selflast->nextbuddy = buddy;
        buddy->prevbuddy = selflast;
        buddylast->nextbuddy = self;
        self->prevbuddy = buddylast;
    }


    static float32_t* larank_kcache_query_row (larank_kcache_t * self, int32_t i, int32_t len)
    {
        ASSERT (i >= 0);
        if (i < self->l && len <= self->rsize[i])
        {
            self->rnext[self->rprev[i]] = self->rnext[i];
            self->rprev[self->rnext[i]] = self->rprev[i];
        }
        else
        {
            int32_t olen, p;
            float32_t *d;
            if (i >= self->l || len >= self->l)
                xminsize (self, CMath::max (1 + i, len));
            olen = self->rsize[i];
            if (olen < len)
            {
                if (olen < 0)
                {
                    self->rdiag[i] = self->func->kernel(i, i);
                    olen = self->rsize[i] = 0;
                }
                xextend (self, i, len);
                d = self->rdata[i];
                self->rsize[i] = olen;
                for (p = olen; p < len; p++)
                    d[p] = larank_kcache_query (self, self->r2i[p], i);
                self->rsize[i] = len;
            }
            self->rnext[self->rprev[i]] = self->rnext[i];
            self->rprev[self->rnext[i]] = self->rprev[i];
            xpurge (self);
        }
        self->rprev[i] = -1;
        self->rnext[i] = self->rnext[-1];
        self->rnext[self->rprev[i]] = i;
        self->rprev[self->rnext[i]] = i;
        return self->rdata[i];
    }

}


// Initializing an output class (basically creating a kernel cache for it)
void LaRankOutput::initialize (CKernel* kfunc, int64_t cache)
{
    kernel = larank_kcache_create (kfunc);
    larank_kcache_set_maximum_size (kernel, cache * 1024 * 1024);
    beta = SG_MALLOC(float32_t, 1);
    g = SG_MALLOC(float32_t, 1);
    *beta=0;
    *g=0;
    l = 0;
}

// Destroying an output class (basically destroying the kernel cache)
void LaRankOutput::destroy ()
{
    larank_kcache_destroy (kernel);
    kernel=NULL;
    SG_FREE(beta);
    SG_FREE(g);
    beta=NULL;
    g=NULL;
}

// !Important! Computing the score of a given input vector for the actual output
float64_t LaRankOutput::computeScore (int32_t x_id)
{
    if (l == 0)
        return 0;
    else
    {
        float32_t *row = larank_kcache_query_row (kernel, x_id, l);
        return CMath::dot (beta, row, l);
    }
}

// !Important! Computing the gradient of a given input vector for the actual output           
float64_t LaRankOutput::computeGradient (int32_t xi_id, int32_t yi, int32_t ythis)
{
    return (yi == ythis ? 1 : 0) - computeScore (xi_id);
}

// Updating the solution in the actual output
void LaRankOutput::update (int32_t x_id, float64_t lambda, float64_t gp)
{
    int32_t *r2i = larank_kcache_r2i (kernel, l);
    int64_t xr = l + 1;
    for (int32_t r = 0; r < l; r++)
        if (r2i[r] == x_id)
        {
            xr = r;
            break;
        }

    // updates the cache order and the beta coefficient
    if (xr < l)
    {
        beta[xr]+=lambda;
    }
    else
    {
        larank_kcache_swap_ri (kernel, l, x_id);
        CMath::resize(g, l, l+1);
        CMath::resize(beta, l, l+1);
        g[l]=gp;
        beta[l]=lambda;
        l++;
    }

    // update stored gradients
    float32_t *row = larank_kcache_query_row (kernel, x_id, l);
    for (int32_t r = 0; r < l; r++)
    {
        float64_t oldg = g[r];
        g[r]=oldg - lambda * row[r];
    }
}

// Linking the cahe of this output to the cache of an other "buddy" output
// so that if a requested value is not found in this cache, you can ask your buddy if it has it.                              
void LaRankOutput::set_kernel_buddy (larank_kcache_t * bud)
{
    larank_kcache_set_buddy (bud, kernel);
}

// Removing useless support vectors (for which beta=0)                
int32_t LaRankOutput::cleanup ()
{
    int32_t count = 0;
    std::vector < int32_t >idx;
    for (int32_t x = 0; x < l; x++)
    {
        if ((beta[x] < FLT_EPSILON) && (beta[x] > -FLT_EPSILON))
        {
            idx.push_back (x);
            count++;
        }
    }
    int32_t new_l = l - count;
    for (int32_t xx = 0; xx < count; xx++)
    {
        int32_t i = idx[xx] - xx;
        for (int32_t r = i; r < (l - 1); r++)
        {
            larank_kcache_swap_rr (kernel, r, int64_t(r) + 1);
            beta[r]=beta[r + 1];
            g[r]=g[r + 1];
        }
    }
    CMath::resize(beta, l, new_l+1);
    CMath::resize(g, l, new_l+1);
    beta[new_l]=0;
    g[new_l]=0;
    l = new_l;
    return count;
}

// --- Below are information or "get" functions --- //
//
float64_t LaRankOutput::getW2 ()
{
    float64_t sum = 0;
    int32_t *r2i = larank_kcache_r2i (kernel, l + 1);
    for (int32_t r = 0; r < l; r++)
    {
        float32_t *row_r = larank_kcache_query_row (kernel, r2i[r], l);
        sum += beta[r] * CMath::dot (beta, row_r, l);
    }
    return sum;
}

float64_t LaRankOutput::getKii (int32_t x_id)
{
    return larank_kcache_query (kernel, x_id, x_id);
}

//
float64_t LaRankOutput::getBeta (int32_t x_id)
{
    int32_t *r2i = larank_kcache_r2i (kernel, l);
    int32_t xr = -1;
    for (int32_t r = 0; r < l; r++)
        if (r2i[r] == x_id)
        {
            xr = r;
            break;
        }
    return (xr < 0 ? 0 : beta[xr]);
}

//
float64_t LaRankOutput::getGradient (int32_t x_id)
{
    int32_t *r2i = larank_kcache_r2i (kernel, l);
    int32_t xr = -1;
    for (int32_t r = 0; r < l; r++)
        if (r2i[r] == x_id)
        {
            xr = r;
            break;
        }
    return (xr < 0 ? 0 : g[xr]);
}
bool LaRankOutput::isSupportVector (int32_t x_id) const
{
    int32_t *r2i = larank_kcache_r2i (kernel, l);
    int32_t xr = -1;
    for (int32_t r = 0; r < l; r++)
        if (r2i[r] == x_id)
        {
            xr = r;
            break;
        }
    return (xr >= 0);
}

//
int32_t LaRankOutput::getSV (float32_t* &sv) const
{
    sv=SG_MALLOC(float32_t, l);
    int32_t *r2i = larank_kcache_r2i (kernel, l);
    for (int32_t r = 0; r < l; r++)
        sv[r]=r2i[r];
    return l;
}

CLaRank::CLaRank (): CMultiClassSVM(ONE_VS_REST), 
    nb_seen_examples (0), nb_removed (0),
    n_pro (0), n_rep (0), n_opt (0),
    w_pro (1), w_rep (1), w_opt (1), y0 (0), dual (0),
    batch_mode(true), step(0)
{
}

CLaRank::CLaRank (float64_t C, CKernel* k, CLabels* lab):
    CMultiClassSVM(ONE_VS_REST, C, k, lab), 
    nb_seen_examples (0), nb_removed (0),
    n_pro (0), n_rep (0), n_opt (0),
    w_pro (1), w_rep (1), w_opt (1), y0 (0), dual (0),
    batch_mode(true), step(0)
{
}

CLaRank::~CLaRank ()
{
    destroy();
}

bool CLaRank::train_machine(CFeatures* data)
{
    tau = 0.0001;

    ASSERT(kernel);
    ASSERT(labels && labels->get_num_labels());

    CSignal::clear_cancel();

    if (data)
    {
        if (data->get_num_vectors() != labels->get_num_labels())
        {
            SG_ERROR("Numbert of vectors (%d) does not match number of labels (%d)\n",
                    data->get_num_vectors(), labels->get_num_labels());
        }
        kernel->init(data, data);
    }

    ASSERT(kernel->get_num_vec_lhs() && kernel->get_num_vec_rhs());

    nb_train=labels->get_num_labels();
    cache = kernel->get_cache_size();

    int32_t n_it = 1;
    float64_t gap = DBL_MAX;

    SG_INFO("Training on %d examples\n", nb_train);
    while (gap > C1 && (!CSignal::cancel_computations()))      // stopping criteria
    {
        float64_t tr_err = 0;
        int32_t ind = step;
        for (int32_t i = 0; i < nb_train; i++)
        {
            int32_t y=labels->get_label(i);
            if (add (i, y) != y)   // call the add function
                tr_err++;

            if (ind && i / ind)
            {
                SG_DEBUG("Done: %d %% Train error (online): %f%%\n",
                        (int32_t) (((float64_t) i) / nb_train * 100), (tr_err / ((float64_t) i + 1)) * 100);
                ind += step;
            }
        }

        SG_DEBUG("End of iteration %d\n", n_it++);
        SG_DEBUG("Train error (online): %f%%\n", (tr_err / nb_train) * 100);
        gap = computeGap ();
        SG_ABS_PROGRESS(gap, -CMath::log10(gap), -CMath::log10(DBL_MAX), -CMath::log10(C1), 6);

        if (!batch_mode)        // skip stopping criteria if online mode
            gap = 0;
    }
    SG_DONE();

    int32_t num_classes = outputs.size();
    create_multiclass_svm(num_classes);
    SG_DEBUG("%d classes\n", num_classes);

    // Used for saving a model file
    int32_t i=0;
    for (outputhash_t::const_iterator it = outputs.begin (); it != outputs.end (); ++it)
    {
        const LaRankOutput* o=&(it->second);

        larank_kcache_t* k=o->getKernel();
        int32_t l=o->get_l();
        float32_t* beta=o->getBetas();
        int32_t *r2i = larank_kcache_r2i (k, l);

        ASSERT(l>0);
        SG_DEBUG("svm[%d] has %d sv, b=%f\n", i, l, 0.0);

        CSVM* svm=new CSVM(l);

        for (int32_t j=0; j<l; j++)
        {
            svm->set_alpha(j, beta[j]);
            svm->set_support_vector(j, r2i[j]);
        }

        svm->set_bias(0);
        set_svm(i, svm);
        i++;
    }
    destroy();

    return true;
}

// LEARNING FUNCTION: add new patterns and run optimization steps selected with adaptative schedule
int32_t CLaRank::add (int32_t x_id, int32_t yi)
{
    ++nb_seen_examples;
    // create a new output object if this one has never been seen before 
    if (!getOutput (yi))
    {
        outputs.insert (std::make_pair (yi, LaRankOutput ()));
        LaRankOutput *cur = getOutput (yi);
        cur->initialize (kernel, cache);
        if (outputs.size () == 1)
            y0 = outputs.begin ()->first;
        // link the cache of this new output to a buddy 
        if (outputs.size () > 1)
        {
            LaRankOutput *out0 = getOutput (y0);
            cur->set_kernel_buddy (out0->getKernel ());
        }
    }

    LaRankPattern tpattern (x_id, yi);
    LaRankPattern & pattern = (patterns.isPattern (x_id)) ? patterns.getPattern (x_id) : tpattern;

    // ProcessNew with the "fresh" pattern
    float64_t time1 = CTime::get_curtime();
    process_return_t pro_ret = process (pattern, processNew);
    float64_t dual_increase = pro_ret.dual_increase;
    float64_t duration = (CTime::get_curtime() - time1);
    float64_t coeff = dual_increase / (0.00001 + duration);
    dual += dual_increase;
    n_pro++;
    w_pro = 0.05 * coeff + (1 - 0.05) * w_pro;

    // ProcessOld & Optimize until ready for a new processnew
    // (Adaptative schedule here)
    for (;;)
    {
        float64_t w_sum = w_pro + w_rep + w_opt;
        float64_t prop_min = w_sum / 20;
        if (w_pro < prop_min)
            w_pro = prop_min;
        if (w_rep < prop_min)
            w_rep = prop_min;
        if (w_opt < prop_min)
            w_opt = prop_min;
        w_sum = w_pro + w_rep + w_opt;
        float64_t r = CMath::random(0.0, w_sum);
        if (r <= w_pro)
        {
            break;
        }
        else if ((r > w_pro) && (r <= w_pro + w_rep))   // ProcessOld here
        {
            float64_t ltime1 = CTime::get_curtime ();
            float64_t ldual_increase = reprocess ();
            float64_t lduration = (CTime::get_curtime () - ltime1);
            float64_t lcoeff = ldual_increase / (0.00001 + lduration);
            dual += ldual_increase;
            n_rep++;
            w_rep = 0.05 * lcoeff + (1 - 0.05) * w_rep;
        }
        else            // Optimize here 
        {
            float64_t ltime1 = CTime::get_curtime ();
            float64_t ldual_increase = optimize ();
            float64_t lduration = (CTime::get_curtime () - ltime1);
            float64_t lcoeff = ldual_increase / (0.00001 + lduration);
            dual += ldual_increase;
            n_opt++;
            w_opt = 0.05 * lcoeff + (1 - 0.05) * w_opt;
        }
    }
    if (nb_seen_examples % 100 == 0)    // Cleanup useless Support Vectors/Patterns sometimes
        nb_removed += cleanup ();
    return pro_ret.ypred;
}

// PREDICTION FUNCTION: main function in la_rank_classify
int32_t CLaRank::predict (int32_t x_id)
{
    int32_t res = -1;
    float64_t score_max = -DBL_MAX;
    for (outputhash_t::iterator it = outputs.begin (); it != outputs.end ();++it)
    {
        float64_t score = it->second.computeScore (x_id);
        if (score > score_max)
        {
            score_max = score;
            res = it->first;
        }
    }
    return res;
}

void CLaRank::destroy ()
{
    for (outputhash_t::iterator it = outputs.begin (); it != outputs.end ();++it)
        it->second.destroy ();
}


// Compute Duality gap (costly but used in stopping criteria in batch mode)                     
float64_t CLaRank::computeGap ()
{
    float64_t sum_sl = 0;
    float64_t sum_bi = 0;
    for (uint32_t i = 0; i < patterns.maxcount (); ++i)
    {
        const LaRankPattern & p = patterns[i];
        if (!p.exists ())
            continue;
        LaRankOutput *out = getOutput (p.y);
        if (!out)
            continue;
        sum_bi += out->getBeta (p.x_id);
        float64_t gi = out->computeGradient (p.x_id, p.y, p.y);
        float64_t gmin = DBL_MAX;
        for (outputhash_t::iterator it = outputs.begin (); it != outputs.end (); ++it)
        {
            if (it->first != p.y && it->second.isSupportVector (p.x_id))
            {
                float64_t g =
                    it->second.computeGradient (p.x_id, p.y, it->first);
                if (g < gmin)
                    gmin = g;
            }
        }
        sum_sl += CMath::max (0.0, gi - gmin);
    }
    return CMath::max (0.0, computeW2 () + C1 * sum_sl - sum_bi);
}

// Nuber of classes so far
uint32_t CLaRank::getNumOutputs () const
{
    return outputs.size ();
}

// Number of Support Vectors
int32_t CLaRank::getNSV ()
{
    int32_t res = 0;
    for (outputhash_t::const_iterator it = outputs.begin (); it != outputs.end (); ++it)
    {
        float32_t* sv=NULL;
        res += it->second.getSV (sv);
        SG_FREE(sv);
    }
    return res;
}

// Norm of the parameters vector
float64_t CLaRank::computeW2 ()
{
    float64_t res = 0;
    for (uint32_t i = 0; i < patterns.maxcount (); ++i)
    {
        const LaRankPattern & p = patterns[i];
        if (!p.exists ())
            continue;
        for (outputhash_t::iterator it = outputs.begin (); it != outputs.end (); ++it)
            if (it->second.getBeta (p.x_id))
                res += it->second.getBeta (p.x_id) * it->second.computeScore (p.x_id);
    }
    return res;
}

// Compute Dual objective value
float64_t CLaRank::getDual ()
{
    float64_t res = 0;
    for (uint32_t i = 0; i < patterns.maxcount (); ++i)
    {
        const LaRankPattern & p = patterns[i];
        if (!p.exists ())
            continue;
        LaRankOutput *out = getOutput (p.y);
        if (!out)
            continue;
        res += out->getBeta (p.x_id);
    }
    return res - computeW2 () / 2;
}

LaRankOutput *CLaRank::getOutput (int32_t index)
{
    outputhash_t::iterator it = outputs.find (index);
    return it == outputs.end ()? NULL : &it->second;
}

// IMPORTANT Main SMO optimization step
CLaRank::process_return_t CLaRank::process (const LaRankPattern & pattern, process_type ptype)
{
    process_return_t pro_ret = process_return_t (0, 0);

    /*
     ** compute gradient and sort   
     */
    std::vector < outputgradient_t > outputgradients;

    outputgradients.reserve (getNumOutputs ());

    std::vector < outputgradient_t > outputscores;
    outputscores.reserve (getNumOutputs ());

    for (outputhash_t::iterator it = outputs.begin (); it != outputs.end (); ++it)
    {
        if (ptype != processOptimize
                || it->second.isSupportVector (pattern.x_id))
        {
            float64_t g =
                it->second.computeGradient (pattern.x_id, pattern.y, it->first);
            outputgradients.push_back (outputgradient_t (it->first, g));
            if (it->first == pattern.y)
                outputscores.push_back (outputgradient_t (it->first, (1 - g)));
            else
                outputscores.push_back (outputgradient_t (it->first, -g));
        }
    }

    std::sort (outputgradients.begin (), outputgradients.end ());

    /*
     ** determine the prediction
     */
    std::sort (outputscores.begin (), outputscores.end ());
    pro_ret.ypred = outputscores[0].output;

    /*
     ** Find yp (1st part of the pair)
     */
    outputgradient_t ygp;
    LaRankOutput *outp = NULL;
    uint32_t p;
    for (p = 0; p < outputgradients.size (); ++p)
    {
        outputgradient_t & current = outputgradients[p];
        LaRankOutput *output = getOutput (current.output);
        bool support = ptype == processOptimize || output->isSupportVector (pattern.x_id);
        bool goodclass = current.output == pattern.y;
        if ((!support && goodclass) ||
                (support && output->getBeta (pattern.x_id) < (goodclass ? C1 : 0)))
        {
            ygp = current;
            outp = output;
            break;
        }
    }
    if (p == outputgradients.size ())
        return pro_ret;

    /*
     ** Find ym (2nd part of the pair)
     */
    outputgradient_t ygm;
    LaRankOutput *outm = NULL;
    int32_t m;
    for (m = outputgradients.size () - 1; m >= 0; --m)
    {
        outputgradient_t & current = outputgradients[m];
        LaRankOutput *output = getOutput (current.output);
        bool support = ptype == processOptimize || output->isSupportVector (pattern.x_id);
        bool goodclass = current.output == pattern.y;
        if (!goodclass || (support && output->getBeta (pattern.x_id) > 0))
        {
            ygm = current;
            outm = output;
            break;
        }
    }
    if (m < 0)
        return pro_ret;

    /*
     ** Throw or Insert pattern
     */
    if ((ygp.gradient - ygm.gradient) < tau)
        return pro_ret;
    if (ptype == processNew)
        patterns.insert (pattern);

    /*
     ** compute lambda and clip it
     */
    float64_t kii = outp->getKii (pattern.x_id);
    float64_t lambda = (ygp.gradient - ygm.gradient) / (2 * kii);
    if (ptype == processOptimize || outp->isSupportVector (pattern.x_id))
    {
        float64_t beta = outp->getBeta (pattern.x_id);
        if (ygp.output == pattern.y)
            lambda = CMath::min (lambda, C1 - beta);
        else
            lambda = CMath::min (lambda, fabs (beta));
    }
    else
        lambda = CMath::min (lambda, C1);

    /*
     ** update the solution
     */
    outp->update (pattern.x_id, lambda, ygp.gradient);
    outm->update (pattern.x_id, -lambda, ygm.gradient);

    pro_ret.dual_increase = lambda * ((ygp.gradient - ygm.gradient) - lambda * kii);
    return pro_ret;
}

// ProcessOld
float64_t CLaRank::reprocess ()
{
    if (patterns.size ())
    {
        for (int32_t n = 0; n < 10; ++n)
        {
            process_return_t pro_ret = process (patterns.sample (), processOld);
            if (pro_ret.dual_increase)
                return pro_ret.dual_increase;
        }
    }
    return 0;
}

// Optimize
float64_t CLaRank::optimize ()
{
    float64_t dual_increase = 0;
    if (patterns.size ())
    {
        for (int32_t n = 0; n < 10; ++n)
        {
            process_return_t pro_ret =
                process (patterns.sample(), processOptimize);
            dual_increase += pro_ret.dual_increase;
        }
    }
    return dual_increase;
}

// remove patterns and return the number of patterns that were removed
uint32_t CLaRank::cleanup ()
{
    /*
    for (outputhash_t::iterator it = outputs.begin (); it != outputs.end (); ++it)
        it->second.cleanup ();

    uint32_t res = 0;
    for (uint32_t i = 0; i < patterns.size (); ++i)
    {
        LaRankPattern & p = patterns[i];
        if (p.exists () && !outputs[p.y].isSupportVector (p.x_id))
        {
            patterns.remove (i);
            ++res;
        }
    }
    return res;
    */
    return 0;
}