RelaxedTree.cpp

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/*
 * 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 3 of the License, or
 * (at your option) any later version.
 *
 * Written (W) 2012 Chiyuan Zhang
 * Copyright (C) 2012 Chiyuan Zhang
 */

#include <limits>
#include <queue>
#include <algorithm>
#include <functional>

#include <shogun/labels/BinaryLabels.h>
#include <shogun/multiclass/tree/RelaxedTreeUtil.h>
#include <shogun/multiclass/tree/RelaxedTree.h>
#include <shogun/kernel/GaussianKernel.h>
#include <shogun/mathematics/Math.h>

using namespace shogun;

CRelaxedTree::CRelaxedTree()
    :m_max_num_iter(3), m_A(0.5), m_B(5), m_svm_C(1), m_svm_epsilon(0.001),
    m_kernel(NULL), m_feats(NULL), m_machine_for_confusion_matrix(NULL), m_num_classes(0)
{
    SG_ADD(&m_max_num_iter, "m_max_num_iter", "max number of iterations in alternating optimization", MS_NOT_AVAILABLE);
    SG_ADD(&m_svm_C, "m_svm_C", "C for svm", MS_AVAILABLE);
    SG_ADD(&m_A, "m_A", "parameter A", MS_AVAILABLE);
    SG_ADD(&m_B, "m_B", "parameter B", MS_AVAILABLE);
    SG_ADD(&m_svm_epsilon, "m_svm_epsilon", "epsilon for svm", MS_AVAILABLE);
}

CRelaxedTree::~CRelaxedTree()
{
    SG_UNREF(m_kernel);
    SG_UNREF(m_feats);
    SG_UNREF(m_machine_for_confusion_matrix);
}

CMulticlassLabels* CRelaxedTree::apply_multiclass(CFeatures* data)
{
    if (data != NULL)
    {
        CDenseFeatures<float64_t> *feats = dynamic_cast<CDenseFeatures<float64_t>*>(data);
        REQUIRE(feats != NULL, ("Require non-NULL dense features of float64_t\n"))
        set_features(feats);
    }

    // init kernels for all sub-machines
    for (int32_t i=0; i<m_machines->get_num_elements(); i++)
    {
        CSVM *machine = (CSVM*)m_machines->get_element(i);
        CKernel *kernel = machine->get_kernel();
        CFeatures* lhs = kernel->get_lhs();
        kernel->init(lhs, m_feats);
        SG_UNREF(machine);
        SG_UNREF(kernel);
        SG_UNREF(lhs);
    }

    CMulticlassLabels *lab = new CMulticlassLabels(m_feats->get_num_vectors());
    SG_REF(lab);
    for (int32_t i=0; i < lab->get_num_labels(); ++i)
    {
        lab->set_int_label(i, int32_t(apply_one(i)));
    }

    return lab;
}

float64_t CRelaxedTree::apply_one(int32_t idx)
{
    bnode_t *node = (bnode_t*) m_root;
    int32_t klass = -1;
    while (node != NULL)
    {
        CSVM *svm = (CSVM *)m_machines->get_element(node->machine());
        float64_t result = svm->apply_one(idx);

        if (result < 0)
        {
            // go left
            if (node->left()) // has left subtree
            {
                node = node->left();
            }
            else // stop here
            {
                for (int32_t i=0; i < node->data.mu.vlen; ++i)
                {
                    if (node->data.mu[i] <= 0 && node->data.mu[i] > -2)
                    {
                        klass = i;
                        break;
                    }
                }
                node = NULL;
            }
        }
        else
        {
            // go right
            if (node->right())
            {
                node = node->right();
            }
            else
            {
                for (int32_t i=0; i <node->data.mu.vlen; ++i)
                {
                    if (node->data.mu[i] >= 0)
                    {
                        klass = i;
                        break;
                    }
                }
                node = NULL;
            }
        }

        SG_UNREF(svm);
    }

    return klass;
}

bool CRelaxedTree::train_machine(CFeatures* data)
{
    if (m_machine_for_confusion_matrix == NULL)
        SG_ERROR("Call set_machine_for_confusion_matrix before training\n")
    if (m_kernel == NULL)
        SG_ERROR("assign a valid kernel before training\n")

    if (data)
    {
        CDenseFeatures<float64_t> *feats = dynamic_cast<CDenseFeatures<float64_t>*>(data);
        if (feats == NULL)
            SG_ERROR("Require non-NULL dense features of float64_t\n")
        set_features(feats);
    }

    CMulticlassLabels *lab = dynamic_cast<CMulticlassLabels *>(m_labels);

    RelaxedTreeUtil util;
    SGMatrix<float64_t> conf_mat = util.estimate_confusion_matrix(m_machine_for_confusion_matrix,
            m_feats, lab, m_num_classes);

    // train root
    SGVector<int32_t> classes(m_num_classes);

    for (int32_t i=0; i < m_num_classes; ++i)
        classes[i] = i;

    SG_UNREF(m_root);
    m_root = train_node(conf_mat, classes);

    std::queue<bnode_t *> node_q;
    node_q.push((bnode_t*) m_root);

    while (node_q.size() != 0)
    {
        bnode_t *node = node_q.front();

        // left node
        SGVector <int32_t> left_classes(m_num_classes);
        int32_t k=0;
        for (int32_t i=0; i < m_num_classes; ++i)
        {
            // active classes are labeled as -1 or 0
            // -2 indicate classes that are already pruned away
            if (node->data.mu[i] <= 0 && node->data.mu[i] > -2)
                left_classes[k++] = i;
        }

        left_classes.vlen = k;

        if (left_classes.vlen >= 2)
        {
            bnode_t *left_node = train_node(conf_mat, left_classes);
            node->left(left_node);
            node_q.push(left_node);
        }

        // right node
        SGVector <int32_t> right_classes(m_num_classes);
        k=0;
        for (int32_t i=0; i < m_num_classes; ++i)
        {
            // active classes are labeled as 0 or +1
            if (node->data.mu[i] >= 0)
                right_classes[k++] = i;
        }

        right_classes.vlen = k;

        if (right_classes.vlen >= 2)
        {
            bnode_t *right_node = train_node(conf_mat, right_classes);
            node->right(right_node);
            node_q.push(right_node);
        }

        node_q.pop();
    }

    //m_root->debug_print(RelaxedTreeNodeData::print_data);

    return true;
}

CRelaxedTree::bnode_t *CRelaxedTree::train_node(const SGMatrix<float64_t> &conf_mat, SGVector<int32_t> classes)
{
    SGVector<int32_t> best_mu;
    CSVM *best_svm = NULL;
    float64_t best_score = std::numeric_limits<float64_t>::max();

    std::vector<CRelaxedTree::entry_t> mu_init = init_node(conf_mat, classes);
    for (std::vector<CRelaxedTree::entry_t>::const_iterator it = mu_init.begin(); it != mu_init.end(); ++it)
    {
        CSVM *svm = new CLibSVM();
        SG_REF(svm);
        svm->set_store_model_features(true);

        SGVector<int32_t> mu = train_node_with_initialization(*it, classes, svm);
        float64_t score = compute_score(mu, svm);

        if (score < best_score)
        {
            best_score = score;
            best_mu = mu;
            SG_UNREF(best_svm);
            best_svm = svm;
        }
        else
        {
            SG_UNREF(svm);
        }
    }

    bnode_t *node = new bnode_t;
    SG_REF(node);

    m_machines->push_back(best_svm);
    node->machine(m_machines->get_num_elements()-1);

    SGVector<int32_t> long_mu(m_num_classes);
    std::fill(&long_mu[0], &long_mu[m_num_classes], -2);
    for (int32_t i=0; i < best_mu.vlen; ++i)
    {
        if (best_mu[i] == 1)
            long_mu[classes[i]] = 1;
        else if (best_mu[i] == -1)
            long_mu[classes[i]] = -1;
        else if (best_mu[i] == 0)
            long_mu[classes[i]] = 0;
    }

    node->data.mu = long_mu;
    return node;
}

float64_t CRelaxedTree::compute_score(SGVector<int32_t> mu, CSVM *svm)
{
    float64_t num_pos=0, num_neg=0;
    for (int32_t i=0; i < mu.vlen; ++i)
    {
        if (mu[i] == 1)
            num_pos++;
        else if (mu[i] == -1)
            num_neg++;
    }

    int32_t totalSV = svm->get_support_vectors().vlen;
    float64_t score = num_neg/(num_neg+num_pos) * totalSV/num_pos +
        num_pos/(num_neg+num_pos)*totalSV/num_neg;
    return score;
}

SGVector<int32_t> CRelaxedTree::train_node_with_initialization(const CRelaxedTree::entry_t &mu_entry, SGVector<int32_t> classes, CSVM *svm)
{
    SGVector<int32_t> mu(classes.vlen), prev_mu(classes.vlen);
    mu.zero();
    mu[mu_entry.first.first] = 1;
    mu[mu_entry.first.second] = -1;

    SGVector<int32_t> long_mu(m_num_classes);
    svm->set_C(m_svm_C, m_svm_C);
    svm->set_epsilon(m_svm_epsilon);

    for (int32_t iiter=0; iiter < m_max_num_iter; ++iiter)
    {
        long_mu.zero();
        for (int32_t i=0; i < classes.vlen; ++i)
        {
            if (mu[i] == 1)
                long_mu[classes[i]] = 1;
            else if (mu[i] == -1)
                long_mu[classes[i]] = -1;
        }

        SGVector<int32_t> subset(m_feats->get_num_vectors());
        SGVector<float64_t> binlab(m_feats->get_num_vectors());
        int32_t k=0;

        CMulticlassLabels *labs = dynamic_cast<CMulticlassLabels *>(m_labels);
        for (int32_t i=0; i < binlab.vlen; ++i)
        {
            int32_t lab = labs->get_int_label(i);
            binlab[i] = long_mu[lab];
            if (long_mu[lab] != 0)
                subset[k++] = i;
        }

        subset.vlen = k;

        CBinaryLabels *binary_labels = new CBinaryLabels(binlab);
        SG_REF(binary_labels);
        binary_labels->add_subset(subset);
        m_feats->add_subset(subset);

        CKernel *kernel = (CKernel *)m_kernel->shallow_copy();
        kernel->init(m_feats, m_feats);
        svm->set_kernel(kernel);
        svm->set_labels(binary_labels);
        svm->train();

        binary_labels->remove_subset();
        m_feats->remove_subset();
        SG_UNREF(binary_labels);

        std::copy(&mu[0], &mu[mu.vlen], &prev_mu[0]);

        mu = color_label_space(svm, classes);

        bool bbreak = true;
        for (int32_t i=0; i < mu.vlen; ++i)
        {
            if (mu[i] != prev_mu[i])
            {
                bbreak = false;
                break;
            }
        }

        if (bbreak)
            break;
    }

    return mu;
}

struct EntryComparator
{
    bool operator() (const CRelaxedTree::entry_t& e1, const CRelaxedTree::entry_t& e2)
    {
        return e1.second < e2.second;
    }
};
std::vector<CRelaxedTree::entry_t> CRelaxedTree::init_node(const SGMatrix<float64_t> &global_conf_mat, SGVector<int32_t> classes)
{
    // local confusion matrix
    SGMatrix<float64_t> conf_mat(classes.vlen, classes.vlen);
    for (index_t i=0; i < conf_mat.num_rows; ++i)
    {
        for (index_t j=0; j < conf_mat.num_cols; ++j)
        {
            conf_mat(i, j) = global_conf_mat(classes[i], classes[j]);
        }
    }

    // make conf matrix symmetry
    for (index_t i=0; i < conf_mat.num_rows; ++i)
    {
        for (index_t j=0; j < conf_mat.num_cols; ++j)
        {
            conf_mat(i,j) += conf_mat(j,i);
        }
    }

    std::vector<CRelaxedTree::entry_t> entries;
    for (index_t i=0; i < classes.vlen; ++i)
    {
        for (index_t j=i+1; j < classes.vlen; ++j)
        {
            entries.push_back(std::make_pair(std::make_pair(i, j), conf_mat(i,j)));
        }
    }

    std::sort(entries.begin(), entries.end(), EntryComparator());

    const size_t max_n_samples = 30;
    int32_t n_samples = std::min(max_n_samples, entries.size());

    return std::vector<CRelaxedTree::entry_t>(entries.begin(), entries.begin() + n_samples);
}

SGVector<int32_t> CRelaxedTree::color_label_space(CSVM *svm, SGVector<int32_t> classes)
{
    SGVector<int32_t> mu(classes.vlen);
    CMulticlassLabels *labels = dynamic_cast<CMulticlassLabels *>(m_labels);

    SGVector<float64_t> resp = eval_binary_model_K(svm);
    ASSERT(resp.vlen == labels->get_num_labels())

    SGVector<float64_t> xi_pos_class(classes.vlen), xi_neg_class(classes.vlen);
    SGVector<float64_t> delta_pos(classes.vlen), delta_neg(classes.vlen);

    for (int32_t i=0; i < classes.vlen; ++i)
    {
        // find number of instances from this class
        int32_t ni=0;
        for (int32_t j=0; j < labels->get_num_labels(); ++j)
        {
            if (labels->get_int_label(j) == classes[i])
            {
                ni++;
            }
        }

        xi_pos_class[i] = 0;
        xi_neg_class[i] = 0;
        for (int32_t j=0; j < resp.vlen; ++j)
        {
            if (labels->get_int_label(j) == classes[i])
            {
                xi_pos_class[i] += std::max(0.0, 1 - resp[j]);
                xi_neg_class[i] += std::max(0.0, 1 + resp[j]);
            }
        }

        delta_pos[i] = 1.0/ni * xi_pos_class[i] - float64_t(m_A)/m_svm_C;
        delta_neg[i] = 1.0/ni * xi_neg_class[i] - float64_t(m_A)/m_svm_C;

        if (delta_pos[i] > 0 && delta_neg[i] > 0)
        {
            mu[i] = 0;
        }
        else
        {
            if (delta_pos[i] < delta_neg[i])
                mu[i] = 1;
            else
                mu[i] = -1;
        }

    }

    // enforce balance constraints
    int32_t B_prime = 0;
    for (int32_t i=0; i < mu.vlen; ++i)
        B_prime += mu[i];

    if (B_prime > m_B)
    {
        enforce_balance_constraints_upper(mu, delta_neg, delta_pos, B_prime, xi_neg_class);
    }
    if (B_prime < -m_B)
    {
        enforce_balance_constraints_lower(mu, delta_neg, delta_pos, B_prime, xi_neg_class);
    }

    int32_t npos = 0;
    for (index_t i=0; i < mu.vlen; ++i)
    {
        if (mu[i] == 1)
            npos++;
    }

    if (npos == 0)
    {
        // no positive class
        index_t min_idx = CMath::arg_min(xi_pos_class.vector, 1, xi_pos_class.vlen);
        mu[min_idx] = 1;
    }

    int32_t nneg = 0;
    for (index_t i=0; i < mu.vlen; ++i)
    {
        if (mu[i] == -1)
            nneg++;
    }

    if (nneg == 0)
    {
        // no negative class
        index_t min_idx = CMath::arg_min(xi_neg_class.vector, 1, xi_neg_class.vlen);
        if (mu[min_idx] == 1 && (npos == 0 || npos == 1))
        {
            // avoid overwritting the only positive class
            float64_t min_val = 0;
            int32_t i, min_i;
            for (i=0; i < xi_neg_class.vlen; ++i)
            {
                if (mu[i] != 1)
                {
                    min_val = xi_neg_class[i];
                    break;
                }
            }
            min_i = i;
            for (i=i+1; i < xi_neg_class.vlen; ++i)
            {
                if (mu[i] != 1 && xi_neg_class[i] < min_val)
                {
                    min_val = xi_neg_class[i];
                    min_i = i;
                }
            }
            mu[min_i] = -1;
        }
        else
        {
            mu[min_idx] = -1;
        }
    }

    return mu;
}

void CRelaxedTree::enforce_balance_constraints_upper(SGVector<int32_t> &mu, SGVector<float64_t> &delta_neg,
        SGVector<float64_t> &delta_pos, int32_t B_prime, SGVector<float64_t>& xi_neg_class)
{
    SGVector<index_t> index_zero = mu.find(0);
    SGVector<index_t> index_pos = mu.find_if(std::bind1st(std::less<int32_t>(), 0));

    int32_t num_zero = index_zero.vlen;
    int32_t num_pos  = index_pos.vlen;

    SGVector<index_t> class_index(num_zero+2*num_pos);
    std::copy(&index_zero[0], &index_zero[num_zero], &class_index[0]);
    std::copy(&index_pos[0], &index_pos[num_pos], &class_index[num_zero]);
    std::copy(&index_pos[0], &index_pos[num_pos], &class_index[num_pos+num_zero]);

    SGVector<int32_t> orig_mu(num_zero + 2*num_pos);
    orig_mu.zero();
    std::fill(&orig_mu[num_zero], &orig_mu[orig_mu.vlen], 1);

    SGVector<int32_t> delta_steps(num_zero+2*num_pos);
    std::fill(&delta_steps[0], &delta_steps[delta_steps.vlen], 1);

    SGVector<int32_t> new_mu(num_zero + 2*num_pos);
    new_mu.zero();
    std::fill(&new_mu[0], &new_mu[num_zero], -1);

    SGVector<float64_t> S_delta(num_zero + 2*num_pos);
    S_delta.zero();
    for (index_t i=0; i < num_zero; ++i)
        S_delta[i] = delta_neg[index_zero[i]];

    for (int32_t i=0; i < num_pos; ++i)
    {
        float64_t delta_k = delta_neg[index_pos[i]];
        float64_t delta_k_0 = -delta_pos[index_pos[i]];

        index_t tmp_index = num_zero + i*2;
        if (delta_k_0 <= delta_k)
        {
            new_mu[tmp_index] = 0;
            new_mu[tmp_index+1] = -1;

            S_delta[tmp_index] = delta_k_0;
            S_delta[tmp_index+1] = delta_k;

            delta_steps[tmp_index] = 1;
            delta_steps[tmp_index+1] = 1;
        }
        else
        {
            new_mu[tmp_index] = -1;
            new_mu[tmp_index+1] = 0;

            S_delta[tmp_index] = (delta_k_0+delta_k)/2;
            S_delta[tmp_index+1] = delta_k_0;

            delta_steps[tmp_index] = 2;
            delta_steps[tmp_index+1] = 1;
        }
    }

    SGVector<index_t> sorted_index = CMath::argsort(S_delta);
    SGVector<float64_t> S_delta_sorted(S_delta.vlen);
    for (index_t i=0; i < sorted_index.vlen; ++i)
    {
        S_delta_sorted[i] = S_delta[sorted_index[i]];
        new_mu[i] = new_mu[sorted_index[i]];
        orig_mu[i] = orig_mu[sorted_index[i]];
        class_index[i] = class_index[sorted_index[i]];
        delta_steps[i] = delta_steps[sorted_index[i]];
    }

    SGVector<int32_t> valid_flag(S_delta.vlen);
    std::fill(&valid_flag[0], &valid_flag[valid_flag.vlen], 1);

    int32_t d=0;
    int32_t ctr=0;

    while (true)
    {
        if (d == B_prime - m_B || d == B_prime - m_B + 1)
            break;

        while (!valid_flag[ctr])
            ctr++;

        if (delta_steps[ctr] == 1)
        {
            mu[class_index[ctr]] = new_mu[ctr];
            d++;
        }
        else
        {
            // this case should happen only when rho >= 1
            if (d <= B_prime - m_B - 2)
            {
                mu[class_index[ctr]] = new_mu[ctr];
                ASSERT(new_mu[ctr] == -1)
                d += 2;
                for (index_t i=0; i < class_index.vlen; ++i)
                {
                    if (class_index[i] == class_index[ctr])
                        valid_flag[i] = 0;
                }
            }
            else
            {
                float64_t Delta_k_minus = 2*S_delta_sorted[ctr];

                // find the next smallest Delta_j or Delta_{j,0}
                float64_t Delta_j_min=0;
                int32_t j=0;
                for (int32_t itr=ctr+1; itr < S_delta_sorted.vlen; ++itr)
                {
                    if (valid_flag[itr] == 0)
                        continue;

                    if (delta_steps[itr] == 1)
                    {
                        j=itr;
                        Delta_j_min = S_delta_sorted[j];
                    }
                }

                // find the largest Delta_i or Delta_{i,0}
                float64_t Delta_i_max = 0;
                int32_t i=-1;
                for (int32_t itr=ctr-1; itr >= 0; --itr)
                {
                    if (delta_steps[itr] == 1 && valid_flag[itr] == 1)
                    {
                        i = itr;
                        Delta_i_max = S_delta_sorted[i];
                    }
                }

                // find the l with the largest Delta_l_minus - Delta_l_0
                float64_t Delta_l_max = std::numeric_limits<float64_t>::min();
                int32_t l=-1;
                for (int32_t itr=ctr-1; itr >= 0; itr--)
                {
                    if (delta_steps[itr] == 2)
                    {
                        float64_t delta_tmp = xi_neg_class[class_index[itr]];
                        if (delta_tmp > Delta_l_max)
                        {
                            l = itr;
                            Delta_l_max = delta_tmp;
                        }
                    }
                }

                // one-step-min = j
                if (Delta_j_min <= Delta_k_minus - Delta_i_max &&
                        Delta_j_min <= Delta_k_minus - Delta_l_max)
                {
                    mu[class_index[j]] = new_mu[j];
                    d++;
                }
                else
                {
                    // one-step-min = Delta_k_minus - Delta_i_max
                    if (Delta_k_minus - Delta_i_max <= Delta_j_min &&
                            Delta_k_minus - Delta_i_max <= Delta_k_minus - Delta_l_max)
                    {
                        mu[class_index[ctr]] = -1;
                        if (i > 0)
                        {
                            mu[class_index[i]] = orig_mu[i];
                            d++;
                        }
                        else
                        {
                            d += 2;
                        }
                    }
                    else
                    {
                        ASSERT(l > 0)
                        mu[class_index[l]] = 0;
                        mu[class_index[ctr]] = -1;
                        d++;
                    }
                }

            }
        }
    }
}

void CRelaxedTree::enforce_balance_constraints_lower(SGVector<int32_t> &mu, SGVector<float64_t> &delta_neg,
        SGVector<float64_t> &delta_pos, int32_t B_prime, SGVector<float64_t>& xi_neg_class)
{
    SGVector<index_t> index_zero = mu.find(0);
    SGVector<index_t> index_neg = mu.find_if(std::bind1st(std::greater<int32_t>(), 0));

    int32_t num_zero = index_zero.vlen;
    int32_t num_neg  = index_neg.vlen;

    SGVector<index_t> class_index(num_zero+2*num_neg);
    std::copy(&index_zero[0], &index_zero[num_zero], &class_index[0]);
    std::copy(&index_neg[0], &index_neg[num_neg], &class_index[num_zero]);
    std::copy(&index_neg[0], &index_neg[num_neg], &class_index[num_neg+num_zero]);

    SGVector<int32_t> orig_mu(num_zero + 2*num_neg);
    orig_mu.zero();
    std::fill(&orig_mu[num_zero], &orig_mu[orig_mu.vlen], -1);

    SGVector<int32_t> delta_steps(num_zero+2*num_neg);
    std::fill(&delta_steps[0], &delta_steps[delta_steps.vlen], 1);

    SGVector<int32_t> new_mu(num_zero + 2*num_neg);
    new_mu.zero();
    std::fill(&new_mu[0], &new_mu[num_zero], 1);

    SGVector<float64_t> S_delta(num_zero + 2*num_neg);
    S_delta.zero();
    for (index_t i=0; i < num_zero; ++i)
        S_delta[i] = delta_pos[index_zero[i]];

    for (int32_t i=0; i < num_neg; ++i)
    {
        float64_t delta_k = delta_pos[index_neg[i]];
        float64_t delta_k_0 = -delta_neg[index_neg[i]];

        index_t tmp_index = num_zero + i*2;
        if (delta_k_0 <= delta_k)
        {
            new_mu[tmp_index] = 0;
            new_mu[tmp_index+1] = 1;

            S_delta[tmp_index] = delta_k_0;
            S_delta[tmp_index+1] = delta_k;

            delta_steps[tmp_index] = 1;
            delta_steps[tmp_index+1] = 1;
        }
        else
        {
            new_mu[tmp_index] = 1;
            new_mu[tmp_index+1] = 0;

            S_delta[tmp_index] = (delta_k_0+delta_k)/2;
            S_delta[tmp_index+1] = delta_k_0;

            delta_steps[tmp_index] = 2;
            delta_steps[tmp_index+1] = 1;
        }
    }

    SGVector<index_t> sorted_index = CMath::argsort(S_delta);
    SGVector<float64_t> S_delta_sorted(S_delta.vlen);
    for (index_t i=0; i < sorted_index.vlen; ++i)
    {
        S_delta_sorted[i] = S_delta[sorted_index[i]];
        new_mu[i] = new_mu[sorted_index[i]];
        orig_mu[i] = orig_mu[sorted_index[i]];
        class_index[i] = class_index[sorted_index[i]];
        delta_steps[i] = delta_steps[sorted_index[i]];
    }

    SGVector<int32_t> valid_flag(S_delta.vlen);
    std::fill(&valid_flag[0], &valid_flag[valid_flag.vlen], 1);

    int32_t d=0;
    int32_t ctr=0;

    while (true)
    {
        if (d == -m_B - B_prime || d == -m_B - B_prime + 1)
            break;

        while (!valid_flag[ctr])
            ctr++;

        if (delta_steps[ctr] == 1)
        {
            mu[class_index[ctr]] = new_mu[ctr];
            d++;
        }
        else
        {
            // this case should happen only when rho >= 1
            if (d >= -m_B - B_prime - 2)
            {
                mu[class_index[ctr]] = new_mu[ctr];
                ASSERT(new_mu[ctr] == 1)
                d += 2;

                for (index_t i=0; i < class_index.vlen; ++i)
                {
                    if (class_index[i] == class_index[ctr])
                        valid_flag[i] = 0;
                }
            }
            else
            {
                float64_t Delta_k_minus = 2*S_delta_sorted[ctr];

                // find the next smallest Delta_j or Delta_{j,0}
                float64_t Delta_j_min=0;
                int32_t j=0;
                for (int32_t itr=ctr+1; itr < S_delta_sorted.vlen; ++itr)
                {
                    if (valid_flag[itr] == 0)
                        continue;

                    if (delta_steps[itr] == 1)
                    {
                        j=itr;
                        Delta_j_min = S_delta_sorted[j];
                    }
                }

                // find the largest Delta_i or Delta_{i,0}
                float64_t Delta_i_max = 0;
                int32_t i=-1;
                for (int32_t itr=ctr-1; itr >= 0; --itr)
                {
                    if (delta_steps[itr] == 1 && valid_flag[itr] == 1)
                    {
                        i = itr;
                        Delta_i_max = S_delta_sorted[i];
                    }
                }

                // find the l with the largest Delta_l_minus - Delta_l_0
                float64_t Delta_l_max = std::numeric_limits<float64_t>::min();
                int32_t l=-1;
                for (int32_t itr=ctr-1; itr >= 0; itr--)
                {
                    if (delta_steps[itr] == 2)
                    {
                        float64_t delta_tmp = xi_neg_class[class_index[itr]];
                        if (delta_tmp > Delta_l_max)
                        {
                            l = itr;
                            Delta_l_max = delta_tmp;
                        }
                    }
                }

                // one-step-min = j
                if (Delta_j_min <= Delta_k_minus - Delta_i_max &&
                        Delta_j_min <= Delta_k_minus - Delta_l_max)
                {
                    mu[class_index[j]] = new_mu[j];
                    d++;
                }
                else
                {
                    // one-step-min = Delta_k_minus - Delta_i_max
                    if (Delta_k_minus - Delta_i_max <= Delta_j_min &&
                            Delta_k_minus - Delta_i_max <= Delta_k_minus - Delta_l_max)
                    {
                        mu[class_index[ctr]] = -1;
                        if (i > 0)
                        {
                            mu[class_index[i]] = orig_mu[i];
                            d++;
                        }
                        else
                        {
                            d += 2;
                        }
                    }
                    else
                    {
                        ASSERT(l > 0)
                        mu[class_index[l]] = 0;
                        mu[class_index[ctr]] = -1;
                        d++;
                    }
                }

            }
        }
    }
}

SGVector<float64_t> CRelaxedTree::eval_binary_model_K(CSVM *svm)
{
    CRegressionLabels *lab = svm->apply_regression(m_feats);
    SGVector<float64_t> resp(lab->get_num_labels());
    for (int32_t i=0; i < resp.vlen; ++i)
        resp[i] = lab->get_label(i) - m_A/m_svm_C;
    SG_UNREF(lab);
    return resp;
}