QDA.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 Fernando José Iglesias García
 * Copyright (C) 2012 Fernando José Iglesias García
 */

#include <shogun/lib/common.h>

#ifdef HAVE_EIGEN3

#include <shogun/multiclass/QDA.h>
#include <shogun/machine/NativeMulticlassMachine.h>
#include <shogun/features/Features.h>
#include <shogun/labels/Labels.h>
#include <shogun/labels/MulticlassLabels.h>
#include <shogun/mathematics/Math.h>

#include <shogun/mathematics/eigen3.h>

using namespace shogun;
using namespace Eigen;

CQDA::CQDA(float64_t tolerance, bool store_covs)
: CNativeMulticlassMachine(), m_tolerance(tolerance),
    m_store_covs(store_covs), m_num_classes(0), m_dim(0)
{
    init();
}

CQDA::CQDA(CDenseFeatures<float64_t>* traindat, CLabels* trainlab, float64_t tolerance, bool store_covs)
: CNativeMulticlassMachine(), m_tolerance(tolerance), m_store_covs(store_covs), m_num_classes(0), m_dim(0)
{
    init();
    set_features(traindat);
    set_labels(trainlab);
}

CQDA::~CQDA()
{
    SG_UNREF(m_features);

    cleanup();
}

void CQDA::init()
{
    SG_ADD(&m_tolerance, "m_tolerance", "Tolerance member.", MS_AVAILABLE);
    SG_ADD(&m_store_covs, "m_store_covs", "Store covariances member", MS_NOT_AVAILABLE);
    SG_ADD((CSGObject**) &m_features, "m_features", "Feature object.", MS_NOT_AVAILABLE);
    SG_ADD(&m_means, "m_means", "Mean vectors list", MS_NOT_AVAILABLE);
    SG_ADD(&m_slog, "m_slog", "Vector used in classification", MS_NOT_AVAILABLE);

    //TODO include SGNDArray objects for serialization

    m_features  = NULL;
}

void CQDA::cleanup()
{
    m_means=SGMatrix<float64_t>();

    m_num_classes = 0;
}

CMulticlassLabels* CQDA::apply_multiclass(CFeatures* data)
{
    if (data)
    {
        if (!data->has_property(FP_DOT))
            SG_ERROR("Specified features are not of type CDotFeatures\n")

        set_features((CDotFeatures*) data);
    }

    if ( !m_features )
        return NULL;

    int32_t num_vecs = m_features->get_num_vectors();
    ASSERT(num_vecs > 0)
    ASSERT( m_dim == m_features->get_dim_feature_space() )

    CDenseFeatures< float64_t >* rf = (CDenseFeatures< float64_t >*) m_features;

    MatrixXd X(num_vecs, m_dim);
    MatrixXd A(num_vecs, m_dim);
    VectorXd norm2(num_vecs*m_num_classes);
    norm2.setZero();

    int32_t vlen;
    bool vfree;
    float64_t* vec;
    for (int k = 0; k < m_num_classes; k++)
    {
        // X = features - means
        for (int i = 0; i < num_vecs; i++)
        {
            vec = rf->get_feature_vector(i, vlen, vfree);
            ASSERT(vec)

            Map< VectorXd > Evec(vec,vlen);
            Map< VectorXd > Em_means_col(m_means.get_column_vector(k), m_dim);

            X.row(i) = Evec - Em_means_col;

            rf->free_feature_vector(vec, i, vfree);
        }

        Map< MatrixXd > Em_M(m_M.get_matrix(k), m_dim, m_dim);
        A = X*Em_M;

        for (int i = 0; i < num_vecs; i++)
            norm2(i + k*num_vecs) = A.row(i).array().square().sum();

#ifdef DEBUG_QDA
    SG_PRINT("\n>>> Displaying A ...\n")
    SGMatrix< float64_t >::display_matrix(A.data(), num_vecs, m_dim);
#endif
    }

    for (int i = 0; i < num_vecs; i++)
        for (int k = 0; k < m_num_classes; k++)
        {
            norm2[i + k*num_vecs] += m_slog[k];
            norm2[i + k*num_vecs] *= -0.5;
        }

#ifdef DEBUG_QDA
    SG_PRINT("\n>>> Displaying norm2 ...\n")
    SGMatrix< float64_t >::display_matrix(norm2.data(), num_vecs, m_num_classes);
#endif

    CMulticlassLabels* out = new CMulticlassLabels(num_vecs);

    for (int i = 0 ; i < num_vecs; i++)
        out->set_label(i, CMath::arg_max(norm2.data()+i, num_vecs, m_num_classes));

    return out;
}

bool CQDA::train_machine(CFeatures* data)
{
    if (!m_labels)
        SG_ERROR("No labels allocated in QDA training\n")

    if ( data )
    {
        if (!data->has_property(FP_DOT))
            SG_ERROR("Speficied features are not of type CDotFeatures\n")

        set_features((CDotFeatures*) data);
    }

    if (!m_features)
        SG_ERROR("No features allocated in QDA training\n")

    SGVector< int32_t > train_labels = ((CMulticlassLabels*) m_labels)->get_int_labels();

    if (!train_labels.vector)
        SG_ERROR("No train_labels allocated in QDA training\n")

    cleanup();

    m_num_classes = ((CMulticlassLabels*) m_labels)->get_num_classes();
    m_dim = m_features->get_dim_feature_space();
    int32_t num_vec  = m_features->get_num_vectors();

    if (num_vec != train_labels.vlen)
        SG_ERROR("Dimension mismatch between features and labels in QDA training")

    int32_t* class_idxs = SG_MALLOC(int32_t, num_vec*m_num_classes); // number of examples of each class
    int32_t* class_nums = SG_MALLOC(int32_t, m_num_classes);
    memset(class_nums, 0, m_num_classes*sizeof(int32_t));
    int32_t class_idx;

    for (int i = 0; i < train_labels.vlen; i++)
    {
        class_idx = train_labels.vector[i];

        if (class_idx < 0 || class_idx >= m_num_classes)
        {
            SG_ERROR("found label out of {0, 1, 2, ..., num_classes-1}...")
            return false;
        }
        else
        {
            class_idxs[ class_idx*num_vec + class_nums[class_idx]++ ] = i;
        }
    }

    for (int i = 0; i < m_num_classes; i++)
    {
        if (class_nums[i] <= 0)
        {
            SG_ERROR("What? One class with no elements\n")
            return false;
        }
    }

    if (m_store_covs)
    {
        // cov_dims will be free in m_covs.destroy_ndarray()
        index_t * cov_dims = SG_MALLOC(index_t, 3);
        cov_dims[0] = m_dim;
        cov_dims[1] = m_dim;
        cov_dims[2] = m_num_classes;
        m_covs = SGNDArray< float64_t >(cov_dims, 3);
    }

    m_means = SGMatrix< float64_t >(m_dim, m_num_classes, true);
    SGMatrix< float64_t > scalings  = SGMatrix< float64_t >(m_dim, m_num_classes);

    // rot_dims will be freed in rotations.destroy_ndarray()
    index_t* rot_dims = SG_MALLOC(index_t, 3);
    rot_dims[0] = m_dim;
    rot_dims[1] = m_dim;
    rot_dims[2] = m_num_classes;
    SGNDArray< float64_t > rotations = SGNDArray< float64_t >(rot_dims, 3);

    CDenseFeatures< float64_t >* rf = (CDenseFeatures< float64_t >*) m_features;

    m_means.zero();

    int32_t vlen;
    bool vfree;
    float64_t* vec;
    for (int k = 0; k < m_num_classes; k++)
    {
        MatrixXd buffer(class_nums[k], m_dim);
        Map< VectorXd > Em_means(m_means.get_column_vector(k), m_dim);
        for (int i = 0; i < class_nums[k]; i++)
        {
            vec = rf->get_feature_vector(class_idxs[k*num_vec + i], vlen, vfree);
            ASSERT(vec)

            Map< VectorXd > Evec(vec, vlen);
            Em_means += Evec;
            buffer.row(i) = Evec;

            rf->free_feature_vector(vec, class_idxs[k*num_vec + i], vfree);
        }

        Em_means /= class_nums[k];

        for (int i = 0; i < class_nums[k]; i++)
            buffer.row(i) -= Em_means;

        // SVD
        float64_t * col = scalings.get_column_vector(k);
        float64_t * rot_mat = rotations.get_matrix(k);

        Eigen::JacobiSVD<MatrixXd> eSvd;
        eSvd.compute(buffer,Eigen::ComputeFullV);
        memcpy(col, eSvd.singularValues().data(), m_dim*sizeof(float64_t));
        memcpy(rot_mat, eSvd.matrixV().data(), m_dim*m_dim*sizeof(float64_t));

        SGVector<float64_t>::vector_multiply(col, col, col, m_dim);
        SGVector<float64_t>::scale_vector(1.0/(class_nums[k]-1), col, m_dim);
        rotations.transpose_matrix(k);

        if (m_store_covs)
        {
            SGMatrix< float64_t > M(m_dim ,m_dim);
            MatrixXd MEig = Map<MatrixXd>(rot_mat,m_dim,m_dim);
            for (int i = 0; i < m_dim; i++)
                for (int j = 0; j < m_dim; j++)
                    M(i,j)*=scalings[k*m_dim + j];
            MatrixXd rotE = Map<MatrixXd>(rot_mat,m_dim,m_dim);
            MatrixXd resE(m_dim,m_dim);
            resE = MEig * rotE.transpose();
            memcpy(m_covs.get_matrix(k),resE.data(),m_dim*m_dim*sizeof(float64_t));
        }
    }

    /* Computation of terms required for classification */
    SGVector< float32_t > sinvsqrt(m_dim);

    // M_dims will be freed in m_M.destroy_ndarray()
    index_t* M_dims = SG_MALLOC(index_t, 3);
    M_dims[0] = m_dim;
    M_dims[1] = m_dim;
    M_dims[2] = m_num_classes;
    m_M = SGNDArray< float64_t >(M_dims, 3);

    m_slog = SGVector< float32_t >(m_num_classes);
    m_slog.zero();

    index_t idx = 0;
    for (int k = 0; k < m_num_classes; k++)
    {
        for (int j = 0; j < m_dim; j++)
        {
            sinvsqrt[j] = 1.0 / CMath::sqrt(scalings[k*m_dim + j]);
            m_slog[k]  += CMath::log(scalings[k*m_dim + j]);
        }

        for (int i = 0; i < m_dim; i++)
            for (int j = 0; j < m_dim; j++)
            {
                idx = k*m_dim*m_dim + i + j*m_dim;
                m_M[idx] = rotations[idx] * sinvsqrt[j];
            }
    }

#ifdef DEBUG_QDA
    SG_PRINT(">>> QDA machine trained with %d classes\n", m_num_classes)

    SG_PRINT("\n>>> Displaying means ...\n")
    SGMatrix< float64_t >::display_matrix(m_means.matrix, m_dim, m_num_classes);

    SG_PRINT("\n>>> Displaying scalings ...\n")
    SGMatrix< float64_t >::display_matrix(scalings.matrix, m_dim, m_num_classes);

    SG_PRINT("\n>>> Displaying rotations ... \n")
    for (int k = 0; k < m_num_classes; k++)
        SGMatrix< float64_t >::display_matrix(rotations.get_matrix(k), m_dim, m_dim);

    SG_PRINT("\n>>> Displaying sinvsqrt ... \n")
    sinvsqrt.display_vector();

    SG_PRINT("\n>>> Diplaying m_M matrices ... \n")
    for (int k = 0; k < m_num_classes; k++)
        SGMatrix< float64_t >::display_matrix(m_M.get_matrix(k), m_dim, m_dim);

    SG_PRINT("\n>>> Exit DEBUG_QDA\n")
#endif

    SG_FREE(class_idxs);
    SG_FREE(class_nums);
    return true;
}

#endif /* HAVE_EIGEN3 */