LocallyLinearEmbedding.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) 2011 Sergey Lisitsyn
 * Copyright (C) 2011 Berlin Institute of Technology and Max-Planck-Society
 */

#include <shogun/converter/LocallyLinearEmbedding.h>
#include <shogun/lib/config.h>
#ifdef HAVE_LAPACK
#include <shogun/converter/EmbeddingConverter.h>
#include <shogun/mathematics/arpack.h>
#include <shogun/mathematics/lapack.h>
#include <shogun/lib/FibonacciHeap.h>
#include <shogun/lib/CoverTree.h>
#include <shogun/base/DynArray.h>
#include <shogun/mathematics/Math.h>
#include <shogun/io/SGIO.h>
#include <shogun/lib/Time.h>
#include <shogun/distance/Distance.h>
#include <shogun/lib/Signal.h>

#ifdef HAVE_PTHREAD
#include <pthread.h>
#endif

using namespace shogun;

#ifndef DOXYGEN_SHOULD_SKIP_THIS
struct LINRECONSTRUCTION_THREAD_PARAM
{
    int32_t idx_start;
    int32_t idx_stop;
    int32_t idx_step;
    int32_t m_k;
    const int32_t* neighborhood_matrix;
    const float64_t* feature_matrix;
    float64_t* z_matrix;
    float64_t* covariance_matrix;
    float64_t* id_vector;
    float64_t* W_matrix;
    float64_t m_reconstruction_shift;
    int32_t dim;
    int32_t N;
    int32_t actual_k;
#ifdef HAVE_PTHREAD

    PTHREAD_LOCK_T* W_matrix_lock;
#endif
};

class LLE_COVERTREE_POINT
{
public:

    LLE_COVERTREE_POINT(int32_t index, const SGMatrix<float64_t>& dmatrix)
    {
        point_index = index;
        distance_matrix = dmatrix;
    }

    inline double distance(const LLE_COVERTREE_POINT& p) const
    {
        return distance_matrix[point_index*distance_matrix.num_rows+p.point_index];
    }

    inline bool operator==(const LLE_COVERTREE_POINT& p) const
    {
        return (p.point_index==point_index);
    }

    int32_t point_index;
    SGMatrix<float64_t> distance_matrix;
};

#endif /* DOXYGEN_SHOULD_SKIP_THIS */

CLocallyLinearEmbedding::CLocallyLinearEmbedding() :
        CEmbeddingConverter()
{
    m_k = 10;
    m_max_k = 60;
    m_auto_k = false;
    m_nullspace_shift = -1e-9;
    m_reconstruction_shift = 1e-3;
#ifdef HAVE_ARPACK
    m_use_arpack = true;
#else
    m_use_arpack = false;
#endif
    init();
}

void CLocallyLinearEmbedding::init()
{
    SG_ADD(&m_auto_k, "auto_k",
      "whether k should be determined automatically in range", MS_AVAILABLE);
    SG_ADD(&m_k, "k", "number of neighbors", MS_AVAILABLE);
    SG_ADD(&m_max_k, "max_k",
      "maximum number of neighbors used to compute optimal one", MS_AVAILABLE);
    m_parameters->add(&m_nullspace_shift, "nullspace_shift",
      "nullspace finding regularization shift");
    SG_ADD(&m_reconstruction_shift, "reconstruction_shift",
      "shift used to regularize reconstruction step", MS_NOT_AVAILABLE);
    SG_ADD(&m_use_arpack, "use_arpack", "whether arpack is being used or not",
        MS_NOT_AVAILABLE);
}


CLocallyLinearEmbedding::~CLocallyLinearEmbedding()
{
}

void CLocallyLinearEmbedding::set_k(int32_t k)
{
    ASSERT(k>0);
    m_k = k;
}

int32_t CLocallyLinearEmbedding::get_k() const
{
    return m_k;
}

void CLocallyLinearEmbedding::set_max_k(int32_t max_k)
{
    ASSERT(max_k>=m_k);
    m_max_k = max_k;
}

int32_t CLocallyLinearEmbedding::get_max_k() const
{
    return m_max_k;
}

void CLocallyLinearEmbedding::set_auto_k(bool auto_k)
{
    m_auto_k = auto_k;
}

bool CLocallyLinearEmbedding::get_auto_k() const
{
    return m_auto_k;
}

void CLocallyLinearEmbedding::set_nullspace_shift(float64_t nullspace_shift)
{
    m_nullspace_shift = nullspace_shift;
}

float64_t CLocallyLinearEmbedding::get_nullspace_shift() const
{
    return m_nullspace_shift;
}

void CLocallyLinearEmbedding::set_reconstruction_shift(float64_t reconstruction_shift)
{
    m_reconstruction_shift = reconstruction_shift;
}

float64_t CLocallyLinearEmbedding::get_reconstruction_shift() const
{
    return m_reconstruction_shift;
}

void CLocallyLinearEmbedding::set_use_arpack(bool use_arpack)
{
    m_use_arpack = use_arpack;
}

bool CLocallyLinearEmbedding::get_use_arpack() const
{
    return m_use_arpack;
}

const char* CLocallyLinearEmbedding::get_name() const
{
    return "LocallyLinearEmbedding";
}

CFeatures* CLocallyLinearEmbedding::apply(CFeatures* features)
{
    ASSERT(features);
    // check features
    if (!(features->get_feature_class()==C_DENSE &&
          features->get_feature_type()==F_DREAL))
    {
        SG_ERROR("Given features are not of SimpleRealFeatures type.\n");
    }
    // shorthand for simplefeatures
    CDenseFeatures<float64_t>* simple_features = (CDenseFeatures<float64_t>*) features;
    SG_REF(features);

    // get and check number of vectors
    int32_t N = simple_features->get_num_vectors();
    if (m_k>=N)
        SG_ERROR("Number of neighbors (%d) should be less than number of objects (%d).\n",
                 m_k, N);

    // compute distance matrix
    SG_DEBUG("Computing distance matrix\n");
    ASSERT(m_distance);
    CTime* time = new CTime();
    time->start();
    m_distance->init(simple_features,simple_features);
    SGMatrix<float64_t> distance_matrix = m_distance->get_distance_matrix();
    m_distance->remove_lhs_and_rhs();
    SG_DEBUG("Distance matrix computation took %fs\n",time->cur_time_diff());
    SG_DEBUG("Calculating neighborhood matrix\n");
    SGMatrix<int32_t> neighborhood_matrix;

    time->start();
    if (m_auto_k)
    {
        neighborhood_matrix = get_neighborhood_matrix(distance_matrix,m_max_k);
        m_k = estimate_k(simple_features,neighborhood_matrix);
        SG_DEBUG("Estimated k with value of %d\n",m_k);
    }
    else
        neighborhood_matrix = get_neighborhood_matrix(distance_matrix,m_k);

    SG_DEBUG("Neighbors finding took %fs\n",time->cur_time_diff());

    // init W (weight) matrix
    float64_t* W_matrix = SG_CALLOC(float64_t, N*N);

    // construct weight matrix
    SG_DEBUG("Constructing weight matrix\n");
    time->start();
    SGMatrix<float64_t> weight_matrix = construct_weight_matrix(simple_features,W_matrix,neighborhood_matrix);
    SG_DEBUG("Weight matrix construction took %.5fs\n", time->cur_time_diff());

    // find null space of weight matrix
    SG_DEBUG("Finding nullspace\n");
    time->start();
    SGMatrix<float64_t> new_feature_matrix = construct_embedding(weight_matrix,m_target_dim);
    SG_DEBUG("Eigenproblem solving took %.5fs\n", time->cur_time_diff());
    delete time;

    SG_UNREF(features);
    return (CFeatures*)(new CDenseFeatures<float64_t>(new_feature_matrix));
}

int32_t CLocallyLinearEmbedding::estimate_k(CDenseFeatures<float64_t>* simple_features, SGMatrix<int32_t> neighborhood_matrix)
{
    int32_t right = m_max_k;
    int32_t left = m_k;
    int32_t left_third;
    int32_t right_third;
    ASSERT(right>=left);
    if (right==left) return left;
    int32_t dim;
    int32_t N;
    float64_t* feature_matrix= simple_features->get_feature_matrix(dim,N);
    float64_t* z_matrix = SG_MALLOC(float64_t,right*dim);
    float64_t* covariance_matrix = SG_MALLOC(float64_t,right*right);
    float64_t* resid_vector = SG_MALLOC(float64_t, right);
    float64_t* id_vector = SG_MALLOC(float64_t, right);
    while (right-left>2)
    {
        left_third = (left*2+right)/3;
        right_third = (right*2+left)/3;
        float64_t left_val = compute_reconstruction_error(left_third,dim,N,feature_matrix,z_matrix,
                                                          covariance_matrix,resid_vector,
                                                          id_vector,neighborhood_matrix);
        float64_t right_val = compute_reconstruction_error(right_third,dim,N,feature_matrix,z_matrix,
                                                           covariance_matrix,resid_vector,
                                                           id_vector,neighborhood_matrix);
        if (left_val<right_val)
            right = right_third;
        else
            left = left_third;
    }
    SG_FREE(z_matrix);
    SG_FREE(covariance_matrix);
    SG_FREE(resid_vector);
    SG_FREE(id_vector);
    return right;
}

float64_t CLocallyLinearEmbedding::compute_reconstruction_error(int32_t k, int dim, int N, float64_t* feature_matrix,
                                                                float64_t* z_matrix, float64_t* covariance_matrix,
                                                                float64_t* resid_vector, float64_t* id_vector,
                                                                SGMatrix<int32_t> neighborhood_matrix)
{
    // todo parse params
    int32_t i,j;
    float64_t total_residual_norm = 0.0;
    for (i=CMath::random(0,20); i<N; i+=N/20)
    {
        for (j=0; j<k; j++)
        {
            cblas_dcopy(dim,feature_matrix+neighborhood_matrix[i*m_k+j]*dim,1,z_matrix+j*dim,1);
            cblas_daxpy(dim,-1.0,feature_matrix+i*dim,1,z_matrix+j*dim,1);
        }
        cblas_dgemm(CblasColMajor,CblasTrans,CblasNoTrans,
                k,k,dim,
                1.0,z_matrix,dim,
                z_matrix,dim,
                0.0,covariance_matrix,k);
        for (j=0; j<k; j++)
        {
            resid_vector[j] = 1.0;
            id_vector[j] = 1.0;
        }
        if (k>dim)
        {
            float64_t trace = 0.0;
            for (j=0; j<k; j++)
                trace += covariance_matrix[j*k+j];
            for (j=0; j<m_k; j++)
                covariance_matrix[j*k+j] += m_reconstruction_shift*trace;
        }
        clapack_dposv(CblasColMajor,CblasLower,k,1,covariance_matrix,k,id_vector,k);
        float64_t norming=0.0;
        for (j=0; j<k; j++)
            norming += id_vector[j];
        cblas_dscal(k,-1.0/norming,id_vector,1);
        cblas_dsymv(CblasColMajor,CblasLower,k,-1.0,covariance_matrix,k,id_vector,1,1.0,resid_vector,1);
        total_residual_norm += cblas_dnrm2(k,resid_vector,1);
    }
    return total_residual_norm/k;
}

SGMatrix<float64_t> CLocallyLinearEmbedding::construct_weight_matrix(CDenseFeatures<float64_t>* simple_features,
                                                                     float64_t* W_matrix, SGMatrix<int32_t> neighborhood_matrix)
{
    int32_t N = simple_features->get_num_vectors();
    int32_t dim = simple_features->get_num_features();
#ifdef HAVE_PTHREAD
    int32_t t;
    int32_t num_threads = parallel->get_num_threads();
    ASSERT(num_threads>0);
    // allocate threads
    pthread_t* threads = SG_MALLOC(pthread_t, num_threads);
    LINRECONSTRUCTION_THREAD_PARAM* parameters = SG_MALLOC(LINRECONSTRUCTION_THREAD_PARAM, num_threads);
    pthread_attr_t attr;
    pthread_attr_init(&attr);
    pthread_attr_setdetachstate(&attr, PTHREAD_CREATE_JOINABLE);
#else
    int32_t num_threads = 1;
#endif
    // init storages to be used
    float64_t* z_matrix = SG_MALLOC(float64_t, m_k*dim*num_threads);
    float64_t* covariance_matrix = SG_MALLOC(float64_t, m_k*m_k*num_threads);
    float64_t* id_vector = SG_MALLOC(float64_t, m_k*num_threads);

    // get feature matrix
    SGMatrix<float64_t> feature_matrix = simple_features->get_feature_matrix();

#ifdef HAVE_PTHREAD
    PTHREAD_LOCK_T W_matrix_lock;
    PTHREAD_LOCK_INIT(&W_matrix_lock);
    for (t=0; t<num_threads; t++)
    {
        parameters[t].idx_start = t;
        parameters[t].idx_step = num_threads;
        parameters[t].idx_stop = N;
        parameters[t].m_k = m_k;
        parameters[t].neighborhood_matrix = neighborhood_matrix.matrix;
        parameters[t].z_matrix = z_matrix+(m_k*dim)*t;
        parameters[t].feature_matrix = feature_matrix.matrix;
        parameters[t].covariance_matrix = covariance_matrix+(m_k*m_k)*t;
        parameters[t].id_vector = id_vector+m_k*t;
        parameters[t].W_matrix = W_matrix;
        parameters[t].m_reconstruction_shift = m_reconstruction_shift;
        parameters[t].dim = feature_matrix.num_rows;
        parameters[t].N = feature_matrix.num_cols;
        parameters[t].actual_k = neighborhood_matrix.num_rows;
        parameters[t].W_matrix_lock = &W_matrix_lock;
        pthread_create(&threads[t], &attr, run_linearreconstruction_thread, (void*)&parameters[t]);
    }
    for (t=0; t<num_threads; t++)
        pthread_join(threads[t], NULL);
    pthread_attr_destroy(&attr);
    SG_FREE(parameters);
    SG_FREE(threads);
#else
    LINRECONSTRUCTION_THREAD_PARAM single_thread_param;
    single_thread_param.idx_start = 0;
    single_thread_param.idx_step = 1;
    single_thread_param.idx_stop = N;
    single_thread_param.m_k = m_k;
    single_thread_param.neighborhood_matrix = neighborhood_matrix.matrix;
    single_thread_param.z_matrix = z_matrix;
    single_thread_param.feature_matrix = feature_matrix.matrix;
    single_thread_param.covariance_matrix = covariance_matrix;
    single_thread_param.id_vector = id_vector;
    single_thread_param.W_matrix = W_matrix;
    single_thread_param.m_reconstruction_shift = m_reconstruction_shift;
    run_linearreconstruction_thread((void*)&single_thread_param);
#endif

    // clean
    SG_FREE(id_vector);
    SG_FREE(z_matrix);
    SG_FREE(covariance_matrix);

    return SGMatrix<float64_t>(W_matrix,N,N);
}

SGMatrix<float64_t> CLocallyLinearEmbedding::construct_embedding(SGMatrix<float64_t> matrix,int dimension)
{
    int i,j;
    ASSERT(matrix.num_cols==matrix.num_rows);
    int N = matrix.num_cols;
    // get eigenvectors with ARPACK or LAPACK
    int eigenproblem_status = 0;

    float64_t* eigenvalues_vector = NULL;
    float64_t* eigenvectors = NULL;
    float64_t* nullspace_features = NULL;
    if (m_use_arpack)
    {
#ifndef HAVE_ARPACK
        SG_ERROR("ARPACK is not supported in this configuration.\n");
#endif
        // using ARPACK (faster)
        eigenvalues_vector = SG_MALLOC(float64_t, dimension+1);
#ifdef HAVE_ARPACK
        arpack_dsxupd(matrix.matrix,NULL,false,N,dimension+1,"LA",true,3,true,false,m_nullspace_shift,0.0,
                      eigenvalues_vector,matrix.matrix,eigenproblem_status);
        matrix.num_rows = dimension+1;
#endif
        if (eigenproblem_status)
            SG_ERROR("ARPACK failed with code: %d", eigenproblem_status);
        nullspace_features = SG_MALLOC(float64_t, N*dimension);
        for (i=0; i<dimension; i++)
        {
            for (j=0; j<N; j++)
                nullspace_features[j*dimension+i] = matrix[j*(dimension+1)+i+1];
        }
        SG_FREE(eigenvalues_vector);
    }
    else
    {
        // using LAPACK (slower)
        eigenvalues_vector = SG_MALLOC(float64_t, N);
        eigenvectors = SG_MALLOC(float64_t,(dimension+1)*N);
        wrap_dsyevr('V','U',N,matrix.matrix,N,2,dimension+2,eigenvalues_vector,eigenvectors,&eigenproblem_status);
        if (eigenproblem_status)
            SG_ERROR("LAPACK failed with code: %d", eigenproblem_status);
        nullspace_features = SG_MALLOC(float64_t, N*dimension);
        // LAPACKed eigenvectors
        for (i=0; i<dimension; i++)
        {
            for (j=0; j<N; j++)
                nullspace_features[j*dimension+i] = eigenvectors[i*N+j];
        }
        SG_FREE(eigenvectors);
        SG_FREE(eigenvalues_vector);
    }
    return SGMatrix<float64_t>(nullspace_features,dimension,N);
}

void* CLocallyLinearEmbedding::run_linearreconstruction_thread(void* p)
{
    LINRECONSTRUCTION_THREAD_PARAM* parameters = (LINRECONSTRUCTION_THREAD_PARAM*)p;
    int32_t idx_start = parameters->idx_start;
    int32_t idx_step = parameters->idx_step;
    int32_t idx_stop = parameters->idx_stop;
    int32_t m_k = parameters->m_k;
    const int32_t* neighborhood_matrix = parameters->neighborhood_matrix;
    float64_t* z_matrix = parameters->z_matrix;
    const float64_t* feature_matrix = parameters->feature_matrix;
    float64_t* covariance_matrix = parameters->covariance_matrix;
    float64_t* id_vector = parameters->id_vector;
    float64_t* W_matrix = parameters->W_matrix;
    float64_t m_reconstruction_shift = parameters->m_reconstruction_shift;
#ifdef HAVE_PTHREAD
    PTHREAD_LOCK_T* W_matrix_lock = parameters->W_matrix_lock;
#endif

    int32_t i,j,k;
    int32_t dim = parameters->dim;
    int32_t N = parameters->N;
    int32_t actual_k = parameters->actual_k;
    float64_t norming,trace;

    for (i=idx_start; i<idx_stop; i+=idx_step)
    {
        // compute local feature matrix containing neighbors of i-th vector
        // center features by subtracting i-th feature column
        for (j=0; j<m_k; j++)
        {
            cblas_dcopy(dim,feature_matrix+neighborhood_matrix[i*actual_k+j]*dim,1,z_matrix+j*dim,1);
            cblas_daxpy(dim,-1.0,feature_matrix+i*dim,1,z_matrix+j*dim,1);
        }

        // compute local covariance matrix
        cblas_dgemm(CblasColMajor,CblasTrans,CblasNoTrans,
                    m_k,m_k,dim,
                    1.0,z_matrix,dim,
                    z_matrix,dim,
                    0.0,covariance_matrix,m_k);

        for (j=0; j<m_k; j++)
            id_vector[j] = 1.0;

        // regularize in case of ill-posed system
        if (m_k>dim)
        {
            // compute tr(C)
            trace = 0.0;
            for (j=0; j<m_k; j++)
                trace += covariance_matrix[j*m_k+j];

            for (j=0; j<m_k; j++)
                covariance_matrix[j*m_k+j] += m_reconstruction_shift*trace;
        }

        // solve system of linear equations: covariance_matrix * X = 1
        // covariance_matrix is a pos-def matrix
        clapack_dposv(CblasColMajor,CblasLower,m_k,1,covariance_matrix,m_k,id_vector,m_k);

        // normalize weights
        norming=0.0;
        for (j=0; j<m_k; j++)
            norming += id_vector[j];

        cblas_dscal(m_k,1.0/norming,id_vector,1);

        memset(covariance_matrix,0,sizeof(float64_t)*m_k*m_k);
        cblas_dger(CblasColMajor,m_k,m_k,1.0,id_vector,1,id_vector,1,covariance_matrix,m_k);

        // put weights into W matrix
        W_matrix[N*i+i] += 1.0;
#ifdef HAVE_PTHREAD
        PTHREAD_LOCK(W_matrix_lock);
#endif
        for (j=0; j<m_k; j++)
        {
            W_matrix[N*i+neighborhood_matrix[i*actual_k+j]] -= id_vector[j];
            W_matrix[N*neighborhood_matrix[i*actual_k+j]+i] -= id_vector[j];
        }
        for (j=0; j<m_k; j++)
        {
            for (k=0; k<m_k; k++)
                W_matrix[N*neighborhood_matrix[i*actual_k+j]+neighborhood_matrix[i*actual_k+k]]+=
                  covariance_matrix[j*m_k+k];
        }
#ifdef HAVE_PTHREAD
        PTHREAD_UNLOCK(W_matrix_lock);
#endif
    }
    return NULL;
}

SGMatrix<int32_t> CLocallyLinearEmbedding::get_neighborhood_matrix(SGMatrix<float64_t> distance_matrix, int32_t k)
{
    int32_t i;
    int32_t N = distance_matrix.num_rows;

    int32_t* neighborhood_matrix = SG_MALLOC(int32_t, N*k);

    float64_t max_dist = SGVector<float64_t>::max(distance_matrix.matrix,N*N);

    CoverTree<LLE_COVERTREE_POINT>* coverTree = new CoverTree<LLE_COVERTREE_POINT>(max_dist);

    for (i=0; i<N; i++)
        coverTree->insert(LLE_COVERTREE_POINT(i,distance_matrix));

    for (i=0; i<N; i++)
    {
        std::vector<LLE_COVERTREE_POINT> neighbors =
           coverTree->kNearestNeighbors(LLE_COVERTREE_POINT(i,distance_matrix),k+1);
        for (std::size_t m=1; m<unsigned(k+1); m++)
            neighborhood_matrix[i*k+m-1] = neighbors[m].point_index;
    }

    delete coverTree;

    return SGMatrix<int32_t>(neighborhood_matrix,k,N);
}
#endif /* HAVE_LAPACK */