HessianLocallyLinearEmbedding.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/preprocessor/HessianLocallyLinearEmbedding.h>
#ifdef HAVE_LAPACK
#include <shogun/mathematics/arpack.h>
#include <shogun/mathematics/lapack.h>
#include <shogun/lib/common.h>
#include <shogun/mathematics/Math.h>
#include <shogun/io/SGIO.h>
#include <shogun/distance/EuclidianDistance.h>
#include <shogun/lib/Signal.h>

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

using namespace shogun;

#ifndef DOXYGEN_SHOULD_SKIP_THIS
struct HESSIANESTIMATION_THREAD_PARAM
{
    int32_t idx_start;
    int32_t idx_step;
    int32_t idx_stop;
    int32_t m_k;
    int32_t dim;
    int32_t N;
    int32_t dp;
    int32_t m_target_dim;
    const int32_t* neighborhood_matrix;
    const float64_t* feature_matrix;
    float64_t* local_feature_matrix;
    float64_t* Yi_matrix;
    float64_t* mean_vector;
    float64_t* s_values_vector;
    float64_t* tau;
    int32_t tau_len;
    float64_t* w_sum_vector;
    float64_t* q_matrix;
    float64_t* W_matrix;
#ifdef HAVE_PTHREAD

    PTHREAD_LOCK_T* W_matrix_lock;
#endif
};
#endif

CHessianLocallyLinearEmbedding::CHessianLocallyLinearEmbedding() :
        CLocallyLinearEmbedding()
{
}

CHessianLocallyLinearEmbedding::~CHessianLocallyLinearEmbedding()
{
}

bool CHessianLocallyLinearEmbedding::init(CFeatures* features)
{
    return true;
}

void CHessianLocallyLinearEmbedding::cleanup()
{
}

SGMatrix<float64_t> CHessianLocallyLinearEmbedding::apply_to_feature_matrix(CFeatures* features)
{
    ASSERT(features);
    // shorthand for simplefeatures
    CSimpleFeatures<float64_t>* simple_features = (CSimpleFeatures<float64_t>*) features;
    SG_REF(features);
    ASSERT(simple_features);

    // get dimensionality and number of vectors of data
    int32_t dim = simple_features->get_num_features();
    if (m_target_dim>dim)
        SG_ERROR("Cannot increase dimensionality: target dimensionality is %d while given features dimensionality is %d.\n",
                 m_target_dim, dim);

    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);

    // loop variables
    int32_t t;

    int32_t dp = m_target_dim*(m_target_dim+1)/2;
    ASSERT(m_k>=(1+m_target_dim+dp));

    // compute distance matrix
    CDistance* distance = new CEuclidianDistance(simple_features,simple_features);
    SGMatrix<int32_t> neighborhood_matrix = get_neighborhood_matrix(distance);

    // init W (weight) matrix
    float64_t* W_matrix = SG_CALLOC(float64_t, N*N);
    
#ifdef HAVE_PTHREAD
    int32_t num_threads = parallel->get_num_threads();
    ASSERT(num_threads>0);
    // allocate threads and params
    pthread_t* threads = SG_MALLOC(pthread_t, num_threads);
    HESSIANESTIMATION_THREAD_PARAM* parameters = SG_MALLOC(HESSIANESTIMATION_THREAD_PARAM, num_threads);

#else
    int32_t num_threads = 1;
#endif

    // init matrices to be used
    float64_t* local_feature_matrix = SG_MALLOC(float64_t, m_k*dim*num_threads);
    float64_t* s_values_vector = SG_MALLOC(float64_t, dim*num_threads);
    int32_t tau_len = CMath::min((1+m_target_dim+dp), m_k);
    float64_t* tau = SG_MALLOC(float64_t, tau_len*num_threads);
    float64_t* mean_vector = SG_MALLOC(float64_t, dim*num_threads);
    float64_t* q_matrix = SG_MALLOC(float64_t, m_k*m_k*num_threads);
    float64_t* w_sum_vector = SG_MALLOC(float64_t, dp*num_threads);
    float64_t* Yi_matrix = SG_MALLOC(float64_t, m_k*(1+m_target_dim+dp)*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_attr_t attr;
    PTHREAD_LOCK_INIT(&W_matrix_lock);
    pthread_attr_init(&attr);
    pthread_attr_setdetachstate(&attr, PTHREAD_CREATE_JOINABLE);

    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].dim = dim;
        parameters[t].m_target_dim = m_target_dim;
        parameters[t].N = N;
        parameters[t].dp = dp;
        parameters[t].neighborhood_matrix = neighborhood_matrix.matrix;
        parameters[t].feature_matrix = feature_matrix.matrix;
        parameters[t].local_feature_matrix = local_feature_matrix + (m_k*dim)*t;
        parameters[t].Yi_matrix = Yi_matrix + (m_k*(1+m_target_dim+dp))*t;
        parameters[t].mean_vector = mean_vector + dim*t;
        parameters[t].s_values_vector = s_values_vector + dim*t;
        parameters[t].tau = tau+tau_len*t;
        parameters[t].tau_len = tau_len;
        parameters[t].w_sum_vector = w_sum_vector + dp*t;
        parameters[t].q_matrix = q_matrix + (m_k*m_k)*t;
        parameters[t].W_matrix = W_matrix;
        parameters[t].W_matrix_lock = &W_matrix_lock;
        pthread_create(&threads[t], &attr, run_hessianestimation_thread, (void*)&parameters[t]);
    }
    for (t=0; t<num_threads; t++)
        pthread_join(threads[t], NULL);
    PTHREAD_LOCK_DESTROY(&W_matrix_lock);
    SG_FREE(parameters);
    SG_FREE(threads);
#else
    HESSIANESTIMATION_THREAD_PARAM single_thread_param;
    single_thread_param.idx_start = t;
    single_thread_param.idx_step = num_threads;
    single_thread_param.idx_stop = N;
    single_thread_param.m_k = m_k;
    single_thread_param.dim = dim;
    single_thread_param.m_target_dim = m_target_dim;
    single_thread_param.N = N;
    single_thread_param.dp = dp;
    single_thread_param.neighborhood_matrix = neighborhood_matrix.matrix;
    single_thread_param.feature_matrix = feature_matrix.matrix;
    single_thread_param.local_feature_matrix = local_feature_matrix;
    single_thread_param.Yi_matrix = Yi_matrix;
    single_thread_param.mean_vector = mean_vector;
    single_thread_param.s_values_vector = s_values_vector;
    single_thread_param.tau = tau;
    single_thread_param.tau_len = tau_len;
    single_thread_param.w_sum_vector = w_sum_vector;
    single_thread_param.q_matrix = q_matrix;
    single_thread_param.W_matrix = W_matrix;
    run_hessianestimation_thread((void*)&single_thread_param);
#endif

    // clean
    SG_FREE(Yi_matrix);
    SG_FREE(s_values_vector);
    SG_FREE(mean_vector);
    SG_FREE(tau);
    SG_FREE(w_sum_vector);
    neighborhood_matrix.destroy_matrix();
    SG_FREE(local_feature_matrix);
    SG_FREE(q_matrix);

    // finally construct embedding
    SGMatrix<float64_t> W_sgmatrix = SGMatrix<float64_t>(W_matrix,N,N);
    simple_features->set_feature_matrix(find_null_space(W_sgmatrix,m_target_dim,false));
    W_sgmatrix.destroy_matrix();

    SG_UNREF(features);
    return simple_features->get_feature_matrix();
}

SGVector<float64_t> CHessianLocallyLinearEmbedding::apply_to_feature_vector(SGVector<float64_t> vector)
{
    SG_NOTIMPLEMENTED;
    return vector;
}

void* CHessianLocallyLinearEmbedding::run_hessianestimation_thread(void* p)
{
    HESSIANESTIMATION_THREAD_PARAM* parameters = (HESSIANESTIMATION_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;
    int32_t dim = parameters->dim;
    int32_t N = parameters->N;
    int32_t dp = parameters->dp;
    int32_t m_target_dim = parameters->m_target_dim;
    const int32_t* neighborhood_matrix = parameters->neighborhood_matrix;
    const float64_t* feature_matrix = parameters->feature_matrix;
    float64_t* local_feature_matrix = parameters->local_feature_matrix;
    float64_t* Yi_matrix = parameters->Yi_matrix;
    float64_t* mean_vector = parameters->mean_vector;
    float64_t* s_values_vector = parameters->s_values_vector;
    float64_t* tau = parameters->tau;
    int32_t tau_len = parameters->tau_len;
    float64_t* w_sum_vector = parameters->w_sum_vector;
    float64_t* q_matrix = parameters->q_matrix;
    float64_t* W_matrix = parameters->W_matrix;
#ifdef HAVE_PTHREAD
    PTHREAD_LOCK_T* W_matrix_lock = parameters->W_matrix_lock;
#endif

    int i,j,k,l;

    for (i=idx_start; i<idx_stop; i+=idx_step)
    {
        // Yi(:,0) = 1
        for (j=0; j<m_k; j++)
            Yi_matrix[j] = 1.0;

        // fill mean vector with zeros
        for (j=0; j<dim; j++)
            mean_vector[j] = 0.0;

        // compute local feature matrix containing neighbors of i-th vector
        for (j=0; j<m_k; j++)
        {
            for (k=0; k<dim; k++)
            {
                local_feature_matrix[j*dim+k] = feature_matrix[neighborhood_matrix[j*N+i]*dim+k];
                mean_vector[k] += local_feature_matrix[j*dim+k];
            }
        }

        // compute mean
        for (j=0; j<dim; j++)
            mean_vector[j] /= m_k;

        // center feature vectors by mean
        for (j=0; j<m_k; j++)
        {
            for (k=0; k<dim; k++)
                local_feature_matrix[j*dim+k] -= mean_vector[k];
        }

        int32_t info = 0;
        // find right eigenvectors of local_feature_matrix
        wrap_dgesvd('N','O', dim,m_k,local_feature_matrix,dim,
                             s_values_vector,
                             NULL,1, NULL,1, &info);
        ASSERT(info==0);

        // Yi(0:m_k,1:1+m_target_dim) = Vh(0:m_k, 0:target_dim)
        for (j=0; j<m_target_dim; j++)
        {
            for (k=0; k<m_k; k++)
                Yi_matrix[(j+1)*m_k+k] = local_feature_matrix[k*dim+j];
        }

        int32_t ct = 0;
        
        // construct 2nd order hessian approx
        for (j=0; j<m_target_dim; j++)
        {
            for (k=0; k<m_target_dim-j; k++)
            {
                for (l=0; l<m_k; l++)
                {
                    Yi_matrix[(ct+k+1+m_target_dim)*m_k+l] = Yi_matrix[(j+1)*m_k+l]*Yi_matrix[(j+k+1)*m_k+l];
                }
            }
            ct += ct + m_target_dim - j;
        }
    
        // perform QR factorization
        wrap_dgeqrf(m_k,(1+m_target_dim+dp),Yi_matrix,m_k,tau,&info);
        ASSERT(info==0);
        wrap_dorgqr(m_k,(1+m_target_dim+dp),tau_len,Yi_matrix,m_k,tau,&info);
        ASSERT(info==0);
        
        float64_t* Pii = (Yi_matrix+m_k*(1+m_target_dim));

        for (j=0; j<dp; j++)
        {
            w_sum_vector[j] = 0.0;
            for (k=0; k<m_k; k++)
            {
                w_sum_vector[j] += Pii[j*m_k+k];
            }
            if (w_sum_vector[j]<0.001) 
                w_sum_vector[j] = 1.0;
            for (k=0; k<m_k; k++)
                Pii[j*m_k+k] /= w_sum_vector[j];
        }
        
        cblas_dgemm(CblasColMajor,CblasNoTrans,CblasTrans,
                    m_k,m_k,dp,
                    1.0,Pii,m_k,
                        Pii,m_k,
                    0.0,q_matrix,m_k);
#ifdef HAVE_PTHREAD
        PTHREAD_LOCK(W_matrix_lock);
#endif
        for (j=0; j<m_k; j++)
        {
            for (k=0; k<m_k; k++)
                W_matrix[N*neighborhood_matrix[k*N+i]+neighborhood_matrix[j*N+i]] += q_matrix[j*m_k+k];
        }
#ifdef HAVE_PTHREAD
        PTHREAD_UNLOCK(W_matrix_lock);
#endif
    }
    return NULL;
}
#endif /* HAVE_LAPACK */