PointSetKernel.h

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//===========================================================================
/*!
 * 
 *
 * \brief       Applies a kernel to two pointsets and comptues the average response
 * 
 * 
 *
 * \author      T.Glasmachers, O. Krause, M. Tuma
 * \date        2010, 2011
 *
 *
 * \par Copyright 1995-2017 Shark Development Team
 * 
 * <BR><HR>
 * This file is part of Shark.
 * <http://shark-ml.org/>
 * 
 * Shark 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 3 of the License, or
 * (at your option) any later version.
 * 
 * Shark 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 Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public License
 * along with Shark.  If not, see <http://www.gnu.org/licenses/>.
 *
 */
//===========================================================================

#ifndef SHARK_MODELS_KERNELS_POINT_SET_KERNEL_H
#define SHARK_MODELS_KERNELS_POINT_SET_KERNEL_H


#include <shark/Models/Kernels/AbstractKernelFunction.h>

namespace shark {


/// \brief Normalized version of a kernel function
///
/// For a positive definite kernel k, the normalized kernel
/// \f[ \tilde k(x, y) := \frac{k(x, y)}{\sqrt{k(x, x) \cdot k(y, y)}} \f]
/// is again a positive definite kernel function.
template<class InputType=RealVector>
class PointSetKernel : public AbstractKernelFunction<typename Batch<InputType>::type >
{
private:
    typedef AbstractKernelFunction<typename Batch<InputType>::type> base_type;
    
    struct InternalState: public State{
        std::vector<boost::shared_ptr<State> > state;
        
        void resize(std::size_t sizeX1,std::size_t sizeX2, AbstractKernelFunction<InputType> const* base){
            state.resize(sizeX1 * sizeX2);
            
            for(std::size_t i = 0; i != state.size();++i){
                state[i] = base->createState();
            } 
        }
    };
public:
    typedef typename base_type::BatchInputType BatchInputType;
    typedef typename base_type::ConstBatchInputReference ConstBatchInputReference;
    typedef typename base_type::ConstInputReference ConstInputReference;
    
    PointSetKernel(AbstractKernelFunction<InputType>* base) : m_base(base){
        SHARK_ASSERT( base != NULL );
        if ( m_base->hasFirstParameterDerivative() ) 
            this->m_features|=base_type::HAS_FIRST_PARAMETER_DERIVATIVE;
    }

    std::string name() const
    { return "PointSetKernel<" + m_base->name() + ">"; }

    RealVector parameterVector() const{
        return m_base->parameterVector();
    }

    void setParameterVector(RealVector const& newParameters){
        m_base->setParameterVector(newParameters);
    }

    std::size_t numberOfParameters() const{
        return m_base->numberOfParameters();
    }
    
    ///\brief creates the internal state of the kernel
    boost::shared_ptr<State> createState()const{
        InternalState* state = new InternalState();
        return boost::shared_ptr<State>(state);
    }

    ///evaluates \f$ k(x,y) \f$
    ///
    /// calculates
    /// \f[ \tilde k(x, y) := \frac{k(x, y)}{\sqrt{k(x, x) \cdot k(y, y)}} \f]
    double eval(ConstInputReference x1, ConstInputReference x2) const{
        RealMatrix response = (*m_base)(x1,x2);
        
        return sum(response)/(response.size1() * response.size2());
    }
    
    
    void eval(ConstBatchInputReference const& batchX1, ConstBatchInputReference const& batchX2, RealMatrix& result, State& state) const{
        InternalState& s = state.toState<InternalState>();
        
        std::size_t sizeX1 = batchSize(batchX1);
        std::size_t sizeX2 = batchSize(batchX2);
        s.resize(sizeX1,sizeX2,m_base);
        result.resize(sizeX1,sizeX2);
        RealMatrix response;
        for(std::size_t i = 0; i != sizeX1; ++i){
            for(std::size_t j = 0; j != sizeX2; ++j){
                m_base->eval(getBatchElement(batchX1,i),getBatchElement(batchX2,j),response,*s.state[i*sizeX2+j]);
                result(i,j) = sum(response)/(response.size1() * response.size2());
            }
        }
    }
    
    void eval(ConstBatchInputReference const& batchX1, ConstBatchInputReference const& batchX2, RealMatrix& result) const{
        std::size_t sizeX1 = batchSize(batchX1);
        std::size_t sizeX2 = batchSize(batchX2);
        result.resize(sizeX1,sizeX2);
        
        RealMatrix response;
        for(std::size_t i = 0; i != sizeX1; ++i){
            for(std::size_t j = 0; j != sizeX2; ++j){
                m_base->eval(getBatchElement(batchX1,i),getBatchElement(batchX2,j),response);
                result(i,j) = sum(response)/(response.size1() * response.size2());
            }
        }
    }

    void weightedParameterDerivative(
        ConstBatchInputReference const& batchX1, 
        ConstBatchInputReference const& batchX2, 
        RealMatrix const& coefficients,
        State const& state, 
        RealVector& gradient
    ) const{
        gradient.resize(numberOfParameters());
        InternalState const& s = state.toState<InternalState>();
        std::size_t sizeX1 = batchSize(batchX1);
        std::size_t sizeX2 = batchSize(batchX2);
        
        for(std::size_t i = 0; i != sizeX1; ++i){
            for(std::size_t j = 0; j != sizeX2; ++j){
                auto x1 = getBatchElement(batchX1,i);
                auto x2 = getBatchElement(batchX2,j);
                std::size_t size1 = batchSize(x1);
                std::size_t size2 = batchSize(x2);
                RealMatrix setCoeff(size1,size2, coefficients(i,j)/(size1 * size2));
                RealVector grad;
                m_base->weightedParameterDerivative(x1,x2,setCoeff,*s.state[i*sizeX2+j],grad);
                noalias(gradient) += grad;
            }
        }
    }

protected:
    /// kernel to normalize
    AbstractKernelFunction<InputType>* m_base;
};

}
#endif