dlib C++ Library - kernel.h

    // Copyright (C) 2007  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_SVm_KERNEL
    #define DLIB_SVm_KERNEL

    #include "kernel_abstract.h"
    #include <cmath>
    #include <limits>
    #include <sstream>
    #include "../matrix.h"
    #include "../algs.h"
    #include "../serialize.h"

    namespace dlib
    {

    // ----------------------------------------------------------------------------------------

        template < typename kernel_type > struct kernel_derivative;

    // ----------------------------------------------------------------------------------------

        template <
            typename T
            >
        struct radial_basis_kernel
        {
            typedef typename T::type scalar_type;
            typedef T sample_type;
            typedef typename T::mem_manager_type mem_manager_type;

            // T must be capable of representing a column vector.
            COMPILE_TIME_ASSERT(T::NC == 1 || T::NC == 0);

            radial_basis_kernel(const scalar_type g) : gamma(g) {}
            radial_basis_kernel() : gamma(0.1) {}
            radial_basis_kernel(
                const radial_basis_kernel& k
            ) : gamma(k.gamma) {}

            const scalar_type gamma;

            scalar_type operator() (
                const sample_type& a,
                const sample_type& b
            ) const
            {
                const scalar_type d = trans(a-b)*(a-b);
                return std::exp(-gamma*d);
            }

            radial_basis_kernel& operator= (
                const radial_basis_kernel& k
            )
            {
                const_cast<scalar_type&>(gamma) = k.gamma;
                return *this;
            }

            bool operator== (
                const radial_basis_kernel& k
            ) const
            {
                return gamma == k.gamma;
            }
        };

        template <
            typename T
            >
        void serialize (
            const radial_basis_kernel<T>& item,
            std::ostream& out
        )
        {
            try
            {
                serialize(item.gamma, out);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while serializing object of type radial_basis_kernel");
            }
        }

        template <
            typename T
            >
        void deserialize (
            radial_basis_kernel<T>& item,
            std::istream& in
        )
        {
            typedef typename T::type scalar_type;
            try
            {
                deserialize(const_cast<scalar_type&>(item.gamma), in);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while deserializing object of type radial_basis_kernel");
            }
        }

        template <
            typename T
            >
        struct kernel_derivative<radial_basis_kernel<T> >
        {
            typedef typename T::type scalar_type;
            typedef T sample_type;
            typedef typename T::mem_manager_type mem_manager_type;

            kernel_derivative(const radial_basis_kernel<T>& k_) : k(k_){}

            const sample_type& operator() (const sample_type& x, const sample_type& y) const
            {
                // return the derivative of the rbf kernel
                temp = 2*k.gamma*(x-y)*k(x,y);
                return temp;
            }

            const radial_basis_kernel<T>& k;
            mutable sample_type temp;
        };

    // ----------------------------------------------------------------------------------------

        template <
            typename T
            >
        struct polynomial_kernel
        {
            typedef typename T::type scalar_type;
            typedef T sample_type;
            typedef typename T::mem_manager_type mem_manager_type;

            // T must be capable of representing a column vector.
            COMPILE_TIME_ASSERT(T::NC == 1 || T::NC == 0);

            polynomial_kernel(const scalar_type g, const scalar_type c, const scalar_type d) : gamma(g), coef(c), degree(d) {}
            polynomial_kernel() : gamma(1), coef(0), degree(1) {}
            polynomial_kernel(
                const polynomial_kernel& k
            ) : gamma(k.gamma), coef(k.coef), degree(k.degree) {}

            typedef T type;
            const scalar_type gamma;
            const scalar_type coef;
            const scalar_type degree;

            scalar_type operator() (
                const sample_type& a,
                const sample_type& b
            ) const
            {
                return std::pow(gamma*(trans(a)*b) + coef, degree);
            }

            polynomial_kernel& operator= (
                const polynomial_kernel& k
            )
            {
                const_cast<scalar_type&>(gamma) = k.gamma;
                const_cast<scalar_type&>(coef) = k.coef;
                const_cast<scalar_type&>(degree) = k.degree;
                return *this;
            }

            bool operator== (
                const polynomial_kernel& k
            ) const
            {
                return (gamma == k.gamma) && (coef == k.coef) && (degree == k.degree);
            }
        };

        template <
            typename T
            >
        void serialize (
            const polynomial_kernel<T>& item,
            std::ostream& out
        )
        {
            try
            {
                serialize(item.gamma, out);
                serialize(item.coef, out);
                serialize(item.degree, out);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while serializing object of type polynomial_kernel");
            }
        }

        template <
            typename T
            >
        void deserialize (
            polynomial_kernel<T>& item,
            std::istream& in
        )
        {
            typedef typename T::type scalar_type;
            try
            {
                deserialize(const_cast<scalar_type&>(item.gamma), in);
                deserialize(const_cast<scalar_type&>(item.coef), in);
                deserialize(const_cast<scalar_type&>(item.degree), in);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while deserializing object of type polynomial_kernel");
            }
        }

        template <
            typename T
            >
        struct kernel_derivative<polynomial_kernel<T> >
        {
            typedef typename T::type scalar_type;
            typedef T sample_type;
            typedef typename T::mem_manager_type mem_manager_type;

            kernel_derivative(const polynomial_kernel<T>& k_) : k(k_){}

            const sample_type& operator() (const sample_type& x, const sample_type& y) const
            {
                // return the derivative of the rbf kernel
                temp = k.degree*k.gamma*x*std::pow(k.gamma*(trans(x)*y) + k.coef, k.degree-1);
                return temp;
            }

            const polynomial_kernel<T>& k;
            mutable sample_type temp;
        };

    // ----------------------------------------------------------------------------------------

        template <
            typename T
            >
        struct sigmoid_kernel
        {
            typedef typename T::type scalar_type;
            typedef T sample_type;
            typedef typename T::mem_manager_type mem_manager_type;

            // T must be capable of representing a column vector.
            COMPILE_TIME_ASSERT(T::NC == 1 || T::NC == 0);

            sigmoid_kernel(const scalar_type g, const scalar_type c) : gamma(g), coef(c) {}
            sigmoid_kernel() : gamma(0.1), coef(-1.0) {}
            sigmoid_kernel(
                const sigmoid_kernel& k
            ) : gamma(k.gamma), coef(k.coef) {}

            typedef T type;
            const scalar_type gamma;
            const scalar_type coef;

            scalar_type operator() (
                const sample_type& a,
                const sample_type& b
            ) const
            {
                return std::tanh(gamma*(trans(a)*b) + coef);
            }

            sigmoid_kernel& operator= (
                const sigmoid_kernel& k
            )
            {
                const_cast<scalar_type&>(gamma) = k.gamma;
                const_cast<scalar_type&>(coef) = k.coef;
                return *this;
            }

            bool operator== (
                const sigmoid_kernel& k
            ) const
            {
                return (gamma == k.gamma) && (coef == k.coef);
            }
        };

        template <
            typename T
            >
        void serialize (
            const sigmoid_kernel<T>& item,
            std::ostream& out
        )
        {
            try
            {
                serialize(item.gamma, out);
                serialize(item.coef, out);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while serializing object of type sigmoid_kernel");
            }
        }

        template <
            typename T
            >
        void deserialize (
            sigmoid_kernel<T>& item,
            std::istream& in
        )
        {
            typedef typename T::type scalar_type;
            try
            {
                deserialize(const_cast<scalar_type&>(item.gamma), in);
                deserialize(const_cast<scalar_type&>(item.coef), in);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while deserializing object of type sigmoid_kernel");
            }
        }

        template <
            typename T
            >
        struct kernel_derivative<sigmoid_kernel<T> >
        {
            typedef typename T::type scalar_type;
            typedef T sample_type;
            typedef typename T::mem_manager_type mem_manager_type;

            kernel_derivative(const sigmoid_kernel<T>& k_) : k(k_){}

            const sample_type& operator() (const sample_type& x, const sample_type& y) const
            {
                // return the derivative of the rbf kernel
                temp = k.gamma*x*(1-std::pow(k(x,y),2));
                return temp;
            }

            const sigmoid_kernel<T>& k;
            mutable sample_type temp;
        };

    // ----------------------------------------------------------------------------------------

        template <typename T>
        struct linear_kernel
        {
            typedef typename T::type scalar_type;
            typedef T sample_type;
            typedef typename T::mem_manager_type mem_manager_type;

            // T must be capable of representing a column vector.
            COMPILE_TIME_ASSERT(T::NC == 1 || T::NC == 0);

            scalar_type operator() (
                const sample_type& a,
                const sample_type& b
            ) const
            {
                return trans(a)*b;
            }

            bool operator== (
                const linear_kernel&
            ) const
            {
                return true;
            }
        };

        template <
            typename T
            >
        void serialize (
            const linear_kernel<T>& ,
            std::ostream&
        ){}

        template <
            typename T
            >
        void deserialize (
            linear_kernel<T>& ,
            std::istream&
        ){}

        template <
            typename T
            >
        struct kernel_derivative<linear_kernel<T> >
        {
            typedef typename T::type scalar_type;
            typedef T sample_type;
            typedef typename T::mem_manager_type mem_manager_type;

            kernel_derivative(const linear_kernel<T>& k_) : k(k_){}

            const sample_type& operator() (const sample_type& x, const sample_type& ) const
            {
                return x;
            }

            const linear_kernel<T>& k;
        };

    // ----------------------------------------------------------------------------------------

        template <typename T>
        struct histogram_intersection_kernel
        {
            typedef typename T::type scalar_type;
            typedef T sample_type;
            typedef typename T::mem_manager_type mem_manager_type;

            scalar_type operator() (
                const sample_type& a,
                const sample_type& b
            ) const
            {
                scalar_type temp = 0;
                for (long i = 0; i < a.size(); ++i)
                {
                    temp += std::min(a(i), b(i));
                }
                return temp;
            }

            bool operator== (
                const histogram_intersection_kernel&
            ) const
            {
                return true;
            }
        };

        template <
            typename T
            >
        void serialize (
            const histogram_intersection_kernel<T>& ,
            std::ostream&
        ){}

        template <
            typename T
            >
        void deserialize (
            histogram_intersection_kernel<T>& ,
            std::istream&
        ){}

    // ----------------------------------------------------------------------------------------

        template <typename T>
        struct offset_kernel
        {
            typedef typename T::scalar_type scalar_type;
            typedef typename T::sample_type sample_type;
            typedef typename T::mem_manager_type mem_manager_type;

            offset_kernel(const T& k, const scalar_type& offset_
            ) : kernel(k), offset(offset_) {}
            offset_kernel() : kernel(T()), offset(0.01) {}
            offset_kernel(
                const offset_kernel& k
            ) : kernel(k.kernel), offset(k.offset) {}

            const T kernel;
            const scalar_type offset;

            scalar_type operator() (
                const sample_type& a,
                const sample_type& b
            ) const
            {
                return kernel(a,b) + offset;
            }

            offset_kernel& operator= (
                const offset_kernel& k
            )
            {
                const_cast<T&>(kernel) = k.kernel;
                const_cast<scalar_type&>(offset) = k.offset;
                return *this;
            }

            bool operator== (
                const offset_kernel& k
            ) const
            {
                return k.kernel == kernel && offset == k.offset;
            }
        };

        template <
            typename T
            >
        void serialize (
            const offset_kernel<T>& item,
            std::ostream& out
        )
        {
            try
            {
                serialize(item.offset, out);
                serialize(item.kernel, out);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while serializing object of type offset_kernel");
            }
        }

        template <
            typename T
            >
        void deserialize (
            offset_kernel<T>& item,
            std::istream& in
        )
        {
            typedef typename offset_kernel<T>::scalar_type scalar_type;
            try
            {
                deserialize(const_cast<scalar_type&>(item.offset), in);
                deserialize(const_cast<T&>(item.kernel), in);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while deserializing object of type offset_kernel");
            }
        }

        template <
            typename T
            >
        struct kernel_derivative<offset_kernel<T> >
        {
            typedef typename T::scalar_type scalar_type;
            typedef typename T::sample_type sample_type;
            typedef typename T::mem_manager_type mem_manager_type;

            kernel_derivative(const offset_kernel<T>& k) : der(k.kernel){}

            const sample_type operator() (const sample_type& x, const sample_type& y) const
            {
                return der(x,y);
            }

            kernel_derivative<T> der;
        };

    // ----------------------------------------------------------------------------------------

    }

    #endif // DLIB_SVm_KERNEL