kernel.h

C＋＋编写的机器学习算法 Lemga is a C++ package which consists of classes for several learning models and gener

// -*- C++ -*-
#ifndef __LEMGA_KERNEL_H__
#define __LEMGA_KERNEL_H__

/** @file
 *  @brief Kernels for SVM etc.
 *
 *  $Id: kernel.h 2499 2005-11-13 09:21:35Z ling $
 */

#include <cmath>
#include <numeric>
#include "learnmodel.h"

#define DOTPROD(x,y) std::inner_product(x.begin(), x.end(), y.begin(), .0)

namespace lemga {

// only for LIBSVM, see Kernel::set_params.
struct SVM_detail;

namespace kernel {

inline REAL norm_1 (const Input& u, const Input& v) {
    REAL sum(0);
    Input::const_iterator x = u.begin(), y = v.begin();
    for (; x != u.end(); ++x, ++y)
        sum += std::fabs(*x - *y);
    return sum;
}

inline REAL norm_2 (const Input& u, const Input& v) {
    REAL sum(0);
    Input::const_iterator x = u.begin(), y = v.begin();
    for (; x != u.end(); ++x, ++y) {
        REAL d = *x - *y;
        sum += d * d;
    }
    return sum;
}

/// The operator() gives the inner-product in the transformed space.
class Kernel {
protected:
    pDataSet ptd;

public:
    virtual ~Kernel () { /* get rid of GCC warnings */ }

    /// The inner-product of two input vectors.
    virtual REAL operator() (const Input&, const Input&) const = 0;
    /// Store a dataset in order to compute the kernel matrix.
    virtual void set_data (const pDataSet& pd) { ptd = pd; }
    /// The inner-product of two stored inputs with index @a i and @a j.
    virtual REAL matrix (UINT i, UINT j) const
    { return operator()(ptd->x(i), ptd->x(j)); }

    /// In order to keep the SVM interface simple and avoid
    /// member functions specific to kernels (e.g., set_gamma()),
    /// we use Kernel to pass kernel parameters to SVM_detail.
    virtual void set_params (SVM_detail*) const = 0;
};

struct Linear : public Kernel {
    virtual REAL operator() (const Input& a, const Input& b) const {
        return DOTPROD(a, b);
    }
    virtual void set_params (SVM_detail*) const;
};

struct Polynomial : public Kernel {
    UINT degree;
    REAL gamma, coef0;
    Polynomial (UINT d, REAL g, REAL c0)
        : degree(d), gamma(g), coef0(c0) {};

    virtual REAL operator() (const Input& a, const Input& b) const {
        return std::pow(gamma * DOTPROD(a, b) + coef0, (REAL) degree);
    }
    virtual void set_params (SVM_detail*) const;
};

struct Stump : public Kernel {
    virtual REAL operator() (const Input& a, const Input& b) const {
        return -norm_1(a, b);
    }
    virtual void set_params (SVM_detail*) const;
};

struct Perceptron : public Kernel {
protected:
    std::vector<REAL> x_norm2; ///< cached inner-product of data input

public:
    virtual REAL operator() (const Input& a, const Input& b) const {
        return -std::sqrt(norm_2(a, b));
    }

    virtual void set_data (const pDataSet& pd) {
        Kernel::set_data(pd);
        const UINT n = ptd->size();
        x_norm2.resize(n);
        for (UINT i = 0; i < n; ++i)
            x_norm2[i] = DOTPROD(ptd->x(i), ptd->x(i));
    }
    virtual REAL matrix (UINT i, UINT j) const {
        REAL n2 = x_norm2[i] + x_norm2[j] - 2*DOTPROD(ptd->x(i), ptd->x(j));
        return (n2 > 0)? -std::sqrt(n2) : 0;   // avoid -0.0
    }

    virtual void set_params (SVM_detail*) const;
};

struct RBF : public Perceptron {
    REAL gamma;
    explicit RBF (REAL g) : gamma(g) {}

    virtual REAL operator() (const Input& a, const Input& b) const {
        return std::exp(-gamma * norm_2(a, b));
    }

    virtual REAL matrix (UINT i, UINT j) const {
        REAL n2 = x_norm2[i] + x_norm2[j] - 2*DOTPROD(ptd->x(i), ptd->x(j));
        return std::exp(-gamma * n2);
    }

    virtual void set_params (SVM_detail*) const;
};

struct Sigmoid : public Kernel {
    REAL gamma, coef0;
    Sigmoid (REAL g, REAL c0) : gamma(g), coef0(c0) {};

    virtual REAL operator() (const Input& a, const Input& b) const {
        return std::tanh(gamma * DOTPROD(a, b) + coef0);
    }
    virtual void set_params (SVM_detail*) const;
};

}} // namespace lemga::kernel

#ifdef  __KERNEL_H__
#warning "This header file may conflict with another `kernel.h' file."
#endif
#define __KERNEL_H__
#endif