Added an implementation of the kernel recursive least squares algorithm

--HG--
extra : convert_revision : svn%3Afdd8eb12-d10e-0410-9acb-85c331704f74/trunk%402228

dlib/svm.h

@@ -4,6 +4,7 @@
 #define DLIB_SVM_HEADER
 
 #include "svm/svm.h"
+#include "svm/krls.h"
 
 #endif // DLIB_SVm_HEADER
 

dlib/svm/krls.h

+// Copyright (C) 2008  Davis E. King (davisking@users.sourceforge.net)
+// License: Boost Software License   See LICENSE.txt for the full license.
+#ifndef DLIB_KRLs_
+#define DLIB_KRLs_
+
+#include <vector>
+
+#include "krls_abstract.h"
+#include "../matrix.h"
+#include "function.h"
+#include "../std_allocator.h"
+
+namespace dlib
+{
+
+// ----------------------------------------------------------------------------------------
+
+    template <typename kernel_type>
+    class krls
+    {
+        /*!
+            This is an implementation of the kernel recursive least squares algorithm described in the paper:
+            The Kernel Recursive Least Squares Algorithm by Yaakov Engel.
+        !*/
+
+    public:
+        typedef typename kernel_type::scalar_type scalar_type;
+        typedef typename kernel_type::sample_type sample_type;
+        typedef typename kernel_type::mem_manager_type mem_manager_type;
+
+
+        explicit krls (
+            const kernel_type& kernel_, 
+            scalar_type tolerance_ = 0.001
+        ) : 
+            kernel(kernel_), 
+            tolerance(tolerance_)
+        {
+            clear();
+        }
+
+        void set_tolerance (scalar_type tolerance_)
+        {
+            tolerance = tolerance_;
+        }
+
+        scalar_type get_tolerance() const
+        {
+            return tolerance;
+        }
+
+        void clear ()
+        {
+            dictionary.clear();
+            alpha.clear();
+
+            K_inv.set_size(0,0);
+            P.set_size(0,0);
+        }
+
+        scalar_type operator() (
+            const sample_type& x
+        ) const
+        {
+            scalar_type temp = 0;
+            for (unsigned long i = 0; i < alpha.size(); ++i)
+                temp += alpha[i]*kernel(dictionary[i], x);
+
+            return temp;
+        }
+
+        void train (
+            const sample_type& x,
+            scalar_type y
+        )
+        {
+            const scalar_type kx = kern(x,x);
+            if (alpha.size() == 0)
+            {
+                // set initial state since this is the first training example we have seen
+
+                K_inv.set_size(1,1);
+                K_inv(0,0) = 1/kx;
+
+                alpha.push_back(y/kx);
+                dictionary.push_back(x);
+                P.set_size(1,1);
+                P(0,0) = 1;
+            }
+            else
+            {
+                // fill in k
+                k.set_size(alpha.size());
+                for (long r = 0; r < k.nr(); ++r)
+                    k(r) = kern(x,dictionary[r]);
+
+                // compute the error we would have if we approximated the new x sample
+                // with the dictionary.  That is, do the ALD test from the KRLS paper.
+                a = K_inv*k;
+                const scalar_type delta = kx - trans(k)*a;
+
+                // if this new vector isn't approximately linearly dependent on the vectors
+                // in our dictionary.
+                if (std::abs(delta) > tolerance)
+                {
+                    // add x to the dictionary
+                    dictionary.push_back(x);
+
+                    // update K_inv by computing the new one in the temp matrix (equation 3.14)
+                    matrix<scalar_type,0,0,mem_manager_type> temp(K_inv.nr()+1, K_inv.nc()+1);
+                    for (long r = 0; r < K_inv.nr(); ++r)
+                    {
+                        for (long c = 0; c < K_inv.nc(); ++c)
+                        {
+                            temp(r,c) = (K_inv + a*trans(a)/delta)(r,c);
+                        }
+                    }
+                    temp(K_inv.nr(), K_inv.nc()) = 1/delta;
+
+                    // update the new sides of K_inv
+                    for (long i = 0; i < K_inv.nr(); ++i)
+                    {
+                        temp(K_inv.nr(),i) = -a(i)/delta;
+                        temp(i,K_inv.nr()) = -a(i)/delta;
+                    }
+                    // put temp into K_inv
+                    temp.swap(K_inv);
+
+
+                    // Now update the P matrix (equation 3.15)
+                    temp.set_size(P.nr()+1, P.nc()+1);
+                    for (long r = 0; r < P.nr(); ++r)
+                    {
+                        for (long c = 0; c < P.nc(); ++c)
+                        {
+                            temp(r,c) = P(r,c);
+                        }
+                    }
+                    // initialize the new sides of P 
+                    for (long i = 0; i < P.nr(); ++i)
+                    {
+                        temp(P.nr(),i) = 0;
+                        temp(i,P.nc()) = 0;
+                    }
+                    temp(P.nr(), P.nc()) = 1;
+                    temp.swap(P);
+
+                    // now update the alpha vector (equation 3.16)
+                    const scalar_type k_a = (y-trans(k)*vector_to_matrix(alpha))/delta;
+                    for (unsigned long i = 0; i < alpha.size(); ++i)
+                    {
+                        alpha[i] -= a(i)*k_a;
+                    }
+                    alpha.push_back(k_a);
+                }
+                else
+                {
+                    q = P*a/(1+trans(a)*P*a);
+
+                    // update P (equation 3.12)
+                    temp_matrix = trans(a)*P;
+                    P -= q*temp_matrix;
+
+                    // update the alpha vector (equation 3.13)
+                    const scalar_type k_a = y-trans(k)*vector_to_matrix(alpha);
+                    for (unsigned long i = 0; i < alpha.size(); ++i)
+                    {
+                        alpha[i] += (K_inv*q*k_a)(i);
+                    }
+                }
+            }
+        }
+
+        void swap (
+            krls& item
+        )
+        {
+            exchange(kernel, item.kernel);
+            dictionary.swap(item.dictionary);
+            alpha.swap(item.alpha);
+            K_inv.swap(item.K_inv);
+            P.swap(item.P);
+            exchange(tolerance, item.tolerance);
+            q.swap(item.q);
+            a.swap(item.a);
+            k.swap(item.k);
+            temp_matrix.swap(item.temp_matrix);
+        }
+
+        unsigned long dictionary_size (
+        ) const { return dictionary.size(); }
+
+        decision_function<kernel_type> get_decision_function (
+        ) const
+        {
+            return decision_function<kernel_type>(
+                vector_to_matrix(alpha),
+                0, // the KRLS algorithm doesn't have a bias term
+                kernel,
+                vector_to_matrix(dictionary)
+            );
+        }
+
+        friend void serialize(const krls& item, std::ostream& out)
+        {
+            serialize(item.kernel, out);
+            serialize(item.dictionary, out);
+            serialize(item.alpha, out);
+            serialize(item.K_inv, out);
+            serialize(item.P, out);
+            serialize(item.tolerance, out);
+        }
+
+        friend void deserialize(krls& item, std::istream& in)
+        {
+            deserialize(item.kernel, in);
+            deserialize(item.dictionary, in);
+            deserialize(item.alpha, in);
+            deserialize(item.K_inv, in);
+            deserialize(item.P, in);
+            deserialize(item.tolerance, in);
+        }
+
+    private:
+
+        inline scalar_type kern (const sample_type& m1, const sample_type& m2) const
+        { 
+            return kernel(m1,m2) + 0.001;
+        }
+
+
+        kernel_type kernel;
+
+        typedef std_allocator<sample_type, mem_manager_type> alloc_sample_type;
+        typedef std_allocator<scalar_type, mem_manager_type> alloc_scalar_type;
+        typedef std::vector<sample_type,alloc_sample_type> dictionary_vector_type;
+        typedef std::vector<scalar_type,alloc_scalar_type> alpha_vector_type;
+
+        dictionary_vector_type dictionary;
+        alpha_vector_type alpha;
+
+        matrix<scalar_type,0,0,mem_manager_type> K_inv;
+        matrix<scalar_type,0,0,mem_manager_type> P;
+
+        scalar_type tolerance;
+
+
+        // temp variables here just so we don't have to reconstruct them over and over.  Thus, 
+        // they aren't really part of the state of this object.
+        matrix<scalar_type,0,1,mem_manager_type> q;
+        matrix<scalar_type,0,1,mem_manager_type> a;
+        matrix<scalar_type,0,1,mem_manager_type> k;
+        matrix<scalar_type,1,0,mem_manager_type> temp_matrix;
+
+    };
+
+// ----------------------------------------------------------------------------------------
+
+    template <typename kernel_type>
+    void swap(krls<kernel_type>& a, krls<kernel_type>& b)
+    { a.swap(b); }
+
+// ----------------------------------------------------------------------------------------
+
+}
+
+#endif // DLIB_KRLs_
+

dlib/svm/krls_abstract.h

+// Copyright (C) 2008  Davis E. King (davisking@users.sourceforge.net)
+// License: Boost Software License   See LICENSE.txt for the full license.
+#undef DLIB_KRLs_ABSTRACT_
+#ifdef DLIB_KRLs_ABSTRACT_
+
+#include <cmath>
+#include "../matrix/matrix_abstract.h"
+#include "../algs.h"
+#include "../serialize.h"
+
+namespace dlib
+{
+
+    template <
+        typename kernel_type
+        >
+    class krls
+    {
+        /*!
+            INITIAL VALUE
+                - dictionary_size() == 0
+
+            WHAT THIS OBJECT REPRESENTS
+                This is an implementation of the kernel recursive least squares algorithm 
+                described in the paper:
+                    The Kernel Recursive Least Squares Algorithm by Yaakov Engel.
+
+                The long and short of this algorithm is that it is an online kernel based 
+                regression algorithm.  You give it samples (x,y) and it learns the function
+                f(x) == y.  For a detailed description of the algorithm read the above paper.
+        !*/
+
+    public:
+        typedef typename kernel_type::scalar_type scalar_type;
+        typedef typename kernel_type::sample_type sample_type;
+        typedef typename kernel_type::mem_manager_type mem_manager_type;
+
+
+        explicit krls (
+            const kernel_type& kernel_, 
+            scalar_type tolerance_ = 0.001
+        );
+        /*!
+            ensures
+                - this object is properly initialized
+                - #get_tolerance() == tolerance_
+                - #get_decision_function().kernel_function == kernel_
+                  (i.e. this object will use the given kernel function)
+        !*/
+
+        void set_tolerance (
+            scalar_type tolerance_
+        );
+        /*!
+            ensures
+                - #get_tolerance() == tolerance_
+        !*/
+
+        scalar_type get_tolerance(
+        ) const;
+        /*!
+            ensures
+                - returns the tolerance to use for the approximately linearly dependent 
+                  test in the KRLS algorithm.  This is a number which governs how 
+                  accurately this object will approximate the decision function it is 
+                  learning.  Smaller values generally result in a more accurate 
+                  estimate while also resulting in a bigger set of support vectors in 
+                  the learned decision function.  Bigger tolerances values result in a 
+                  less accurate decision function but also in less support vectors.
+        !*/
+
+        void clear (
+        );
+        /*!
+            ensures
+                - clears out all learned data and puts this object back to its
+                  initial state.
+                  (e.g. #get_decision_function().support_vectors.size() == 0)
+                - #get_tolerance() == get_tolerance()
+                  (i.e. doesn't change the value of the tolerance)
+        !*/
+
+        scalar_type operator() (
+            const sample_type& x
+        ) const;
+        /*!
+            ensures
+                - returns the current y estimate for the given x
+        !*/
+
+        void train (
+            const sample_type& x,
+            scalar_type y
+        );
+        /*!
+            ensures
+                - trains this object that the given x should be mapped to the given y
+        !*/
+
+        void swap (
+            krls& item
+        );
+        /*!
+            ensures
+                - swaps *this with item
+        !*/
+
+        unsigned long dictionary_size (
+        ) const;
+        /*!
+            ensures
+                - returns the number of "support vectors" in the dictionary.  That is,
+                  returns a number equal to get_decision_function().support_vectors.size()
+        !*/
+
+        decision_function<kernel_type> get_decision_function (
+        ) const;
+        /*!
+            ensures
+                - returns a decision function F that represents the function learned
+                  by this object so far.  I.e. it is the case that:
+                    - for all x: F(x) == (*this)(x)
+        !*/
+
+    };
+
+// ----------------------------------------------------------------------------------------
+
+    template <
+        typename kernel_type
+        >
+    void swap(
+        krls<kernel_type>& a, 
+        krls<kernel_type>& b
+    )
+    { a.swap(b); }
+    /*!
+        provides a global swap function
+    !*/
+
+    template <
+        typename kernel_type
+        >
+    void serialize (
+        const krls<kernel_type>& item,
+        std::ostream& out
+    );
+    /*!
+        provides serialization support for krls objects
+    !*/
+
+    template <
+        typename kernel_type 
+        >
+    void deserialize (
+        krls<kernel_type>& item,
+        std::istream& in 
+    );
+    /*!
+        provides serialization support for krls objects
+    !*/
+
+// ----------------------------------------------------------------------------------------
+
+}
+
+#endif // DLIB_KRLs_ABSTRACT_
+