Made the interface to the approximate_distance_function() a little cleaner and

improved its specification a bit.

--HG--
extra : convert_revision : svn%3Afdd8eb12-d10e-0410-9acb-85c331704f74/trunk%404127

dlib/svm/reduced.h

@@ -403,28 +403,27 @@ namespace dlib
 
     template <
         typename K,
-        typename stop_strategy_type
+        typename stop_strategy_type,
+        typename T
         >
     distance_function<K> approximate_distance_function (
         stop_strategy_type stop_strategy,
         const distance_function<K>& target,
-        const distance_function<K>& starting_point
+        const T& starting_basis
     )
     {
         // make sure requires clause is not broken
         DLIB_ASSERT(target.get_basis_vectors().size() > 0 &&
-                    starting_point.get_basis_vectors().size() > 0 &&
-                    target.get_kernel() == starting_point.get_kernel(),
+                    starting_basis.size() > 0,
                     "\t  distance_function approximate_distance_function()"
                     << "\n\t Invalid inputs were given to this function."
-                    << "\n\t target.get_basis_vectors().size():         " << target.get_basis_vectors().size() 
-                    << "\n\t starting_point.get_basis_vectors().size(): " << starting_point.get_basis_vectors().size() 
-                    << "\n\t target.kernel_function == starting_point.kernel_function: " << (target.get_kernel() == starting_point.get_kernel())
+                    << "\n\t target.get_basis_vectors().size(): " << target.get_basis_vectors().size() 
+                    << "\n\t starting_basis.size():             " << starting_basis.size() 
         );
 
         using namespace red_impl;
         // The next few statements just find the best weights with which to approximate 
-        // the target object with the set of vectors in the starting_point object.  This
+        // the target object with the set of basis vectors in starting_basis.  This
         // is really just a simple application of some linear algebra.  For the details 
         // see page 554 of Learning with kernels by Scholkopf and Smola where they talk 
         // about "Optimal Expansion Coefficients."
@@ -437,9 +436,9 @@ namespace dlib
         matrix<scalar_type,0,1,mem_manager_type> beta;
 
         // Now we compute the fist approximate distance function.  
-        beta = pinv(kernel_matrix(kern,starting_point.get_basis_vectors())) *
-            (kernel_matrix(kern,starting_point.get_basis_vectors(),target.get_basis_vectors())*target.get_alpha());
-        matrix<sample_type,0,1,mem_manager_type> out_vectors(starting_point.get_basis_vectors());
+        beta = pinv(kernel_matrix(kern,starting_basis)) *
+            (kernel_matrix(kern,starting_basis,target.get_basis_vectors())*target.get_alpha());
+        matrix<sample_type,0,1,mem_manager_type> out_vectors(vector_to_matrix(starting_basis));
 
 
         // Now setup to do a global optimization of all the parameters in the approximate 
@@ -552,10 +551,9 @@ namespace dlib
             linearly_independent_subset_finder<kernel_type> lisf(kern, num_bv);
             fill_lisf(lisf,x);
 
-            distance_function<kernel_type> approx(ones_matrix<scalar_type>(lisf.size(),1), kern, vector_to_matrix(lisf));
-            const distance_function<kernel_type> target = dec_funct;
-
-            approx = approximate_distance_function(objective_delta_stop_strategy(eps), target, approx);
+            distance_function<kernel_type> approx, target;
+            target = dec_funct;
+            approx = approximate_distance_function(objective_delta_stop_strategy(eps), target, lisf);
 
             decision_function<kernel_type> new_df(approx.get_alpha(), 
                                                   0,

dlib/svm/reduced_abstract.h

@@ -110,34 +110,40 @@ namespace dlib
 
     template <
         typename K,
-        typename stop_strategy_type
+        typename stop_strategy_type,
+        typename T
         >
     distance_function<K> approximate_distance_function (
         stop_strategy_type stop_strategy,
         const distance_function<K>& target,
-        const distance_function<K>& starting_point
+        const T& starting_basis
     );
     /*!
         requires
             - stop_strategy == an object that defines a stop strategy such as one of 
               the objects from dlib/optimization/optimization_stop_strategies_abstract.h
-            - target.get_basis_vectors().size() > 0 && starting_point.get_basis_vectors().size() > 0
-              (i.e. target and starting_point have to have some basis vectors in them)
-            - target.get_kernel() == starting_point.get_kernel()
-              (i.e. both distance functions must use the same kernel)
+            - requirements on starting_basis
+                - T must be a dlib::matrix type or something convertible to a matrix via vector_to_matrix()
+                  (e.g. a std::vector).  Additionally, starting_basis must contain K::sample_type
+                  objects which can be supplied to the kernel function used by target.
+                - is_vector(starting_basis) == true
+                - starting_basis.size() > 0
+            - target.get_basis_vectors().size() > 0 
             - kernel_derivative<K> is defined
               (i.e. The analytic derivative for the given kernel must be defined)
-            - K::sample_type must be a dlib::matrix object and the basis_vectors inside the
-              distance_functions must be column vectors.
+            - K::sample_type must be a dlib::matrix object and the basis_vectors inside target
+              and starting_basis must be column vectors.
         ensures
-            - This function attempts to find a distance function object which is close
+            - This routine attempts to find a distance_function object which is close
               to the given target.  That is, it searches for an X such that target(X) is
-              minimized.  The optimization begins with the initial guess contained in 
-              starting_point and searches for an X which locally minimizes target(X).  Since
-              this problem can have many local minima the quality of the starting point
-              can significantly influence the results.   
-            - The returned distance_function will contain the same number of basis vectors
-              as the given starting_point object.  
+              minimized.  The optimization begins with an X in the span of the elements
+              of starting_basis and searches for an X which locally minimizes target(X).  
+              Since this problem can have many local minima, the quality of the starting 
+              basis can significantly influence the results.   
+            - The optimization is over all variables in a distance_function, however,
+              the size of the basis set is constrained to no more than starting_basis.size().
+              That is, in the returned distance_function DF, we will have: 
+                - DF.get_basis_vectors().size() <= starting_basis.size()
             - The optimization is carried out until the stop_strategy indicates it 
               should stop.
     !*/