dlib C++ Library - linear_manifold_regularizer_abstract.h

    // Copyright (C) 2010  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #undef DLIB_LINEAR_MANIFOLD_ReGULARIZER_ABSTRACT_Hh_
    #ifdef DLIB_LINEAR_MANIFOLD_ReGULARIZER_ABSTRACT_Hh_

    #include <limits>
    #include <vector>
    #include "../serialize.h"
    #include "../matrix.h"

    namespace dlib
    {

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

        template <
            typename matrix_type
            >
        class linear_manifold_regularizer
        {
            /*!
                REQUIREMENTS ON matrix_type
                    Must be some type of dlib::matrix.

                INITIAL VALUE
                    - dimensionality() == 0

                WHAT THIS OBJECT REPRESENTS
                    Many learning algorithms attempt to minimize a function that, at a high
                    level, looks like this:
                        f(w) == complexity + training_set_error

                    The idea is to find the set of parameters, w, that gives low error on
                    your training data but also is not "complex" according to some particular
                    measure of complexity.  This strategy of penalizing complexity is
                    usually called regularization.

                    In the above setting, all the training data consists of labeled samples.
                    However, it would be nice to be able to benefit from unlabeled data.
                    The idea of manifold regularization is to extract useful information from
                    unlabeled data by first defining which data samples are "close" to each other
                    (perhaps by using their 3 nearest neighbors) and then adding a term to
                    the above function that penalizes any decision rule which produces
                    different outputs on data samples which we have designated as being close.

                    It turns out that it is possible to transform these manifold regularized
                    learning problems into the normal form shown above by applying a certain kind
                    of preprocessing to all our data samples.  Once this is done we can use a
                    normal learning algorithm, such as the svm_c_linear_trainer, on just the
                    labeled data samples and obtain the same output as the manifold regularized
                    learner would have produced.

                    The linear_manifold_regularizer is a tool for creating this preprocessing
                    transformation.  In particular, the transformation is linear.  That is, it
                    is just a matrix you multiply with all your samples.  For a more detailed
                    discussion of this topic you should consult the following paper.  In
                    particular, see section 4.2.  This object computes the inverse T matrix
                    described in that section.

                        Linear Manifold Regularization for Large Scale Semi-supervised Learning
                        by Vikas Sindhwani, Partha Niyogi, and Mikhail Belkin
            !*/

        public:
            typedef typename matrix_type::mem_manager_type mem_manager_type;
            typedef typename matrix_type::type scalar_type;
            typedef typename matrix_type::layout_type layout_type;
            typedef matrix<scalar_type,0,0,mem_manager_type,layout_type> general_matrix;

            template <
                typename vector_type1,
                typename vector_type2,
                typename weight_function_type
                >
            void build (
                const vector_type1& samples,
                const vector_type2& edges,
                const weight_function_type& weight_funct
            );
            /*!
                requires
                    - vector_type1 == a type with an interface compatible with std::vector and it must
                      in turn contain dlib::matrix objects.
                    - vector_type2 == a type with an interface compatible with std::vector and
                      it must in turn contain objects with an interface compatible with dlib::sample_pair
                    - edges.size() > 0
                    - contains_duplicate_pairs(edges) == false
                    - max_index_plus_one(edges) <= samples.size()
                    - weight_funct(edges[i]) must be a valid expression that evaluates to a
                      floating point number >= 0
                ensures
                    - #dimensionality() == samples[0].size()
                    - This function sets up the transformation matrix describe above.  The manifold
                      regularization is done assuming that the samples are meant to be "close"
                      according to the graph defined by the given edges.  I.e:
                        - for all valid i:  samples[edges[i].index1()] is close to samples[edges[i].index2()].
                          How much we care about these two samples having similar outputs according
                          to the learned rule is given by weight_funct(edges[i]).  Bigger weights mean
                          we care more.
            !*/

            long dimensionality (
            ) const;
            /*!
                ensures
                    - returns the number of rows and columns in the transformation matrix
                      produced by this object.
            !*/

            general_matrix get_transformation_matrix (
                scalar_type intrinsic_regularization_strength
            ) const;
            /*!
                requires
                    - intrinsic_regularization_strength >= 0
                ensures
                    - returns a matrix that represents the preprocessing transformation described above.
                    - You must choose how important the manifold regularizer is relative to the basic
                      "don't be complex" regularizer described above.  The intrinsic_regularization_strength
                      is the parameter that controls this trade-off.  A large value of
                      intrinsic_regularization_strength means that more emphasis should be placed on
                      finding decision rules which produce the same output on similar samples.  On
                      the other hand, a small value would mean that we don't care much about the
                      manifold regularizer.  For example, using 0 will cause this function to return the
                      identity matrix.
                    - The returned matrix will have dimensionality() rows and columns.
            !*/

        };

    }

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

    #endif // DLIB_LINEAR_MANIFOLD_ReGULARIZER_ABSTRACT_Hh_