// Copyright (C) 2008 Davis E. King (davis@dlib.net) // License: Boost Software License See LICENSE.txt for the full license. #undef DLIB_KCENTROId_ABSTRACT_ #ifdef DLIB_KCENTROId_ABSTRACT_ #include "../algs.h" #include "../serialize.h" #include "kernel_abstract.h" namespace dlib{template < typename kernel_type > classkcentroid{/*! REQUIREMENTS ON kernel_type is a kernel function object as defined in dlib/svm/kernel_abstract.h INITIAL VALUE - dictionary_size() == 0 - samples_trained() == 0 WHAT THIS OBJECT REPRESENTS This object represents a weighted sum of sample points in a kernel induced feature space. It can be used to kernelize any algorithm that requires only the ability to perform vector addition, subtraction, scalar multiplication, and inner products. An example use of this object is as an online algorithm for recursively estimating the centroid of a sequence of training points. This object then allows you to compute the distance between the centroid and any test points. So you can use this object to predict how similar a test point is to the data this object has been trained on (larger distances from the centroid indicate dissimilarity/anomalous points). Also note that the algorithm internally keeps a set of "dictionary vectors" that are used to represent the centroid. You can force the algorithm to use no more than a set number of vectors by setting the 3rd constructor argument to whatever you want. This object uses the sparsification technique described in the paper The Kernel Recursive Least Squares Algorithm by Yaakov Engel. This technique allows us to keep the number of dictionary vectors down to a minimum. In fact, the object has a user selectable tolerance parameter that controls the trade off between accuracy and number of stored dictionary vectors. !*/ 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;kcentroid( ); /*! ensures - this object is properly initialized - #tolerance() == 0.001 - #get_kernel() == kernel_type() (i.e. whatever the kernel's default value is) - #max_dictionary_size() == 1000000 - #remove_oldest_first() == false !*/ explicitkcentroid( const kernel_type& kernel_, scalar_type tolerance_ = 0.001,unsignedlongmax_dictionary_size_ = 1000000,boolremove_oldest_first_ = false ); /*! requires - tolerance > 0 - max_dictionary_size_ > 1 ensures - this object is properly initialized - #tolerance() == tolerance_ - #get_kernel() == kernel_ - #max_dictionary_size() == max_dictionary_size_ - #remove_oldest_first() == remove_oldest_first_ !*/ const kernel_type&get_kernel( ) const; /*! ensures - returns a const reference to the kernel used by this object !*/unsignedlongmax_dictionary_size( ) const; /*! ensures - returns the maximum number of dictionary vectors this object will use at a time. That is, dictionary_size() will never be greater than max_dictionary_size(). !*/boolremove_oldest_first( ) const; /*! ensures - When the maximum dictionary size is reached this object sometimes needs to discard dictionary vectors when new samples are added via one of the train functions. When this happens this object chooses the dictionary vector to discard based on the setting of the remove_oldest_first() parameter. - if (remove_oldest_first() == true) then - This object discards the oldest dictionary vectors when necessary. This is an appropriate mode when using this object in an online setting and the input training samples come from a slowly varying distribution. - else (remove_oldest_first() == false) then - This object discards the most linearly dependent dictionary vectors when necessary. This it the default behavior and should be used in most cases. !*/unsignedlongdictionary_size( ) const; /*! ensures - returns the number of basis vectors in the dictionary. These are the basis vectors used by this object to represent a point in kernel feature space. !*/ scalar_typesamples_trained( ) const; /*! ensures - returns the number of samples this object has been trained on so far !*/ scalar_typetolerance( ) const; /*! ensures - returns the tolerance to use for the approximately linearly dependent test used for sparsification (see the KRLS paper for details). This is a number which governs how accurately this object will approximate the centroid it is learning. Smaller values generally result in a more accurate estimate while also resulting in a bigger set of vectors in the dictionary. Bigger tolerances values result in a less accurate estimate but also in less dictionary vectors. (Note that in any case, the max_dictionary_size() limits the number of dictionary vectors no matter the setting of the tolerance) - The exact meaning of the tolerance parameter is the following: Imagine that we have an empirical_kernel_map that contains all the current dictionary vectors. Then the tolerance is the minimum projection error (as given by empirical_kernel_map::project()) required to cause us to include a new vector in the dictionary. So each time you call train() the kcentroid basically just computes the projection error for that new sample and if it is larger than the tolerance then that new sample becomes part of the dictionary. !*/voidclear_dictionary( ); /*! ensures - clears out all learned data (e.g. #dictionary_size() == 0) - #samples_seen() == 0 !*/ scalar_typeoperator() ( const kcentroid& x ) const; /*! requires - x.get_kernel() == get_kernel() ensures - returns the distance in kernel feature space between this centroid and the centroid represented by x. !*/ scalar_typeoperator() ( const sample_type& x ) const; /*! ensures - returns the distance in kernel feature space between the sample x and the current estimate of the centroid of the training samples given to this object so far. !*/ scalar_typeinner_product( const sample_type& x ) const; /*! ensures - returns the inner product of the given x point and the current estimate of the centroid of the training samples given to this object so far. !*/ scalar_typeinner_product( const kcentroid& x ) const; /*! requires - x.get_kernel() == get_kernel() ensures - returns the inner product between x and this centroid object. !*/ scalar_typesquared_norm( ) const; /*! ensures - returns the squared norm of the centroid vector represented by this object. I.e. returns this->inner_product(*this) !*/voidtrain( const sample_type& x ); /*! ensures - adds the sample x into the current estimate of the centroid - also note that calling this function is equivalent to calling train(x, samples_trained()/(samples_trained()+1.0, 1.0/(samples_trained()+1.0). That is, this function finds the normal unweighted centroid of all training points. !*/voidtrain( const sample_type& x, scalar_type cscale, scalar_type xscale ); /*! ensures - adds the sample x into the current estimate of the centroid but uses a user given scale. That is, this function performs: - new_centroid = cscale*old_centroid + xscale*x - This function allows you to weight different samples however you want. !*/voidscale_by( scalar_type cscale ); /*! ensures - multiplies the current centroid vector by the given scale value. This function is equivalent to calling train(some_x_value, cscale, 0). So it performs: - new_centroid == cscale*old_centroid !*/ scalar_typetest_and_train( const sample_type& x ); /*! ensures - calls train(x) - returns (*this)(x) - The reason this function exists is because train() and operator() both compute some of the same things. So this function is more efficient than calling both individually. !*/ scalar_typetest_and_train( const sample_type& x, scalar_type cscale, scalar_type xscale ); /*! ensures - calls train(x,cscale,xscale) - returns (*this)(x) - The reason this function exists is because train() and operator() both compute some of the same things. So this function is more efficient than calling both individually. !*/voidswap( kcentroid& item ); /*! ensures - swaps *this with item !*/ distance_function<kernel_type>get_distance_function( ) const; /*! ensures - returns a distance function F that represents the point learned by this object so far. I.e. it is the case that: - for all x: F(x) == (*this)(x) !*/}; // ---------------------------------------------------------------------------------------- template < typename kernel_type >voidswap( kcentroid<kernel_type>& a, kcentroid<kernel_type>& b ){a.swap(b);}/*! provides a global swap function !*/ template < typename kernel_type >voidserialize( const kcentroid<kernel_type>& item, std::ostream& out ); /*! provides serialization support for kcentroid objects !*/ template < typename kernel_type >voiddeserialize( kcentroid<kernel_type>& item, std::istream& in ); /*! provides serialization support for kcentroid objects !*/ // ----------------------------------------------------------------------------------------}#endif // DLIB_KCENTROId_ABSTRACT_