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-rw-r--r-- | ml/dlib/dlib/svm/krls.h | 358 |
1 files changed, 358 insertions, 0 deletions
diff --git a/ml/dlib/dlib/svm/krls.h b/ml/dlib/dlib/svm/krls.h new file mode 100644 index 000000000..6c72e45e8 --- /dev/null +++ b/ml/dlib/dlib/svm/krls.h @@ -0,0 +1,358 @@ +// Copyright (C) 2008 Davis E. King (davis@dlib.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, + unsigned long max_dictionary_size_ = 1000000 + ) : + kernel(kernel_), + my_tolerance(tolerance_), + my_max_dictionary_size(max_dictionary_size_) + { + // make sure requires clause is not broken + DLIB_ASSERT(tolerance_ >= 0, + "\tkrls::krls()" + << "\n\t You have to give a positive tolerance" + << "\n\t this: " << this + << "\n\t tolerance: " << tolerance_ + ); + + clear_dictionary(); + } + + scalar_type tolerance() const + { + return my_tolerance; + } + + unsigned long max_dictionary_size() const + { + return my_max_dictionary_size; + } + + const kernel_type& get_kernel ( + ) const + { + return kernel; + } + + void clear_dictionary () + { + dictionary.clear(); + alpha.clear(); + + K_inv.set_size(0,0); + K.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]*kern(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) + { + // just ignore this sample if it is the zero vector (or really close to being zero) + if (std::abs(kx) > std::numeric_limits<scalar_type>::epsilon()) + { + // 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; + K.set_size(1,1); + K(0,0) = 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; + scalar_type delta = kx - trans(k)*a; + + // if this new vector isn't approximately linearly dependent on the vectors + // in our dictionary. + if (delta > my_tolerance) + { + if (dictionary.size() >= my_max_dictionary_size) + { + // We need to remove one of the old members of the dictionary before + // we proceed with adding a new one. So remove the oldest one. + remove_dictionary_vector(0); + + // recompute these guys since they were computed with the old + // kernel matrix + k = remove_row(k,0); + a = K_inv*k; + delta = kx - trans(k)*a; + } + + // 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); + // update the middle part of the matrix + set_subm(temp, get_rect(K_inv)) = K_inv + a*trans(a)/delta; + // update the right column of the matrix + set_subm(temp, 0, K_inv.nr(),K_inv.nr(),1) = -a/delta; + // update the bottom row of the matrix + set_subm(temp, K_inv.nr(), 0, 1, K_inv.nr()) = trans(-a/delta); + // update the bottom right corner of the matrix + temp(K_inv.nr(), K_inv.nc()) = 1/delta; + // put temp into K_inv + temp.swap(K_inv); + + + + + // update K (the kernel matrix) + temp.set_size(K.nr()+1, K.nc()+1); + set_subm(temp, get_rect(K)) = K; + // update the right column of the matrix + set_subm(temp, 0, K.nr(),K.nr(),1) = k; + // update the bottom row of the matrix + set_subm(temp, K.nr(), 0, 1, K.nr()) = trans(k); + temp(K.nr(), K.nc()) = kx; + // put temp into K + temp.swap(K); + + + + + // Now update the P matrix (equation 3.15) + temp.set_size(P.nr()+1, P.nc()+1); + set_subm(temp, get_rect(P)) = P; + // initialize the new sides of P + set_rowm(temp,P.nr()) = 0; + set_colm(temp,P.nr()) = 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)*mat(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)*mat(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); + K.swap(item.K); + P.swap(item.P); + exchange(my_tolerance, item.my_tolerance); + q.swap(item.q); + a.swap(item.a); + k.swap(item.k); + temp_matrix.swap(item.temp_matrix); + exchange(my_max_dictionary_size, item.my_max_dictionary_size); + } + + unsigned long dictionary_size ( + ) const { return dictionary.size(); } + + decision_function<kernel_type> get_decision_function ( + ) const + { + return decision_function<kernel_type>( + mat(alpha), + -sum(mat(alpha))*tau, + kernel, + mat(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.K, out); + serialize(item.P, out); + serialize(item.my_tolerance, out); + serialize(item.my_max_dictionary_size, 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.K, in); + deserialize(item.P, in); + deserialize(item.my_tolerance, in); + deserialize(item.my_max_dictionary_size, in); + } + + private: + + inline scalar_type kern (const sample_type& m1, const sample_type& m2) const + { + return kernel(m1,m2) + tau; + } + + void remove_dictionary_vector ( + long i + ) + /*! + requires + - 0 <= i < dictionary.size() + ensures + - #dictionary.size() == dictionary.size() - 1 + - #alpha.size() == alpha.size() - 1 + - updates the K_inv matrix so that it is still a proper inverse of the + kernel matrix + - also removes the necessary row and column from the K matrix + - uses the this->a variable so after this function runs that variable + will contain a different value. + !*/ + { + // remove the dictionary vector + dictionary.erase(dictionary.begin()+i); + + // remove the i'th vector from the inverse kernel matrix. This formula is basically + // just the reverse of the way K_inv is updated by equation 3.14 during normal training. + K_inv = removerc(K_inv,i,i) - remove_row(colm(K_inv,i)/K_inv(i,i),i)*remove_col(rowm(K_inv,i),i); + + // now compute the updated alpha values to take account that we just removed one of + // our dictionary vectors + a = (K_inv*remove_row(K,i)*mat(alpha)); + + // now copy over the new alpha values + alpha.resize(alpha.size()-1); + for (unsigned long k = 0; k < alpha.size(); ++k) + { + alpha[k] = a(k); + } + + // update the P matrix as well + P = removerc(P,i,i); + + // update the K matrix as well + K = removerc(K,i,i); + } + + + 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> K; + matrix<scalar_type,0,0,mem_manager_type> P; + + scalar_type my_tolerance; + unsigned long my_max_dictionary_size; + + + // 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; + + const static scalar_type tau; + + }; + + template <typename kernel_type> + const typename kernel_type::scalar_type krls<kernel_type>::tau = static_cast<typename kernel_type::scalar_type>(0.01); + +// ---------------------------------------------------------------------------------------- + + template <typename kernel_type> + void swap(krls<kernel_type>& a, krls<kernel_type>& b) + { a.swap(b); } + +// ---------------------------------------------------------------------------------------- + +} + +#endif // DLIB_KRLs_ + |