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Added a simple kernel based one class classifier.
--HG-- extra : convert_revision : svn%3Afdd8eb12-d10e-0410-9acb-85c331704f74/trunk%402247
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Davis King
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@ -5,6 +5,7 @@
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#include "svm/svm.h"
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#include "svm/krls.h"
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#include "svm/one_class.h"
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#endif // DLIB_SVm_HEADER
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268
dlib/svm/one_class.h
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268
dlib/svm/one_class.h
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// Copyright (C) 2008 Davis E. King (davisking@users.sourceforge.net)
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// License: Boost Software License See LICENSE.txt for the full license.
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#ifndef DLIB_ONE_CLASs_
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#define DLIB_ONE_CLASs_
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#include <vector>
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#include "one_class_abstract.h"
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#include "../matrix.h"
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#include "function.h"
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#include "../std_allocator.h"
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namespace dlib
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{
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// ----------------------------------------------------------------------------------------
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template <typename kernel_type>
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class one_class
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{
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/*!
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This is an implementation of an online algorithm for recursively estimating the
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center of mass of a sequence of training points. It uses the sparsification technique
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described in the paper The Kernel Recursive Least Squares Algorithm by Yaakov Engel.
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To understand the code it would also be useful to consult page 114 of the book Kernel
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Methods for Pattern Analysis by Taylor and Cristianini as well as page 554
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(particularly equation 18.31) of the book Learning with Kernels by Scholkopf and Smola.
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!*/
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public:
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typedef typename kernel_type::scalar_type scalar_type;
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typedef typename kernel_type::sample_type sample_type;
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typedef typename kernel_type::mem_manager_type mem_manager_type;
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explicit one_class (
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const kernel_type& kernel_,
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scalar_type tolerance_ = 0.001
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) :
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kernel(kernel_),
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tolerance(tolerance_)
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{
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clear();
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}
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void set_tolerance (scalar_type tolerance_)
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{
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tolerance = tolerance_;
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}
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scalar_type get_tolerance() const
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{
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return tolerance;
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}
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void clear ()
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{
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dictionary.clear();
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alpha.clear();
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K_inv.set_size(0,0);
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samples_seen = 0;
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bias = 0;
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}
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scalar_type operator() (
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const sample_type& x
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) const
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{
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scalar_type temp = 0;
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for (unsigned long i = 0; i < alpha.size(); ++i)
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temp += alpha[i]*kernel(dictionary[i], x);
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return std::sqrt(kernel(x,x) + bias - 2*temp);
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}
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void train (
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const sample_type& x
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)
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{
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const scalar_type kx = kernel(x,x);
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if (alpha.size() == 0)
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{
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// set initial state since this is the first training example we have seen
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K_inv.set_size(1,1);
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K_inv(0,0) = 1/kx;
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K.set_size(1,1);
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K(0,0) = kx;
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alpha.push_back(1.0);
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dictionary.push_back(x);
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}
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else
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{
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// fill in k
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k.set_size(alpha.size());
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for (long r = 0; r < k.nr(); ++r)
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k(r) = kernel(x,dictionary[r]);
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// compute the error we would have if we approximated the new x sample
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// with the dictionary. That is, do the ALD test from the KRLS paper.
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a = K_inv*k;
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const scalar_type delta = kx - trans(k)*a;
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// if this new vector isn't approximately linearly dependent on the vectors
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// in our dictionary.
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if (std::abs(delta) > tolerance)
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{
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// add x to the dictionary
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dictionary.push_back(x);
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// update K_inv by computing the new one in the temp matrix (equation 3.14)
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matrix<scalar_type,0,0,mem_manager_type> temp(K_inv.nr()+1, K_inv.nc()+1);
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for (long r = 0; r < K_inv.nr(); ++r)
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{
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for (long c = 0; c < K_inv.nc(); ++c)
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{
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temp(r,c) = (K_inv + a*trans(a)/delta)(r,c);
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}
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}
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temp(K_inv.nr(), K_inv.nc()) = 1/delta;
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// update the new sides of K_inv
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for (long i = 0; i < K_inv.nr(); ++i)
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{
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temp(K_inv.nr(),i) = -a(i)/delta;
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temp(i,K_inv.nr()) = -a(i)/delta;
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}
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// put temp into K_inv
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temp.swap(K_inv);
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// update K (the kernel matrix)
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temp.set_size(K.nr()+1, K.nc()+1);
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for (long r = 0; r < K.nr(); ++r)
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{
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for (long c = 0; c < K.nc(); ++c)
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{
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temp(r,c) = K(r,c);
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}
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}
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temp(K.nr(), K.nc()) = kx;
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// update the new sides of K
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for (long i = 0; i < K.nr(); ++i)
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{
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temp(K.nr(),i) = k(i);
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temp(i,K.nr()) = k(i);
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}
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// put temp into K
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temp.swap(K);
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// now update the alpha vector
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const double alpha_scale = samples_seen/(samples_seen+1);
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for (unsigned long i = 0; i < alpha.size(); ++i)
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{
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alpha[i] *= alpha_scale;
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}
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alpha.push_back(1.0-alpha_scale);
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}
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else
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{
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// update the alpha vector so that this new sample has been added into
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// the mean vector we are accumulating
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const double alpha_scale = samples_seen/(samples_seen+1);
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const double a_scale = 1.0-alpha_scale;
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for (unsigned long i = 0; i < alpha.size(); ++i)
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{
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alpha[i] = alpha_scale*alpha[i] + a_scale*a(i);
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}
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}
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}
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// recompute the bias term
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bias = sum(pointwise_multiply(K, vector_to_matrix(alpha)*trans(vector_to_matrix(alpha))));
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++samples_seen;
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}
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void swap (
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one_class& item
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)
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{
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exchange(kernel, item.kernel);
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dictionary.swap(item.dictionary);
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alpha.swap(item.alpha);
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K_inv.swap(item.K_inv);
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K.swap(item.K);
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exchange(tolerance, item.tolerance);
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exchange(samples_seen, item.samples_seen);
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exchange(bias, item.bias);
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a.swap(item.a);
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k.swap(item.k);
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}
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unsigned long dictionary_size (
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) const { return dictionary.size(); }
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friend void serialize(const one_class& item, std::ostream& out)
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{
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serialize(item.kernel, out);
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serialize(item.dictionary, out);
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serialize(item.alpha, out);
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serialize(item.K_inv, out);
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serialize(item.K, out);
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serialize(item.tolerance, out);
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serialize(item.samples_seen, out);
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serialize(item.bias, out);
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}
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friend void deserialize(one_class& item, std::istream& in)
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{
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deserialize(item.kernel, in);
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deserialize(item.dictionary, in);
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deserialize(item.alpha, in);
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deserialize(item.K_inv, in);
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deserialize(item.K, in);
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deserialize(item.tolerance, in);
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deserialize(item.samples_seen, in);
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deserialize(item.bias, in);
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}
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private:
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typedef std_allocator<sample_type, mem_manager_type> alloc_sample_type;
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typedef std_allocator<scalar_type, mem_manager_type> alloc_scalar_type;
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typedef std::vector<sample_type,alloc_sample_type> dictionary_vector_type;
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typedef std::vector<scalar_type,alloc_scalar_type> alpha_vector_type;
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kernel_type kernel;
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dictionary_vector_type dictionary;
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alpha_vector_type alpha;
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matrix<scalar_type,0,0,mem_manager_type> K_inv;
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matrix<scalar_type,0,0,mem_manager_type> K;
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scalar_type tolerance;
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scalar_type samples_seen;
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scalar_type bias;
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// temp variables here just so we don't have to reconstruct them over and over. Thus,
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// they aren't really part of the state of this object.
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matrix<scalar_type,0,1,mem_manager_type> a;
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matrix<scalar_type,0,1,mem_manager_type> k;
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};
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// ----------------------------------------------------------------------------------------
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template <typename kernel_type>
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void swap(one_class<kernel_type>& a, one_class<kernel_type>& b)
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{ a.swap(b); }
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// ----------------------------------------------------------------------------------------
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}
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#endif // DLIB_ONE_CLASs_
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162
dlib/svm/one_class_abstract.h
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162
dlib/svm/one_class_abstract.h
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@ -0,0 +1,162 @@
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// Copyright (C) 2008 Davis E. King (davisking@users.sourceforge.net)
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// License: Boost Software License See LICENSE.txt for the full license.
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#undef DLIB_ONE_CLASs_ABSTRACT_
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#ifdef DLIB_ONE_CLASs_ABSTRACT_
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#include <cmath>
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#include "../matrix/matrix_abstract.h"
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#include "../algs.h"
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#include "../serialize.h"
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#include "kernel_abstract.h"
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namespace dlib
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{
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template <
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typename kernel_type
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>
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class one_class
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{
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/*!
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REQUIREMENTS ON kernel_type
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is a kernel function object as defined in dlib/svm/kernel_abstract.h
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INITIAL VALUE
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- dictionary_size() == 0
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WHAT THIS OBJECT REPRESENTS
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This is an implementation of an online algorithm for recursively estimating the
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center of mass of a sequence of training points. It uses the sparsification technique
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described in the paper The Kernel Recursive Least Squares Algorithm by Yaakov Engel.
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This object then allows you to compute the distance between the center of mass
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and any test points. So you can use this object to predict how similar a test
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point is to the data this object has been trained on (larger distances from the
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centroid indicate dissimilarity/anomalous points).
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!*/
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public:
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typedef typename kernel_type::scalar_type scalar_type;
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typedef typename kernel_type::sample_type sample_type;
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typedef typename kernel_type::mem_manager_type mem_manager_type;
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explicit one_class (
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const kernel_type& kernel_,
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scalar_type tolerance_ = 0.001
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);
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/*!
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ensures
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- this object is properly initialized
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- #get_tolerance() == tolerance_
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- #get_decision_function().kernel_function == kernel_
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(i.e. this object will use the given kernel function)
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!*/
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void set_tolerance (
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scalar_type tolerance_
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);
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/*!
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ensures
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- #get_tolerance() == tolerance_
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!*/
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scalar_type get_tolerance(
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) const;
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/*!
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ensures
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- returns the tolerance to use for the approximately linearly dependent
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test used for sparsification (see the KRLS paper for details). This is
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a number which governs how accurately this object will approximate the
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centroid it is learning. Smaller values generally result in a more accurate
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estimate while also resulting in a bigger set of support vectors in
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the learned dictionary. Bigger tolerances values result in a
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less accurate estimate but also in less support vectors.
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!*/
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void clear (
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);
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/*!
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ensures
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- clears out all learned data and puts this object back to its
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initial state. (e.g. #dictionary_size() == 0)
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- #get_tolerance() == get_tolerance()
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(i.e. doesn't change the value of the tolerance)
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!*/
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scalar_type operator() (
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const sample_type& x
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) const;
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/*!
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ensures
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- returns the distance in feature space between the sample x and the
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current estimate of the centroid of the training samples given
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to this object so far.
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!*/
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void train (
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const sample_type& x
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);
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/*!
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ensures
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- adds the sample x into the current estimate of the centroid
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!*/
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void swap (
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one_class& item
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);
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/*!
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ensures
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- swaps *this with item
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!*/
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unsigned long dictionary_size (
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) const;
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/*!
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ensures
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- returns the number of "support vectors" in the dictionary.
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!*/
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};
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// ----------------------------------------------------------------------------------------
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template <
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typename kernel_type
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>
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void swap(
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one_class<kernel_type>& a,
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one_class<kernel_type>& b
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) { a.swap(b); }
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/*!
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provides a global swap function
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!*/
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template <
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typename kernel_type
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>
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void serialize (
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const one_class<kernel_type>& item,
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std::ostream& out
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);
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/*!
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provides serialization support for one_class objects
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!*/
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template <
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typename kernel_type
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>
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void deserialize (
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one_class<kernel_type>& item,
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std::istream& in
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);
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/*!
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provides serialization support for one_class objects
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!*/
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// ----------------------------------------------------------------------------------------
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}
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#endif // DLIB_ONE_CLASs_ABSTRACT_
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