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<font color='#009900'>// Copyright (C) 2008 Davis E. King (davis@dlib.net)
</font><font color='#009900'>// License: Boost Software License See LICENSE.txt for the full license.
</font><font color='#0000FF'>#undef</font> DLIB_KCENTROId_ABSTRACT_
<font color='#0000FF'>#ifdef</font> DLIB_KCENTROId_ABSTRACT_
<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='../algs.h.html'>../algs.h</a>"
<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='../serialize.h.html'>../serialize.h</a>"
<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='kernel_abstract.h.html'>kernel_abstract.h</a>"
<font color='#0000FF'>namespace</font> dlib
<b>{</b>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> kernel_type
<font color='#5555FF'>></font>
<font color='#0000FF'>class</font> <b><a name='kcentroid'></a>kcentroid</b>
<b>{</b>
<font color='#009900'>/*!
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.
!*/</font>
<font color='#0000FF'>public</font>:
<font color='#0000FF'>typedef</font> <font color='#0000FF'>typename</font> kernel_type::scalar_type scalar_type;
<font color='#0000FF'>typedef</font> <font color='#0000FF'>typename</font> kernel_type::sample_type sample_type;
<font color='#0000FF'>typedef</font> <font color='#0000FF'>typename</font> kernel_type::mem_manager_type mem_manager_type;
<b><a name='kcentroid'></a>kcentroid</b> <font face='Lucida Console'>(</font>
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
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
!*/</font>
<font color='#0000FF'>explicit</font> <b><a name='kcentroid'></a>kcentroid</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> kernel_type<font color='#5555FF'>&</font> kernel_,
scalar_type tolerance_ <font color='#5555FF'>=</font> <font color='#979000'>0.001</font>,
<font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> max_dictionary_size_ <font color='#5555FF'>=</font> <font color='#979000'>1000000</font>,
<font color='#0000FF'><u>bool</u></font> remove_oldest_first_ <font color='#5555FF'>=</font> <font color='#979000'>false</font>
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
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_
!*/</font>
<font color='#0000FF'>const</font> kernel_type<font color='#5555FF'>&</font> <b><a name='get_kernel'></a>get_kernel</b> <font face='Lucida Console'>(</font>
<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
<font color='#009900'>/*!
ensures
- returns a const reference to the kernel used by this object
!*/</font>
<font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> <b><a name='max_dictionary_size'></a>max_dictionary_size</b><font face='Lucida Console'>(</font>
<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
<font color='#009900'>/*!
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().
!*/</font>
<font color='#0000FF'><u>bool</u></font> <b><a name='remove_oldest_first'></a>remove_oldest_first</b> <font face='Lucida Console'>(</font>
<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
<font color='#009900'>/*!
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.
!*/</font>
<font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> <b><a name='dictionary_size'></a>dictionary_size</b> <font face='Lucida Console'>(</font>
<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
<font color='#009900'>/*!
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.
!*/</font>
scalar_type <b><a name='samples_trained'></a>samples_trained</b> <font face='Lucida Console'>(</font>
<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
<font color='#009900'>/*!
ensures
- returns the number of samples this object has been trained on so far
!*/</font>
scalar_type <b><a name='tolerance'></a>tolerance</b><font face='Lucida Console'>(</font>
<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
<font color='#009900'>/*!
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.
!*/</font>
<font color='#0000FF'><u>void</u></font> <b><a name='clear_dictionary'></a>clear_dictionary</b> <font face='Lucida Console'>(</font>
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
ensures
- clears out all learned data (e.g. #dictionary_size() == 0)
- #samples_seen() == 0
!*/</font>
scalar_type <b><a name='operator'></a>operator</b><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> kcentroid<font color='#5555FF'>&</font> x
<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
<font color='#009900'>/*!
requires
- x.get_kernel() == get_kernel()
ensures
- returns the distance in kernel feature space between this centroid and the
centroid represented by x.
!*/</font>
scalar_type <b><a name='operator'></a>operator</b><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> sample_type<font color='#5555FF'>&</font> x
<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
<font color='#009900'>/*!
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.
!*/</font>
scalar_type <b><a name='inner_product'></a>inner_product</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> sample_type<font color='#5555FF'>&</font> x
<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
<font color='#009900'>/*!
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.
!*/</font>
scalar_type <b><a name='inner_product'></a>inner_product</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> kcentroid<font color='#5555FF'>&</font> x
<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
<font color='#009900'>/*!
requires
- x.get_kernel() == get_kernel()
ensures
- returns the inner product between x and this centroid object.
!*/</font>
scalar_type <b><a name='squared_norm'></a>squared_norm</b> <font face='Lucida Console'>(</font>
<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
<font color='#009900'>/*!
ensures
- returns the squared norm of the centroid vector represented by this
object. I.e. returns this->inner_product(*this)
!*/</font>
<font color='#0000FF'><u>void</u></font> <b><a name='train'></a>train</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> sample_type<font color='#5555FF'>&</font> x
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
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.
!*/</font>
<font color='#0000FF'><u>void</u></font> <b><a name='train'></a>train</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> sample_type<font color='#5555FF'>&</font> x,
scalar_type cscale,
scalar_type xscale
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
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.
!*/</font>
<font color='#0000FF'><u>void</u></font> <b><a name='scale_by'></a>scale_by</b> <font face='Lucida Console'>(</font>
scalar_type cscale
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
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
!*/</font>
scalar_type <b><a name='test_and_train'></a>test_and_train</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> sample_type<font color='#5555FF'>&</font> x
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
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.
!*/</font>
scalar_type <b><a name='test_and_train'></a>test_and_train</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> sample_type<font color='#5555FF'>&</font> x,
scalar_type cscale,
scalar_type xscale
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
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.
!*/</font>
<font color='#0000FF'><u>void</u></font> <b><a name='swap'></a>swap</b> <font face='Lucida Console'>(</font>
kcentroid<font color='#5555FF'>&</font> item
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
ensures
- swaps *this with item
!*/</font>
distance_function<font color='#5555FF'><</font>kernel_type<font color='#5555FF'>></font> <b><a name='get_distance_function'></a>get_distance_function</b> <font face='Lucida Console'>(</font>
<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
<font color='#009900'>/*!
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)
!*/</font>
<b>}</b>;
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> kernel_type
<font color='#5555FF'>></font>
<font color='#0000FF'><u>void</u></font> <b><a name='swap'></a>swap</b><font face='Lucida Console'>(</font>
kcentroid<font color='#5555FF'><</font>kernel_type<font color='#5555FF'>></font><font color='#5555FF'>&</font> a,
kcentroid<font color='#5555FF'><</font>kernel_type<font color='#5555FF'>></font><font color='#5555FF'>&</font> b
<font face='Lucida Console'>)</font> <b>{</b> a.<font color='#BB00BB'>swap</font><font face='Lucida Console'>(</font>b<font face='Lucida Console'>)</font>; <b>}</b>
<font color='#009900'>/*!
provides a global swap function
!*/</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> kernel_type
<font color='#5555FF'>></font>
<font color='#0000FF'><u>void</u></font> <b><a name='serialize'></a>serialize</b> <font face='Lucida Console'>(</font>
<font color='#0000FF'>const</font> kcentroid<font color='#5555FF'><</font>kernel_type<font color='#5555FF'>></font><font color='#5555FF'>&</font> item,
std::ostream<font color='#5555FF'>&</font> out
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
provides serialization support for kcentroid objects
!*/</font>
<font color='#0000FF'>template</font> <font color='#5555FF'><</font>
<font color='#0000FF'>typename</font> kernel_type
<font color='#5555FF'>></font>
<font color='#0000FF'><u>void</u></font> <b><a name='deserialize'></a>deserialize</b> <font face='Lucida Console'>(</font>
kcentroid<font color='#5555FF'><</font>kernel_type<font color='#5555FF'>></font><font color='#5555FF'>&</font> item,
std::istream<font color='#5555FF'>&</font> in
<font face='Lucida Console'>)</font>;
<font color='#009900'>/*!
provides serialization support for kcentroid objects
!*/</font>
<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<b>}</b>
<font color='#0000FF'>#endif</font> <font color='#009900'>// DLIB_KCENTROId_ABSTRACT_
</font>
</pre></body></html>