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    00002 /*                                                                      */
    00003 /*        Copyright 2008-2009 by  Ullrich Koethe and Rahul Nair         */
    00004 /*                                                                      */
    00005 /*    This file is part of the VIGRA computer vision library.           */
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    00010 /*        vigra@informatik.uni-hamburg.de                               */
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    00035
    00036 #ifndef VIGRA_SAMPLING_HXX
    00037 #define VIGRA_SAMPLING_HXX
    00038
    00039 #include "array_vector.hxx"
    00040 #include "random.hxx"
    00041 #include <map>
    00042 #include <memory>
    00043 #include <cmath>
    00044
    00045 namespace vigra
    00046 {
    00047
    00048 /** \addtogroup MachineLearning Machine Learning
    00049 **/
    00050 //@{
    00051
    00052
    00053 /**\brief Options object for the Sampler class.
    00054
    00055   <b>usage:</b>
    00056
    00057   \code
    00058   SamplerOptions opt =  SamplerOptions()
    00059                                .withReplacement()
    00060                                .sampleProportion(0.5);
    00061   \endcode
    00062
    00063   Note that the return value of all methods is <tt>*this</tt> which makes
    00064   concatenating of options as above possible.
    00065 */
    00066 class SamplerOptions
    00067 {
    00068   public:
    00069
    00070     double sample_proportion;
    00071     unsigned int sample_size;
    00072     bool   sample_with_replacement;
    00073     bool   stratified_sampling;
    00074
    00075     SamplerOptions()
    00076     : sample_proportion(1.0),
    00077       sample_size(0),
    00078       sample_with_replacement(true),
    00079       stratified_sampling(false)
    00080     {}
    00081
    00082         /**\brief Sample from training population with replacement.
    00083          *
    00084          * <br> Default: true
    00085          */
    00086     SamplerOptions& withReplacement(bool in = true)
    00087     {
    00088         sample_with_replacement = in;
    00089         return *this;
    00090     }
    00091
    00092         /**\brief Sample from training population without replacement.
    00093          *
    00094          * <br> Default (if you don't call this function): false
    00095          */
    00096     SamplerOptions& withoutReplacement(bool in = true)
    00097     {
    00098         sample_with_replacement = !in;
    00099         return *this;
    00100     }
    00101
    00102         /**\brief Draw the given number of samples.
    00103          * If stratifiedSampling is true, the \a size is equally distributed
    00104          * accross all strata (e.g. <tt>size / strataCount</tt> samples are taken
    00105          * from each stratum, subject to rounding).
    00106          *
    00107          * <br> Default: 0 (i.e. determine the count by means of sampleProportion())
    00108          */
    00109     SamplerOptions& sampleSize(unsigned int size)
    00110     {
    00111         sample_size = size;
    00112         return *this;
    00113     }
    00114
    00115
    00116         /**\brief Determine the number of samples to draw as a proportion of the total
    00117          * number. That is, we draw <tt>count = totalCount * proportion</tt> samples.
    00118          * This option is overridden when an absolute count is specified by sampleSize().
    00119          *
    00120          * If stratifiedSampling is true, the count is equally distributed
    00121          * accross all strata (e.g. <tt>totalCount * proportion / strataCount</tt> samples are taken
    00122          * from each stratum).
    00123          *
    00124          * <br> Default: 1.0
    00125          */
    00126     SamplerOptions& sampleProportion(double proportion)
    00127     {
    00128         vigra_precondition(proportion >= 0.0,
    00129                "SamplerOptions::sampleProportion(): argument must not be negative.");
    00130         sample_proportion = proportion;
    00131         return *this;
    00132     }
    00133
    00134         /**\brief Draw equally many samples from each "stratum".
    00135          *  A stratum is a group of like entities, e.g. pixels belonging
    00136          *  to the same object class. This is useful to create balanced samples
    00137          *  when the class probabilities are very unbalanced (e.g.
    00138          *  when there are many background and few foreground pixels).
    00139          *  Stratified sampling thus avoids that a trained classifier is biased
    00140          *  towards the majority class.
    00141          *
    00142          * <br> Default (if you don't call this function): false
    00143          */
    00144     SamplerOptions& stratified(bool in = true)
    00145     {
    00146         stratified_sampling = in;
    00147         return *this;
    00148     }
    00149 };
    00150
    00151 /************************************************************/
    00152 /*                                                          */
    00153 /*                        Sampler                           */
    00154 /*                                                          */
    00155 /************************************************************/
    00156
    00157 /** \brief Create random samples from a sequence of indices.
    00158
    00159     Selecting data items at random is a basic task of machine learning,
    00160     for example in boostrapping, RandomForest training, and cross validation.
    00161     This class implements various ways to select random samples via their indices.
    00162     Indices are assumed to be consecutive in
    00163     the range <tt>0 &lt;= index &lt; total_sample_count</tt>.
    00164
    00165     The class always contains a current sample which can be accessed by
    00166     the index operator or by the function sampledIndices(). The indices
    00167     that are not in the current sample (out-of-bag indices) can be accessed
    00168     via the function oobIndices().
    00169
    00170     The sampling method (with/without replacement, stratified or not) and the
    00171     number of samples to draw are determined by the option object
    00172     SamplerOptions.
    00173
    00174     <b>Usage:</b>
    00175
    00176     <b>\#include</b> <<a href="sampling_8hxx-source.html">vigra/sampling.hxx</a>><br>
    00177     Namespace: vigra
    00178
    00179     Create a Sampler with default options, i.e. sample as many indices as there
    00180     are data elements, with replacement. On average, the sample will contain
    00181     <tt>0.63*totalCount</tt> distinct indices.
    00182
    00183     \code
    00184     int totalCount = 10000;   // total number of data elements
    00185     int numberOfSamples = 20; // repeat experiment 20 times
    00186     Sampler<> sampler(totalCount);
    00187     for(int k=0; k<numberOfSamples; ++k)
    00188     {
    00189         // process current sample
    00190         for(int i=0; i<sampler.sampleSize(); ++i)
    00191         {
    00192             int currentIndex = sampler[i];
    00193             processData(data[currentIndex]);
    00194         }
    00195         // create next sample
    00196         sampler.sample();
    00197     }
    00198     \endcode
    00199
    00200     Create a Sampler for stratified sampling, without replacement.
    00201
    00202     \code
    00203     // prepare the strata (i.e. specify which stratum each element belongs to)
    00204     int stratumSize1 = 2000, stratumSize2 = 8000,
    00205         totalCount = stratumSize1 + stratumSize2;
    00206     ArrayVerctor<int> strata(totalCount);
    00207     for(int i=0; i<stratumSize1; ++i)
    00208         strata[i] = 1;
    00209     for(int i=stratumSize1; i<stratumSize2; ++i)
    00210         strata[i] = 2;
    00211
    00212     int sampleSize = 200; // i.e. sample 100 elements from each of the two strata
    00213     int numberOfSamples = 20; // repeat experiment 20 times
    00214     Sampler<> stratifiedSampler(strata.begin(), strata.end(),
    00215                      SamplerOptions().withoutReplacement().stratified().sampleSize(sampleSize));
    00216
    00217     for(int k=0; k<numberOfSamples; ++k)
    00218     {
    00219         // process current sample
    00220         for(int i=0; i<sampler.sampleSize(); ++i)
    00221         {
    00222             int currentIndex = sampler[i];
    00223             processData(data[currentIndex]);
    00224         }
    00225         // create next sample
    00226         sampler.sample();
    00227     }
    00228     \endcode
    00229 */
    00230 template<class Random = MersenneTwister >
    00231 class Sampler
    00232 {
    00233   public:
    00234         /** Internal type of the indices.
    00235             Currently, 64-bit indices are not supported because this
    00236             requires extension of the random number generator classes.
    00237         */
    00238     typedef Int32                               IndexType;
    00239
    00240     typedef ArrayVector     <IndexType>  IndexArrayType;
    00241
    00242         /** Type of the array view object that is returned by
    00243             sampledIndices() and oobIndices().
    00244         */
    00245     typedef ArrayVectorView <IndexType>  IndexArrayViewType;
    00246
    00247   private:
    00248     typedef std::map<IndexType, IndexArrayType> StrataIndicesType;
    00249     typedef std::map<IndexType, int> StrataSizesType;
    00250     typedef ArrayVector     <bool>       IsUsedArrayType;
    00251     typedef ArrayVectorView <bool>       IsUsedArrayViewType;
    00252
    00253     static const int oobInvalid = -1;
    00254
    00255     int total_count_, sample_size_;
    00256     mutable int current_oob_count_;
    00257     StrataIndicesType     strata_indices_;
    00258     StrataSizesType       strata_sample_size_;
    00259     IndexArrayType        current_sample_;
    00260     mutable IndexArrayType        current_oob_sample_;
    00261     IsUsedArrayType       is_used_;
    00262     Random const & random_;
    00263     SamplerOptions options_;
    00264
    00265     void initStrataCount()
    00266     {
    00267         // compute how many samples to take from each stratum
    00268         // (may be unequal if sample_size_ is not a multiple of strataCount())
    00269         int strata_sample_size = (int)std::ceil(double(sample_size_) / strataCount());
    00270         int strata_total_count = strata_sample_size * strataCount();
    00271
    00272         for(StrataIndicesType::iterator i = strata_indices_.begin();
    00273              i != strata_indices_.end(); ++i)
    00274         {
    00275             if(strata_total_count > sample_size_)
    00276             {
    00277                 strata_sample_size_[i->first] = strata_sample_size - 1;
    00278                 --strata_total_count;
    00279             }
    00280             else
    00281             {
    00282                 strata_sample_size_[i->first] = strata_sample_size;
    00283             }
    00284         }
    00285     }
    00286
    00287   public:
    00288
    00289         /** Create a sampler for \a totalCount data objects.
    00290
    00291             In each invocation of <tt>sample()</tt> below, it will sample
    00292             indices according to the options passed. If no options are given,
    00293             <tt>totalCount</tt> indices will be drawn with replacement.
    00294         */
    00295     Sampler(UInt32 totalCount, SamplerOptions const & opt = SamplerOptions(),
    00296             Random const & rnd = Random(RandomSeed))
    00297     : total_count_(totalCount),
    00298       sample_size_(opt.sample_size == 0
    00299                          ? (int)(std::ceil(total_count_ * opt.sample_proportion))
    00300                          : opt.sample_size),
    00301       current_oob_count_(oobInvalid),
    00302       current_sample_(sample_size_),
    00303       current_oob_sample_(total_count_),
    00304       is_used_(total_count_),
    00305       random_(rnd),
    00306       options_(opt)
    00307     {
    00308         vigra_precondition(opt.sample_with_replacement || sample_size_ <= total_count_,
    00309           "Sampler(): Cannot draw without replacement when data size is smaller than sample count.");
    00310
    00311         vigra_precondition(!opt.stratified_sampling,
    00312           "Sampler(): Stratified sampling requested, but no strata given.");
    00313
    00314         // initialize a single stratum containing all data
    00315         strata_indices_[0].resize(total_count_);
    00316         for(int i=0; i<total_count_; ++i)
    00317             strata_indices_[0][i] = i;
    00318
    00319         initStrataCount();
    00320         //this is screwing up the random forest tests.
    00321         //sample();
    00322     }
    00323
    00324         /** Create a sampler for stratified sampling.
    00325
    00326             <tt>strataBegin</tt> and <tt>strataEnd</tt> must refer to a sequence
    00327             which specifies for each sample the stratum it belongs to. The
    00328             total number of data objects will be set to <tt>strataEnd - strataBegin</tt>.
    00329             Equally many samples (subject to rounding) will be drawn from each stratum,
    00330             unless the option object explicitly requests unstratified sampling,
    00331             in which case the strata are ignored.
    00332         */
    00333     template <class Iterator>
    00334     Sampler(Iterator strataBegin, Iterator strataEnd, SamplerOptions const & opt = SamplerOptions(),
    00335             Random const & rnd = Random(RandomSeed))
    00336     : total_count_(strataEnd - strataBegin),
    00337       sample_size_(opt.sample_size == 0
    00338                          ? (int)(std::ceil(total_count_ * opt.sample_proportion))
    00339                          : opt.sample_size),
    00340       current_oob_count_(oobInvalid),
    00341       current_sample_(sample_size_),
    00342       current_oob_sample_(total_count_),
    00343       is_used_(total_count_),
    00344       random_(rnd),
    00345       options_(opt)
    00346     {
    00347         vigra_precondition(opt.sample_with_replacement || sample_size_ <= total_count_,
    00348           "Sampler(): Cannot draw without replacement when data size is smaller than sample count.");
    00349
    00350         // copy the strata indices
    00351         if(opt.stratified_sampling)
    00352         {
    00353             for(int i = 0; strataBegin != strataEnd; ++i, ++strataBegin)
    00354             {
    00355                 strata_indices_[*strataBegin].push_back(i);
    00356             }
    00357         }
    00358         else
    00359         {
    00360             strata_indices_[0].resize(total_count_);
    00361             for(int i=0; i<total_count_; ++i)
    00362                 strata_indices_[0][i] = i;
    00363         }
    00364
    00365         vigra_precondition(sample_size_ >= (int)strata_indices_.size(),
    00366             "Sampler(): Requested sample count must be at least as large as the number of strata.");
    00367
    00368         initStrataCount();
    00369         //this is screwing up the random forest tests.
    00370         //sample();
    00371     }
    00372
    00373         /** Return the k-th index in the current sample.
    00374          */
    00375     IndexType operator[](int k) const
    00376     {
    00377         return current_sample_[k];
    00378     }
    00379
    00380         /** Create a new sample.
    00381          */
    00382     void sample();
    00383
    00384         /** The total number of data elements.
    00385          */
    00386     int totalCount() const
    00387     {
    00388         return total_count_;
    00389     }
    00390
    00391         /** The number of data elements that have been sampled.
    00392          */
    00393     int sampleSize() const
    00394     {
    00395         return sample_size_;
    00396     }
    00397
    00398         /** Same as sampleSize().
    00399          */
    00400     int size() const
    00401     {
    00402         return sample_size_;
    00403     }
    00404
    00405         /** The number of strata to be used.
    00406             Will be 1 if no strata are given. Will be ognored when
    00407             stratifiedSampling() is false.
    00408          */
    00409     int strataCount() const
    00410     {
    00411         return strata_indices_.size();
    00412     }
    00413
    00414         /** Whether to use stratified sampling.
    00415             (If this is false, strata will be ignored even if present.)
    00416          */
    00417     bool stratifiedSampling() const
    00418     {
    00419         return options_.stratified_sampling;
    00420     }
    00421
    00422         /** Whether sampling should be performed with replacement.
    00423          */
    00424     bool withReplacement() const
    00425     {
    00426         return options_.sample_with_replacement;
    00427     }
    00428
    00429         /** Return an array view containing the indices in the current sample.
    00430          */
    00431     IndexArrayViewType sampledIndices() const
    00432     {
    00433         return current_sample_;
    00434     }
    00435
    00436         /** Return an array view containing the out-of-bag indices.
    00437             (i.e. the indices that are not in the current sample)
    00438          */
    00439     IndexArrayViewType oobIndices() const
    00440     {
    00441         if(current_oob_count_ == oobInvalid)
    00442         {
    00443             current_oob_count_ = 0;
    00444             for(int i = 0; i<total_count_; ++i)
    00445             {
    00446                 if(!is_used_[i])
    00447                 {
    00448                     current_oob_sample_[current_oob_count_] = i;
    00449                     ++current_oob_count_;
    00450                 }
    00451             }
    00452         }
    00453         return current_oob_sample_.subarray(0, current_oob_count_);
    00454     }
    00455     IsUsedArrayType const & is_used() const
    00456     {
    00457         return is_used_;
    00458     }
    00459 };
    00460
    00461
    00462 template<class Random>
    00463 void Sampler<Random>::sample()
    00464 {
    00465     current_oob_count_ = oobInvalid;
    00466     is_used_.init(false);
    00467
    00468     if(options_.sample_with_replacement)
    00469     {
    00470         //Go thru all strata
    00471         int j = 0;
    00472         StrataIndicesType::iterator iter;
    00473         for(iter = strata_indices_.begin(); iter != strata_indices_.end(); ++iter)
    00474         {
    00475             // do sampling with replacement in each strata and copy data.
    00476             int stratum_size = iter->second.size();
    00477             for(int i = 0; i < (int)strata_sample_size_[iter->first]; ++i, ++j)
    00478             {
    00479                 current_sample_[j] = iter->second[random_.uniformInt(stratum_size)];
    00480                 is_used_[current_sample_[j]] = true;
    00481             }
    00482         }
    00483     }
    00484     else
    00485     {
    00486         //Go thru all strata
    00487         int j = 0;
    00488         StrataIndicesType::iterator iter;
    00489         for(iter = strata_indices_.begin(); iter != strata_indices_.end(); ++iter)
    00490         {
    00491             // do sampling without replacement in each strata and copy data.
    00492             int stratum_size = iter->second.size();
    00493             for(int i = 0; i < (int)strata_sample_size_[iter->first]; ++i, ++j)
    00494             {
    00495                 std::swap(iter->second[i], iter->second[i+ random_.uniformInt(stratum_size - i)]);
    00496                 current_sample_[j] = iter->second[i];
    00497                 is_used_[current_sample_[j]] = true;
    00498             }
    00499         }
    00500     }
    00501 }
    00502
    00503 template<class Random =RandomTT800 >
    00504 class PoissonSampler
    00505 {
    00506 public:
    00507     Random  randfloat;
    00508     typedef Int32                               IndexType;
    00509     typedef vigra::ArrayVector     <IndexType>  IndexArrayType;
    00510     IndexArrayType        used_indices_;
    00511     double lambda;
    00512     int minIndex;
    00513     int maxIndex;
    00514
    00515     PoissonSampler(double lambda,IndexType minIndex,IndexType maxIndex)
    00516     : lambda(lambda),
    00517       minIndex(minIndex),
    00518       maxIndex(maxIndex)
    00519     {}
    00520
    00521     void sample(  )
    00522     {
    00523         used_indices_.clear();
    00524         IndexType i;
    00525         for(i=minIndex;i<maxIndex;++i)
    00526         {
    00527             //from http://en.wikipedia.org/wiki/Poisson_distribution
    00528             int k=0;
    00529             double p=1;
    00530             double L=exp(-lambda);
    00531             do
    00532             {
    00533                 ++k;
    00534                 p*=randfloat.uniform53();
    00535
    00536             }while(p>L);
    00537             --k;
    00538             //Insert i this many time
    00539             while(k>0)
    00540             {
    00541                 used_indices_.push_back(i);
    00542                 --k;
    00543             }
    00544         }
    00545     }
    00546
    00547     IndexType const & operator[](int in) const
    00548     {
    00549         return used_indices_[in];
    00550     }
    00551
    00552     int numOfSamples() const
    00553     {
    00554         return used_indices_.size();
    00555     }
    00556 };
    00557
    00558 //@}
    00559
    00560 } // namespace vigra
    00561
    00562 #endif /*VIGRA_SAMPLING_HXX*/

© Ullrich Köthe (ullrich.koethe@iwr.uni-heidelberg.de) Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany | html generated using doxygen and Python vigra 1.7.1 (3 Dec 2010)