ITK  5.3.0
Insight Toolkit
Examples/Statistics/KdTreeBasedKMeansClustering.cxx
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// Software Guide : BeginLatex
//
// \index{Statistics!k-means clustering (using k-d tree)}
//
// \index{itk::Statistics::KdTree\-Based\-Kmeans\-Estimator}
//
// K-means clustering is a popular clustering algorithm because it is simple
// and usually converges to a reasonable solution. The k-means algorithm
// works as follows:
//
// \begin{enumerate}
// \item{Obtains the initial k means input from the user.}
// \item{Assigns each measurement vector in a sample container to its
// closest mean among the k number of means (i.e., update the membership of
// each measurement vectors to the nearest of the k clusters).}
// \item{Calculates each cluster's mean from the newly assigned
// measurement vectors (updates the centroid (mean) of k clusters).}
// \item{Repeats step 2 and step 3 until it meets the termination
// criteria.}
// \end{enumerate}
//
// The most common termination criterion is that if there is no
// measurement vector that changes its cluster membership from the
// previous iteration, then the algorithm stops.
//
// The \subdoxygen{Statistics}{KdTreeBasedKmeansEstimator} is a variation of
// this logic. The k-means clustering algorithm is computationally very
// expensive because it has to recalculate the mean at each iteration. To
// update the mean values, we have to calculate the distance between k means
// and each and every measurement vector. To reduce the computational burden,
// the KdTreeBasedKmeansEstimator uses a special data structure: the
// k-d tree (\subdoxygen{Statistics}{KdTree}) with additional
// information. The additional information includes the number and the vector
// sum of measurement vectors under each node under the tree architecture.
//
// With such additional information and the k-d tree data structure,
// we can reduce the computational cost of the distance calculation
// and means. Instead of calculating each measurement vector and k
// means, we can simply compare each node of the k-d tree and the k
// means. This idea of utilizing a k-d tree can be found in multiple
// articles \cite{Alsabti1998} \cite{Pelleg1999}
// \cite{Kanungo2000}. Our implementation of this scheme follows the
// article by the Kanungo et al \cite{Kanungo2000}.
//
// We use the \subdoxygen{Statistics}{ListSample} as the input sample, the
// \doxygen{Vector} as the measurement vector. The following code
// snippet includes their header files.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
#include "itkVector.h"
#include "itkListSample.h"
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Since our k-means algorithm requires a \subdoxygen{Statistics}{KdTree}
// object as an input, we include the KdTree class header file. As mentioned
// above, we need a k-d tree with the vector sum and the number of
// measurement vectors. Therefore we use the
// \subdoxygen{Statistics}{WeightedCentroidKdTreeGenerator} instead of the
// \subdoxygen{Statistics}{KdTreeGenerator} that generate a k-d tree without
// such additional information.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
#include "itkKdTree.h"
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The KdTreeBasedKmeansEstimator class is the implementation of the
// k-means algorithm. It does not create k clusters. Instead, it
// returns the mean estimates for the k clusters.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// To generate the clusters, we must create k instances of\newline
// \subdoxygen{Statistics}{DistanceToCentroidMembershipFunction} function as
// the membership functions for each cluster and plug
// that---along with a sample---into an
// \subdoxygen{Statistics}{SampleClassifierFilter} object to get a
// \subdoxygen{Statistics}{MembershipSample} that stores pairs of measurement
// vectors and their associated class labels (k labels).
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// We will fill the sample with random variables from two normal
// distribution using the \subdoxygen{Statistics}{NormalVariateGenerator}.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
// Software Guide : EndCodeSnippet
int
main()
{
// Software Guide : BeginLatex
//
// Since the \code{NormalVariateGenerator} class only supports 1-D, we
// define our measurement vector type as one component vector. We
// then, create a \code{ListSample} object for data inputs. Each
// measurement vector is of length 1. We set this using the
// \code{SetMeasurementVectorSize()} method.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
using MeasurementVectorType = itk::Vector<double, 1>;
SampleType::Pointer sample = SampleType::New();
sample->SetMeasurementVectorSize(1);
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The following code snippet creates a NormalVariateGenerator
// object. Since the random variable generator returns values
// according to the standard normal distribution (The mean is zero,
// and the standard deviation is one), before pushing random values
// into the \code{sample}, we change the mean and standard
// deviation. We want two normal (Gaussian) distribution data. We have
// two for loops. Each for loop uses different mean and standard
// deviation. Before we fill the \code{sample} with the second
// distribution data, we call \code{Initialize(random seed)} method,
// to recreate the pool of random variables in the
// \code{normalGenerator}.
//
// To see the probability density plots from the two distribution,
// refer to the Figure~\ref{fig:TwoNormalDensityFunctionPlot}.
//
// \begin{figure}
// \center
// \includegraphics[width=0.8\textwidth]{TwoNormalDensityFunctionPlot}
// \itkcaption[Two normal distributions plot]{Two normal distributions'
// probability density plot
// (The means are 100 and 200, and the standard deviation is 30 )}
// \protect\label{fig:TwoNormalDensityFunctionPlot}
// \end{figure}
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
using NormalGeneratorType = itk::Statistics::NormalVariateGenerator;
NormalGeneratorType::Pointer normalGenerator = NormalGeneratorType::New();
normalGenerator->Initialize(101);
MeasurementVectorType mv;
double mean = 100;
double standardDeviation = 30;
for (unsigned int i = 0; i < 100; ++i)
{
mv[0] = (normalGenerator->GetVariate() * standardDeviation) + mean;
sample->PushBack(mv);
}
normalGenerator->Initialize(3024);
mean = 200;
standardDeviation = 30;
for (unsigned int i = 0; i < 100; ++i)
{
mv[0] = (normalGenerator->GetVariate() * standardDeviation) + mean;
sample->PushBack(mv);
}
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// We create a k-d tree. To see the details on the k-d tree generation, see
// the Section~\ref{sec:KdTree}.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
using TreeGeneratorType =
TreeGeneratorType::Pointer treeGenerator = TreeGeneratorType::New();
treeGenerator->SetSample(sample);
treeGenerator->SetBucketSize(16);
treeGenerator->Update();
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// Once we have the k-d tree, it is a simple procedure to produce k
// mean estimates.
//
// We create the KdTreeBasedKmeansEstimator. Then, we provide the initial
// mean values using the \code{SetParameters()}. Since we are dealing with
// two normal distribution in a 1-D space, the size of the mean value array
// is two. The first element is the first mean value, and the second is the
// second mean value. If we used two normal distributions in a 2-D space,
// the size of array would be four, and the first two elements would be the
// two components of the first normal distribution's mean vector. We
// plug-in the k-d tree using the \code{SetKdTree()}.
//
// The remaining two methods specify the termination condition. The
// estimation process stops when the number of iterations reaches the
// maximum iteration value set by the \code{SetMaximumIteration()}, or the
// distances between the newly calculated mean (centroid) values and
// previous ones are within the threshold set by the
// \code{SetCentroidPositionChangesThreshold()}. The final step is
// to call the \code{StartOptimization()} method.
//
// The for loop will print out the mean estimates from the estimation
// process.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
using TreeType = TreeGeneratorType::KdTreeType;
EstimatorType::Pointer estimator = EstimatorType::New();
EstimatorType::ParametersType initialMeans(2);
initialMeans[0] = 0.0;
initialMeans[1] = 0.0;
estimator->SetParameters(initialMeans);
estimator->SetKdTree(treeGenerator->GetOutput());
estimator->SetMaximumIteration(200);
estimator->SetCentroidPositionChangesThreshold(0.0);
estimator->StartOptimization();
EstimatorType::ParametersType estimatedMeans = estimator->GetParameters();
for (unsigned int i = 0; i < 2; ++i)
{
std::cout << "cluster[" << i << "] " << std::endl;
std::cout << " estimated mean : " << estimatedMeans[i] << std::endl;
}
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// If we are only interested in finding the mean estimates, we might
// stop. However, to illustrate how a classifier can be formed using
// the statistical classification framework. We go a little bit
// further in this example.
//
// Since the k-means algorithm is an minimum distance classifier using
// the estimated k means and the measurement vectors. We use the
// DistanceToCentroidMembershipFunction class as membership functions.
// Our choice for the decision rule is the
// \subdoxygen{Statistics}{MinimumDecisionRule} that returns the
// index of the membership functions that have the smallest value for
// a measurement vector.
//
// After creating a SampleClassifier filter object and a
// MinimumDecisionRule object, we plug-in the \code{decisionRule} and
// the \code{sample} to the classifier filter. Then, we must specify
// the number of classes that will be considered using the
// \code{SetNumberOfClasses()} method.
//
// The remainder of the following code snippet shows how to use
// user-specified class labels. The classification result will be stored
// in a MembershipSample object, and for each measurement vector, its
// class label will be one of the two class labels, 100 and 200
// (\code{unsigned int}).
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
using MembershipFunctionType =
MeasurementVectorType>;
using DecisionRuleType = itk::Statistics::MinimumDecisionRule;
DecisionRuleType::Pointer decisionRule = DecisionRuleType::New();
ClassifierType::Pointer classifier = ClassifierType::New();
classifier->SetDecisionRule(decisionRule);
classifier->SetInput(sample);
classifier->SetNumberOfClasses(2);
using ClassLabelVectorObjectType =
ClassifierType::ClassLabelVectorObjectType;
using ClassLabelVectorType = ClassifierType::ClassLabelVectorType;
using ClassLabelType = ClassifierType::ClassLabelType;
ClassLabelVectorObjectType::Pointer classLabelsObject =
ClassLabelVectorObjectType::New();
ClassLabelVectorType & classLabelsVector = classLabelsObject->Get();
ClassLabelType class1 = 200;
classLabelsVector.push_back(class1);
ClassLabelType class2 = 100;
classLabelsVector.push_back(class2);
classifier->SetClassLabels(classLabelsObject);
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The \code{classifier} is almost ready to do the classification
// process except that it needs two membership functions that
// represents two clusters respectively.
//
// In this example, the two clusters are modeled by two Euclidean distance
// functions. The distance function (model) has only one parameter, its mean
// (centroid) set by the \code{SetCentroid()} method. To plug-in two
// distance functions, we create a MembershipFunctionVectorObject that
// contains a MembershipFunctionVector with two components and add it using
// the \code{SetMembershipFunctions} method. Then invocation of the
// \code{Update()} method will perform the classification.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
using MembershipFunctionVectorObjectType =
ClassifierType::MembershipFunctionVectorObjectType;
using MembershipFunctionVectorType =
ClassifierType::MembershipFunctionVectorType;
MembershipFunctionVectorObjectType::Pointer membershipFunctionVectorObject =
MembershipFunctionVectorObjectType::New();
MembershipFunctionVectorType & membershipFunctionVector =
membershipFunctionVectorObject->Get();
int index = 0;
for (unsigned int i = 0; i < 2; ++i)
{
MembershipFunctionType::Pointer membershipFunction =
MembershipFunctionType::New();
MembershipFunctionType::CentroidType centroid(
sample->GetMeasurementVectorSize());
for (unsigned int j = 0; j < sample->GetMeasurementVectorSize(); ++j)
{
centroid[j] = estimatedMeans[index++];
}
membershipFunction->SetCentroid(centroid);
membershipFunctionVector.push_back(membershipFunction);
}
classifier->SetMembershipFunctions(membershipFunctionVectorObject);
classifier->Update();
// Software Guide : EndCodeSnippet
// Software Guide : BeginLatex
//
// The following code snippet prints out the measurement vectors and
// their class labels in the \code{sample}.
//
// Software Guide : EndLatex
// Software Guide : BeginCodeSnippet
const ClassifierType::MembershipSampleType * membershipSample =
classifier->GetOutput();
ClassifierType::MembershipSampleType::ConstIterator iter =
membershipSample->Begin();
while (iter != membershipSample->End())
{
std::cout << "measurement vector = " << iter.GetMeasurementVector()
<< " class label = " << iter.GetClassLabel() << std::endl;
++iter;
}
// Software Guide : EndCodeSnippet
return EXIT_SUCCESS;
}
itk::Statistics::DistanceToCentroidMembershipFunction
DistanceToCentroidMembershipFunction models class membership using a distance metric.
Definition: itkDistanceToCentroidMembershipFunction.h:45
itk::Statistics::WeightedCentroidKdTreeGenerator
This class generates a KdTree object with centroid information.
Definition: itkWeightedCentroidKdTreeGenerator.h:67
itkSampleClassifierFilter.h
itk::Vector
A templated class holding a n-Dimensional vector.
Definition: itkVector.h:62
itk::Statistics::ListSample
This class is the native implementation of the a Sample with an STL container.
Definition: itkListSample.h:51
itkKdTreeBasedKmeansEstimator.h
itk::Statistics::NormalVariateGenerator
Normal random variate generator.
Definition: itkNormalVariateGenerator.h:98
itkMinimumDecisionRule.h
itk::Statistics::KdTreeBasedKmeansEstimator
fast k-means algorithm implementation using k-d tree structure
Definition: itkKdTreeBasedKmeansEstimator.h:74
itkListSample.h
itkKdTree.h
itkNormalVariateGenerator.h
itkVector.h
itk::Statistics::SampleClassifierFilter
Sample classification class.
Definition: itkSampleClassifierFilter.h:45
itk::Statistics::MinimumDecisionRule
A decision rule that returns the class label with the smallest discriminant score.
Definition: itkMinimumDecisionRule.h:38
itkWeightedCentroidKdTreeGenerator.h