/// <summary>
/// Initializes a new instance of the <see cref="SimpleHeadPoseEstimator"/> class with the model files to estimate head pose.
/// </summary>
/// <param name="rollModelFile">The model file path to estimate roll angle.</param>
/// <param name="pitchModelFile">The model file path to estimate pitch angle.</param>
/// <param name="yawModelFile">The model file path to estimate yaw angle.</param>
/// <exception cref="FileNotFoundException"><paramref name="rollModelFile"/>, <paramref name="pitchModelFile"/> or <paramref name="yawModelFile"/> does not exist.</exception>
public SimpleHeadPoseEstimator(string rollModelFile,
string pitchModelFile,
string yawModelFile)
{
if (!File.Exists(rollModelFile))
{
throw new FileNotFoundException($"{nameof(rollModelFile)} does not exist.", nameof(rollModelFile));
}
if (!File.Exists(pitchModelFile))
{
throw new FileNotFoundException($"{nameof(pitchModelFile)} does not exist.", nameof(pitchModelFile));
}
if (!File.Exists(yawModelFile))
{
throw new FileNotFoundException($"{nameof(yawModelFile)} does not exist.", nameof(yawModelFile));
}
// gamma parameter is meaningless
this._RollKernel = new RadialBasisKernel <double, Matrix <double> >(0.1, 0, 0);
this._PitchKernel = new RadialBasisKernel <double, Matrix <double> >(0.1, 0, 0);
this._YawKernel = new RadialBasisKernel <double, Matrix <double> >(0.1, 0, 0);
this._RollEstimator = new Krls <double, RadialBasisKernel <double, Matrix <double> > >(this._RollKernel);
this._PitchEstimator = new Krls <double, RadialBasisKernel <double, Matrix <double> > >(this._PitchKernel);
this._YawEstimator = new Krls <double, RadialBasisKernel <double, Matrix <double> > >(this._YawKernel);
Krls <double, RadialBasisKernel <double, Matrix <double> > > .Deserialize(rollModelFile, ref this._RollEstimator);
Krls <double, RadialBasisKernel <double, Matrix <double> > > .Deserialize(pitchModelFile, ref this._PitchEstimator);
Krls <double, RadialBasisKernel <double, Matrix <double> > > .Deserialize(yawModelFile, ref this._YawEstimator);
}
private static void Main()
{
// Here we declare that our samples will be 1 dimensional column vectors. The reason for
// using a matrix here is that in general you can use N dimensional vectors as inputs to the
// krls object. But here we only have 1 dimension to make the example simple.
// Now we are making a typedef for the kind of kernel we want to use. I picked the
// radial basis kernel because it only has one parameter and generally gives good
// results without much fiddling.
// Here we declare an instance of the krls object. The first argument to the constructor
// is the kernel we wish to use. The second is a parameter that determines the numerical
// accuracy with which the object will perform part of the regression algorithm. Generally
// smaller values give better results but cause the algorithm to run slower (because it tries
// to use more "dictionary vectors" to represent the function it is learning.
// You just have to play with it to decide what balance of speed and accuracy is right
// for your problem. Here we have set it to 0.001.
//
// The last argument is the maximum number of dictionary vectors the algorithm is allowed
// to use. The default value for this field is 1,000,000 which is large enough that you
// won't ever hit it in practice. However, here we have set it to the much smaller value
// of 7. This means that once the krls object accumulates 7 dictionary vectors it will
// start discarding old ones in favor of new ones as it goes through the training process.
// In other words, the algorithm "forgets" about old training data and focuses on recent
// training samples. So the bigger the maximum dictionary size the longer its memory will
// be. But in this example program we are doing filtering so we only care about the most
// recent data. So using a small value is appropriate here since it will result in much
// faster filtering and won't introduce much error.
using (var rbk = new RadialBasisKernel <double, Matrix <double> >(0.1, 1, 1))
using (var test = new Krls <double, RadialBasisKernel <double, Matrix <double> > >(rbk, 0.001))
{
// now we train our object on a few samples of the sinc function.
using (var m = Matrix <double> .CreateTemplateParameterizeMatrix(1, 1))
{
for (double x = -10; x <= 4; x += 1)
{
m[0] = x;
test.Train(m, Sinc(x));
}
// now we output the value of the sinc function for a few test points as well as the
// value predicted by krls object.
m[0] = 2.5;
Console.WriteLine($"{Sinc(m[0])} {test.Operator(m)}");
m[0] = 0.1;
Console.WriteLine($"{Sinc(m[0])} {test.Operator(m)}");
m[0] = -4;
Console.WriteLine($"{Sinc(m[0])} {test.Operator(m)}");
m[0] = 5.0;
Console.WriteLine($"{Sinc(m[0])} {test.Operator(m)}");
// The output is as follows:
// 0.239389 0.239362
// 0.998334 0.998333
// -0.189201 -0.189201
// -0.191785 -0.197267
// The first column is the true value of t he sinc function and the second
// column is the output from the krls estimate.
// Another thing that is worth knowing is that just about everything in dlib is serializable.
// So for example, you can save the test object to disk and recall it later like so:
Krls <double, RadialBasisKernel <double, Matrix <double> > > .Serialize(test, "saved_krls_object.dat");
// Now let's open that file back up and load the krls object it contains.
using (var rbk2 = new RadialBasisKernel <double, Matrix <double> >(0.1, 1, 1))
{
var test2 = new Krls <double, RadialBasisKernel <double, Matrix <double> > >(rbk2, 0.001);
Krls <double, RadialBasisKernel <double, Matrix <double> > > .Deserialize("saved_krls_object.dat", ref test2);
// If you don't want to save the whole krls object (it might be a bit large)
// you can save just the decision function it has learned so far. You can get
// the decision function out of it by calling test.get_decision_function() and
// then you can serialize that object instead. E.g.
var funct = test2.GetDecisionFunction();
DecisionFunction <double, RadialBasisKernel <double, Matrix <double> > > .Serialize(funct, "saved_krls_function.dat");
}
}
}
}
private static int Main()
{
// The svm functions use column vectors to contain a lot of the data on which they
// operate. So the first thing we do here is declare a convenient typedef.
// This typedef declares a matrix with 2 rows and 1 column. It will be the object that
// contains each of our 2 dimensional samples. (Note that if you wanted more than 2
// features in this vector you can simply change the 2 to something else. Or if you
// don't know how many features you want until runtime then you can put a 0 here and
// use the matrix.set_size() member function)
//typedef matrix<double, 2, 1 > sample_type;
// This is a typedef for the type of kernel we are going to use in this example. In
// this case I have selected the radial basis kernel that can operate on our 2D
// sample_type objects
//typedef radial_basis_kernel<sample_type> kernel_type;
// Now we make objects to contain our samples and their respective labels.
var samples = new List <SampleType>();
var labels = new List <double>();
// Now let's put some data into our samples and labels objects. We do this by looping
// over a bunch of points and labeling them according to their distance from the
// origin.
for (var r = -20; r <= 20; ++r)
{
for (var c = -20; c <= 20; ++c)
{
var samp = new SampleType();
samp.SetSize(2, 1);
samp[0] = r;
samp[1] = c;
samples.Add(samp);
// if this point is less than 10 from the origin
if (Math.Sqrt((double)r * r + c * c) <= 10)
{
labels.Add(+1);
}
else
{
labels.Add(-1);
}
}
}
// Here we normalize all the samples by subtracting their mean and dividing by their
// standard deviation. This is generally a good idea since it often heads off
// numerical stability problems and also prevents one large feature from smothering
// others. Doing this doesn't matter much in this example so I'm just doing this here
// so you can see an easy way to accomplish this with the library.
using (var normalizer = new VectorNormalizer <SampleType>())
{
// let the normalizer learn the mean and standard deviation of the samples
normalizer.Train(samples);
// now normalize each sample
for (var i = 0; i < samples.Count; ++i)
{
var ret = normalizer.Operator(samples[i]);
samples[i].Dispose();
samples[i] = ret;
}
// Now that we have some data we want to train on it. However, there are two
// parameters to the training. These are the nu and gamma parameters. Our choice for
// these parameters will influence how good the resulting decision function is. To
// test how good a particular choice of these parameters is we can use the
// cross_validate_trainer() function to perform n-fold cross validation on our training
// data. However, there is a problem with the way we have sampled our distribution
// above. The problem is that there is a definite ordering to the samples. That is,
// the first half of the samples look like they are from a different distribution than
// the second half. This would screw up the cross validation process but we can fix it
// by randomizing the order of the samples with the following function call.
Dlib.RandomizeSamples(samples, labels);
// The nu parameter has a maximum value that is dependent on the ratio of the +1 to -1
// labels in the training data. This function finds that value.
double maxNu = Dlib.MaximumNu(labels);
// here we make an instance of the svm_nu_trainer object that uses our kernel type.
using (var trainer = new SvmNuTrainer <double, RadialBasisKernel <double, Matrix <double> > >())
{
// Now we loop over some different nu and gamma values to see how good they are. Note
// that this is a very simple way to try out a few possible parameter choices. You
// should look at the model_selection_ex.cpp program for examples of more sophisticated
// strategies for determining good parameter choices.
Console.WriteLine("doing cross validation");
for (var gamma = 0.00001; gamma <= 1; gamma *= 5)
{
for (var nu = 0.00001; nu < maxNu; nu *= 5)
{
// tell the trainer the parameters we want to use
using (var kernel = new RadialBasisKernel <double, Matrix <double> >(gamma, 0, 0))
{
trainer.Kernel = kernel;
trainer.Nu = nu;
Console.Write($"gamma: {gamma} nu: {nu}");
// Print out the cross validation accuracy for 3-fold cross validation using
// the current gamma and nu. cross_validate_trainer() returns a row vector.
// The first element of the vector is the fraction of +1 training examples
// correctly classified and the second number is the fraction of -1 training
// examples correctly classified.
using (var ret = Dlib.CrossValidateTrainer(trainer, samples, labels, 3))
Console.Write($" cross validation accuracy: {ret}");
}
}
}
// From looking at the output of the above loop it turns out that a good value for nu
// and gamma for this problem is 0.15625 for both. So that is what we will use.
// Now we train on the full set of data and obtain the resulting decision function. We
// use the value of 0.15625 for nu and gamma. The decision function will return values
// >= 0 for samples it predicts are in the +1 class and numbers < 0 for samples it
// predicts to be in the -1 class.
using (var kernel = new RadialBasisKernel <double, Matrix <double> >(0.15625, 0, 0))
{
trainer.Kernel = kernel;
trainer.Nu = 0.15625;
// Here we are making an instance of the normalized_function object. This object
// provides a convenient way to store the vector normalization information along with
// the decision function we are going to learn.
var learnedFunction = new NormalizedFunction <double, DecisionFunction <double, RadialBasisKernel <double, Matrix <double> > > >();
learnedFunction.Normalizer = normalizer; // save normalization information
using (var function = trainer.Train(samples, labels))
{
learnedFunction.Function = function; // perform the actual SVM training and save the results
// print out the number of support vectors in the resulting decision function
Console.WriteLine();
// ToDo: must support nested matrix
//Console.WriteLine($"number of support vectors in our learned_function is {learnedFunction.Function.basis_vectors.size()}");
}
// Now let's try this decision_function on some samples we haven't seen before.
using (var sample = new SampleType())
{
sample.SetSize(2, 1);
sample[0] = 3.123;
sample[1] = 2;
Console.WriteLine($"This is a +1 class example, the classifier output is {learnedFunction.Operator(sample)}");
sample[0] = 3.123;
sample[1] = 9.3545;
Console.WriteLine($"This is a +1 class example, the classifier output is {learnedFunction.Operator(sample)}");
sample[0] = 13.123;
sample[1] = 9.3545;
Console.WriteLine($"This is a -1 class example, the classifier output is {learnedFunction.Operator(sample)}");
sample[0] = 13.123;
sample[1] = 0;
Console.WriteLine($"This is a -1 class example, the classifier output is {learnedFunction.Operator(sample)}");
}
// We can also train a decision function that reports a well conditioned probability
// instead of just a number > 0 for the +1 class and < 0 for the -1 class. An example
// of doing that follows:
var learnedProbabilisticFunction = new NormalizedFunction <double, ProbabilisticDecisionFunction <double, RadialBasisKernel <double, Matrix <double> > > >();
learnedProbabilisticFunction.Normalizer = normalizer;
using (var function = Dlib.TrainProbabilisticDecisionFunction <double,
RadialBasisKernel <double, Matrix <double> >,
SvmNuTrainer <double, RadialBasisKernel <double, Matrix <double> > > >(trainer, samples, labels, 3))
{
learnedProbabilisticFunction.Function = function;
// Now we have a function that returns the probability that a given sample is of the +1 class.
// print out the number of support vectors in the resulting decision function.
// (it should be the same as in the one above)
Console.WriteLine();
// ToDo: must support nested matrix
//Console.WriteLine($"number of support vectors in our learned_pfunct is {learnedProbabilisticFunction.Function.DecisionFunct.BasisVectors.size()}");
}
using (var sample = new SampleType())
{
sample.SetSize(2, 1);
sample[0] = 3.123;
sample[1] = 2;
Console.WriteLine($"This +1 class example should have high probability. Its probability is: {learnedProbabilisticFunction.Operator(sample)}");
sample[0] = 3.123;
sample[1] = 9.3545;
Console.WriteLine($"This +1 class example should have high probability. Its probability is: {learnedProbabilisticFunction.Operator(sample)}");
sample[0] = 13.123;
sample[1] = 9.3545;
Console.WriteLine($"This -1 class example should have low probability. Its probability is: {learnedProbabilisticFunction.Operator(sample)}");
sample[0] = 13.123;
sample[1] = 0;
Console.WriteLine($"This -1 class example should have low probability. Its probability is: {learnedProbabilisticFunction.Operator(sample)}");
}
// Another thing that is worth knowing is that just about everything in dlib is
// serializable. So for example, you can save the learned_pfunct object to disk and
// recall it later like so:
NormalizedFunction <double, ProbabilisticDecisionFunction <double, RadialBasisKernel <double, Matrix <double> > > > .Serialize("saved_function.dat", learnedProbabilisticFunction);
// Now let's open that file back up and load the function object it contains.
learnedProbabilisticFunction.Dispose();
learnedProbabilisticFunction = NormalizedFunction <double, ProbabilisticDecisionFunction <double, RadialBasisKernel <double, Matrix <double> > > > .Deserialize("saved_function.dat");
// Note that there is also an example program that comes with dlib called
// the file_to_code_ex.cpp example. It is a simple program that takes a
// file and outputs a piece of C++ code that is able to fully reproduce the
// file's contents in the form of a std::string object. So you can use that
// along with the std::istringstream to save learned decision functions
// inside your actual C++ code files if you want.
// Note that there is also an example program that comes with dlib called the
// file_to_code_ex.cpp example. It is a simple program that takes a file and outputs a
// piece of C++ code that is able to fully reproduce the file's contents in the form of
// a std::string object. So you can use that along with the std::istringstream to save
// learned decision functions inside your actual C++ code files if you want.
// Lastly, note that the decision functions we trained above involved well over 200
// basis vectors. Support vector machines in general tend to find decision functions
// that involve a lot of basis vectors. This is significant because the more basis
// vectors in a decision function, the longer it takes to classify new examples. So
// dlib provides the ability to find an approximation to the normal output of a trainer
// using fewer basis vectors.
// Here we determine the cross validation accuracy when we approximate the output using
// only 10 basis vectors. To do this we use the reduced2() function. It takes a
// trainer object and the number of basis vectors to use and returns a new trainer
// object that applies the necessary post processing during the creation of decision
// function objects.
using (var reduced = Dlib.Reduced2 <double,
RadialBasisKernel <double, Matrix <double> >,
SvmNuTrainer <double, RadialBasisKernel <double, Matrix <double> > > >(trainer, 10))
{
Console.WriteLine();
using (var ret = Dlib.CrossValidateTrainer(reduced, samples, labels, 3))
Console.Write($"cross validation accuracy with only 10 support vectors: {ret}");
}
// Let's print out the original cross validation score too for comparison.
using (var ret2 = Dlib.CrossValidateTrainer(trainer, samples, labels, 3))
Console.Write($"cross validation accuracy with all the original support vectors: {ret2}");
// When you run this program you should see that, for this problem, you can reduce the
// number of basis vectors down to 10 without hurting the cross validation accuracy.
// To get the reduced decision function out we would just do this:
using (var reduced = Dlib.Reduced2 <double,
RadialBasisKernel <double, Matrix <double> >,
SvmNuTrainer <double, RadialBasisKernel <double, Matrix <double> > > >(trainer, 10))
using (var function = reduced.Train(samples, labels))
learnedFunction.Function = function;
// And similarly for the probabilistic_decision_function:
using (var reduced = Dlib.Reduced2 <double,
RadialBasisKernel <double, Matrix <double> >,
SvmNuTrainer <double, RadialBasisKernel <double, Matrix <double> > > >(trainer, 10))
using (var function = Dlib.TrainProbabilisticDecisionFunction(reduced, samples, labels, 3))
learnedProbabilisticFunction.Function = function;
learnedFunction.Dispose();
learnedProbabilisticFunction.Dispose();
}
}
}
return(0);
}
private static int Main()
{
// The svm functions use column vectors to contain a lot of the data on which they
// operate. So the first thing we do here is declare a convenient typedef.
// This typedef declares a matrix with 2 rows and 1 column. It will be the
// object that contains each of our 2 dimensional samples. (Note that if you wanted
// more than 2 features in this vector you can simply change the 2 to something else.
// Or if you don't know how many features you want until runtime then you can put a 0
// here and use the matrix.set_size() member function)
//typedef matrix<double, 2, 1 > sample_type;
// This is a typedef for the type of kernel we are going to use in this example.
// In this case I have selected the radial basis kernel that can operate on our
// 2D sample_type objects
//typedef radial_basis_kernel<sample_type> kernel_type;
// Here we create an instance of the pegasos svm trainer object we will be using.
using (var trainer = new SvmPegasos <double, RadialBasisKernel <double, Matrix <double> > >())
using (var kernel = new RadialBasisKernel <double, Matrix <double> >(0.005, 0, 0))
{
// Here we setup the parameters to this object. See the dlib documentation for a
// description of what these parameters are.
trainer.SetLambda(0.00001);
trainer.Kernel = kernel;
// Set the maximum number of support vectors we want the trainer object to use
// in representing the decision function it is going to learn. In general,
// supplying a bigger number here will only ever give you a more accurate
// answer. However, giving a smaller number will make the algorithm run
// faster and decision rules that involve fewer support vectors also take
// less time to evaluate.
trainer.MaxNumSupportVector = 10;
var samples = new List <SampleType>();
var labels = new List <double>();
// make an instance of a sample matrix so we can use it below
var center = new SampleType();
center.SetSize(2, 1);
center.Assign(new[] { 20d, 20d });
// Now let's go into a loop and randomly generate 1000 samples.
Dlib.SRand((uint)(DateTime.UtcNow - new DateTime(1970, 1, 1, 0, 0, 0, 0)).TotalSeconds);
for (var i = 0; i < 10000; ++i)
{
// Make a random sample vector.
using (var r = Dlib.RandM(2, 1))
{
var sample = r * 40 - center;
// Now if that random vector is less than 10 units from the origin then it is in
// the +1 class.
if (Dlib.Length(sample) <= 10)
{
// let the svm_pegasos learn about this sample
trainer.Train(sample, +1);
// save this sample so we can use it with the batch training examples below
samples.Add(sample);
labels.Add(+1);
}
else
{
// let the svm_pegasos learn about this sample
trainer.Train(sample, -1);
// save this sample so we can use it with the batch training examples below
samples.Add(sample);
labels.Add(-1);
}
}
}
// Now we have trained our SVM. Let's see how well it did.
// Each of these statements prints out the output of the SVM given a particular sample.
// The SVM outputs a number > 0 if a sample is predicted to be in the +1 class and < 0
// if a sample is predicted to be in the -1 class.
// Now let's try this decision_function on some samples we haven't seen before.
using (var sample = new SampleType())
{
sample.SetSize(2, 1);
sample[0] = 3.123;
sample[1] = 4;
Console.WriteLine($"This is a +1 example, its SVM output is: {trainer.Operator(sample)}");
sample[0] = 13.123;
sample[1] = 9.3545;
Console.WriteLine($"This is a -1 example, its SVM output is: {trainer.Operator(sample)}");
sample[0] = 13.123;
sample[1] = 0;
Console.WriteLine($"This is a -1 example, its SVM output is: {trainer.Operator(sample)}");
}
// The previous part of this example program showed you how to perform online training
// with the pegasos algorithm. But it is often the case that you have a dataset and you
// just want to perform batch learning on that dataset and get the resulting decision
// function. To support this the dlib library provides functions for converting an online
// training object like svm_pegasos into a batch training object.
// First let's clear out anything in the trainer object.
trainer.Clear();
// Now to begin with, you might want to compute the cross validation score of a trainer object
// on your data. To do this you should use the batch_cached() function to convert the svm_pegasos object
// into a batch training object. Note that the second argument to batch_cached() is the minimum
// learning rate the trainer object must report for the batch_cached() function to consider training
// complete. So smaller values of this parameter cause training to take longer but may result
// in a more accurate solution.
// Here we perform 4-fold cross validation and print the results
using (var batchTrainer = Dlib.BatchCached <double,
RadialBasisKernel <double, Matrix <double> >,
SvmPegasos <double, RadialBasisKernel <double, Matrix <double> > > >(trainer, 0.1))
using (var ret = Dlib.CrossValidateTrainer(batchTrainer, samples, labels, 4))
Console.Write($"cross validation: {ret}");
// Here is an example of creating a decision function. Note that we have used the verbose_batch_cached()
// function instead of batch_cached() as above. They do the same things except verbose_batch_cached() will
// print status messages to standard output while training is under way.
using (var verboseBatchCached = Dlib.VerboseBatchCached <double,
RadialBasisKernel <double, Matrix <double> >,
SvmPegasos <double, RadialBasisKernel <double, Matrix <double> > > >(trainer, 0.1))
using (var df = verboseBatchCached.Train(samples, labels))
using (var sample = new SampleType())
{
sample.SetSize(2, 1);
sample[0] = 3.123;
sample[1] = 4;
Console.WriteLine($"This is a +1 example, its SVM output is: {df.Operator(sample)}");
sample[0] = 13.123;
sample[1] = 9.3545;
Console.WriteLine($"This is a -1 example, its SVM output is: {df.Operator(sample)}");
sample[0] = 13.123;
sample[1] = 0;
Console.WriteLine($"This is a -1 example, its SVM output is: {df.Operator(sample)}");
}
}
return(0);
}
private static void Main()
{
// Here we declare that our samples will be 1 dimensional column vectors. The reason for
// using a matrix here is that in general you can use N dimensional vectors as inputs to the
// krls object. But here we only have 1 dimension to make the example simple.
// Now we are making a typedef for the kind of kernel we want to use. I picked the
// radial basis kernel because it only has one parameter and generally gives good
// results without much fiddling.
// Here we declare an instance of the krls object. The first argument to the constructor
// is the kernel we wish to use. The second is a parameter that determines the numerical
// accuracy with which the object will perform part of the regression algorithm. Generally
// smaller values give better results but cause the algorithm to run slower (because it tries
// to use more "dictionary vectors" to represent the function it is learning.
// You just have to play with it to decide what balance of speed and accuracy is right
// for your problem. Here we have set it to 0.001.
//
// The last argument is the maximum number of dictionary vectors the algorithm is allowed
// to use. The default value for this field is 1,000,000 which is large enough that you
// won't ever hit it in practice. However, here we have set it to the much smaller value
// of 7. This means that once the krls object accumulates 7 dictionary vectors it will
// start discarding old ones in favor of new ones as it goes through the training process.
// In other words, the algorithm "forgets" about old training data and focuses on recent
// training samples. So the bigger the maximum dictionary size the longer its memory will
// be. But in this example program we are doing filtering so we only care about the most
// recent data. So using a small value is appropriate here since it will result in much
// faster filtering and won't introduce much error.
using (var rbk = new RadialBasisKernel <double, Matrix <double> >(0.05, 1, 1))
using (var test = new Krls <double, RadialBasisKernel <double, Matrix <double> > >(rbk, 0.001, 7))
{
using (var rnd = new Rand())
{
// Now let's loop over a big range of values from the sinc() function. Each time
// adding some random noise to the data we send to the krls object for training.
using (var m = Matrix <double> .CreateTemplateParameterizeMatrix(1, 1))
{
double mseNoise = 0;
double mse = 0;
double count = 0;
for (double x = -20; x <= 20; x += 0.01)
{
m[0] = x;
// get a random number between -0.5 and 0.5
double noise = rnd.GetRandomDouble() - 0.5;
// train on this new sample
test.Train(m, Sinc(x) + noise);
// once we have seen a bit of data start measuring the mean squared prediction error.
// Also measure the mean squared error due to the noise.
if (x > -19)
{
++count;
mse += Math.Pow(Sinc(x) - test.Operator(m), 2);
mseNoise += Math.Pow(noise, 2);
}
}
mse /= count;
mseNoise /= count;
// Output the ratio of the error from the noise and the mean squared prediction error.
Console.WriteLine($"prediction error: {mse}");
Console.WriteLine($"noise: {mseNoise}");
Console.WriteLine($"ratio of noise to prediction error: {mseNoise / mse}");
// When the program runs it should print the following:
// prediction error: 0.00735201
// noise: 0.0821628
// ratio of noise to prediction error: 11.1756
// And we see that the noise has been significantly reduced by filtering the points
// through the krls object.
}
}
}
}
private static void Main()
{
// Here we declare that our samples will be 2 dimensional column vectors.
// (Note that if you don't know the dimensionality of your vectors at compile time
// you can change the 2 to a 0 and then set the size at runtime)
// Now we are making a typedef for the kind of kernel we want to use. I picked the
// radial basis kernel because it only has one parameter and generally gives good
// results without much fiddling.
using (var rbk = new RadialBasisKernel <double, Matrix <double> >(0.1d, 2, 1))
{
// Here we declare an instance of the kcentroid object. The kcentroid has 3 parameters
// you need to set. The first argument to the constructor is the kernel we wish to
// use. The second is a parameter that determines the numerical accuracy with which
// the object will perform the centroid estimation. Generally, smaller values
// give better results but cause the algorithm to attempt to use more dictionary vectors
// (and thus run slower and use more memory). The third argument, however, is the
// maximum number of dictionary vectors a kcentroid is allowed to use. So you can use
// it to control the runtime complexity.
using (var test = new KCentroid <double, RadialBasisKernel <double, Matrix <double> > >(rbk, 0.01, 15))
{
// now we train our object on a few samples of the sinc function.
using (var m = Matrix <double> .CreateTemplateParameterizeMatrix(2, 1))
{
for (double x = -15; x <= 8; x += 1)
{
m[0] = x;
m[1] = Sinc(x);
test.Train(m);
}
using (var rs = new RunningStats <double>())
{
// Now let's output the distance from the centroid to some points that are from the sinc function.
// These numbers should all be similar. We will also calculate the statistics of these numbers
// by accumulating them into the running_stats object called rs. This will let us easily
// find the mean and standard deviation of the distances for use below.
Console.WriteLine("Points that are on the sinc function:");
m[0] = -1.5; m[1] = Sinc(m[0]); Console.WriteLine($" {test.Operator(m)}"); rs.Add(test.Operator(m));
m[0] = -1.5; m[1] = Sinc(m[0]); Console.WriteLine($" {test.Operator(m)}"); rs.Add(test.Operator(m));
m[0] = -0; m[1] = Sinc(m[0]); Console.WriteLine($" {test.Operator(m)}"); rs.Add(test.Operator(m));
m[0] = -0.5; m[1] = Sinc(m[0]); Console.WriteLine($" {test.Operator(m)}"); rs.Add(test.Operator(m));
m[0] = -4.1; m[1] = Sinc(m[0]); Console.WriteLine($" {test.Operator(m)}"); rs.Add(test.Operator(m));
m[0] = -1.5; m[1] = Sinc(m[0]); Console.WriteLine($" {test.Operator(m)}"); rs.Add(test.Operator(m));
m[0] = -0.5; m[1] = Sinc(m[0]); Console.WriteLine($" {test.Operator(m)}"); rs.Add(test.Operator(m));
Console.WriteLine();
// Let's output the distance from the centroid to some points that are NOT from the sinc function.
// These numbers should all be significantly bigger than previous set of numbers. We will also
// use the rs.scale() function to find out how many standard deviations they are away from the
// mean of the test points from the sinc function. So in this case our criterion for "significantly bigger"
// is > 3 or 4 standard deviations away from the above points that actually are on the sinc function.
Console.WriteLine("Points that are NOT on the sinc function:");
m[0] = -1.5; m[1] = Sinc(m[0]) + 4; Console.WriteLine($" {test.Operator(m)} is {rs.Scale(test.Operator(m))} standard deviations from sinc.");
m[0] = -1.5; m[1] = Sinc(m[0]) + 3; Console.WriteLine($" {test.Operator(m)} is {rs.Scale(test.Operator(m))} standard deviations from sinc.");
m[0] = -0; m[1] = -Sinc(m[0]); Console.WriteLine($" {test.Operator(m)} is {rs.Scale(test.Operator(m))} standard deviations from sinc.");
m[0] = -0.5; m[1] = -Sinc(m[0]); Console.WriteLine($" {test.Operator(m)} is {rs.Scale(test.Operator(m))} standard deviations from sinc.");
m[0] = -4.1; m[1] = Sinc(m[0]) + 2; Console.WriteLine($" {test.Operator(m)} is {rs.Scale(test.Operator(m))} standard deviations from sinc.");
m[0] = -1.5; m[1] = Sinc(m[0]) + 0.9; Console.WriteLine($" {test.Operator(m)} is {rs.Scale(test.Operator(m))} standard deviations from sinc.");
m[0] = -0.5; m[1] = Sinc(m[0]) + 1; Console.WriteLine($" {test.Operator(m)} is {rs.Scale(test.Operator(m))} standard deviations from sinc.");
// And finally print out the mean and standard deviation of points that are actually from sinc().
Console.WriteLine($"\nmean: {rs.Mean}");
Console.WriteLine($"standard deviation: {rs.StdDev}");
// The output is as follows:
/*
* Points that are on the sinc function:
* 0.869913
* 0.869913
* 0.873408
* 0.872807
* 0.870432
* 0.869913
* 0.872807
*
* Points that are NOT on the sinc function:
* 1.06366 is 119.65 standard deviations from sinc.
* 1.02212 is 93.8106 standard deviations from sinc.
* 0.921382 is 31.1458 standard deviations from sinc.
* 0.918439 is 29.3147 standard deviations from sinc.
* 0.931428 is 37.3949 standard deviations from sinc.
* 0.898018 is 16.6121 standard deviations from sinc.
* 0.914425 is 26.8183 standard deviations from sinc.
*
* mean: 0.871313
* standard deviation: 0.00160756
*/
// So we can see that in this example the kcentroid object correctly indicates that
// the non-sinc points are definitely not points from the sinc function.
}
}
}
}
}
private static void Main()
{
// Here we declare that our samples will be 2 dimensional column vectors.
// (Note that if you don't know the dimensionality of your vectors at compile time
// you can change the 2 to a 0 and then set the size at runtime)
// Now we are making a typedef for the kind of kernel we want to use. I picked the
// radial basis kernel because it only has one parameter and generally gives good
// results without much fiddling.
using (var rbk = new RadialBasisKernel <double, Matrix <double> >(0.1d, 2, 1))
{
// Here we declare an instance of the kcentroid object. It is the object used to
// represent each of the centers used for clustering. The kcentroid has 3 parameters
// you need to set. The first argument to the constructor is the kernel we wish to
// use. The second is a parameter that determines the numerical accuracy with which
// the object will perform part of the learning algorithm. Generally, smaller values
// give better results but cause the algorithm to attempt to use more dictionary vectors
// (and thus run slower and use more memory). The third argument, however, is the
// maximum number of dictionary vectors a kcentroid is allowed to use. So you can use
// it to control the runtime complexity.
using (var kc = new KCentroid <double, RadialBasisKernel <double, Matrix <double> > >(rbk, 0.01, 8))
{
// Now we make an instance of the kkmeans object and tell it to use kcentroid objects
// that are configured with the parameters from the kc object we defined above.
using (var test = new KKMeans <double, RadialBasisKernel <double, Matrix <double> > >(kc))
{
var samples = new List <Matrix <double> >();
using (var m = Matrix <double> .CreateTemplateParameterizeMatrix(2, 1))
using (var rnd = new Rand())
{
// we will make 50 points from each class
const int num = 50;
// make some samples near the origin
var radius = 0.5d;
for (var i = 0; i < num; ++i)
{
double sign = 1;
if (rnd.GetRandomDouble() < 0.5)
{
sign = -1;
}
m[0] = 2 * radius * rnd.GetRandomDouble() - radius;
m[1] = sign * Math.Sqrt(radius * radius - m[0] * m[0]);
// add this sample to our set of samples we will run k-means
samples.Add(m.Clone());
}
// make some samples in a circle around the origin but far away
radius = 10.0;
for (var i = 0; i < num; ++i)
{
double sign = 1;
if (rnd.GetRandomDouble() < 0.5)
{
sign = -1;
}
m[0] = 2 * radius * rnd.GetRandomDouble() - radius;
m[1] = sign * Math.Sqrt(radius * radius - m[0] * m[0]);
// add this sample to our set of samples we will run k-means
samples.Add(m.Clone());
}
// make some samples in a circle around the point (25,25)
radius = 4.0;
for (var i = 0; i < num; ++i)
{
double sign = 1;
if (rnd.GetRandomDouble() < 0.5)
{
sign = -1;
}
m[0] = 2 * radius * rnd.GetRandomDouble() - radius;
m[1] = sign * Math.Sqrt(radius * radius - m[0] * m[0]);
// translate this point away from the origin
m[0] += 25;
m[1] += 25;
// add this sample to our set of samples we will run k-means
samples.Add(m.Clone());
}
// tell the kkmeans object we made that we want to run k-means with k set to 3.
// (i.e. we want 3 clusters)
test.NumberOfCenters = 3;
// You need to pick some initial centers for the k-means algorithm. So here
// we will use the dlib::pick_initial_centers() function which tries to find
// n points that are far apart (basically).
var initialCenters = Dlib.PickInitialCenters(3, samples, test.Kernel);
// now run the k-means algorithm on our set of samples.
test.Train(samples, initialCenters);
// now loop over all our samples and print out their predicted class. In this example
// all points are correctly identified.
for (var i = 0; i < samples.Count / 3; ++i)
{
Console.Write($"{test.Operator(samples[i])} ");
Console.Write($"{test.Operator(samples[i + num])} ");
Console.WriteLine($"{test.Operator(samples[i + 2 * num])}");
}
// Now print out how many dictionary vectors each center used. Note that
// the maximum number of 8 was reached. If you went back to the kcentroid
// constructor and changed the 8 to some bigger number you would see that these
// numbers would go up. However, 8 is all we need to correctly cluster this dataset.
Console.WriteLine($"num dictionary vectors for center 0: {test.GetKCentroid(0).DictionarySize}");
Console.WriteLine($"num dictionary vectors for center 1: {test.GetKCentroid(1).DictionarySize}");
Console.WriteLine($"num dictionary vectors for center 2: {test.GetKCentroid(2).DictionarySize}");
// Finally, we can also solve the same kind of non-linear clustering problem with
// spectral_cluster(). The output is a vector that indicates which cluster each sample
// belongs to. Just like with kkmeans, it assigns each point to the correct cluster.
using (var tmp = new RadialBasisKernel <double, Matrix <double> >(0.1, 2, 1))
{
var assignments = Dlib.SpectralCluster(tmp, samples, 3);
using (var mat = Dlib.Mat(assignments))
Console.WriteLine($"{mat}");
}
}
samples.DisposeElement();
}
}
}
}
