HiddenGradientDescentLearningT Class

public class HiddenGradientDescentLearning<T> : BaseHiddenConditionalRandomFieldLearning<T>, 
	ISupervisedLearning<HiddenConditionalRandomField<T>, T[], int>, IParallel, ISupportsCancellation, 
	IHiddenConditionalRandomFieldLearning<T>, IConvergenceLearning, IDisposable

Public Class HiddenGradientDescentLearning(Of T)
	Inherits BaseHiddenConditionalRandomFieldLearning(Of T)
	Implements ISupervisedLearning(Of HiddenConditionalRandomField(Of T), T(), Integer), 
	IParallel, ISupportsCancellation, IHiddenConditionalRandomFieldLearning(Of T), IConvergenceLearning, IDisposable

// Let's say we would like to do a very simple mechanism for gesture recognition. 
// In this example, we will be trying to create a classifier that can distinguish 
// between the words "hello", "car", and "wardrobe". 

// Let's say we decided to acquire some data, and we asked some people to perform 
// those words in front of a Kinect camera, and, using Microsoft's SDK, we were able 
// to captured the x and y coordinates of each hand while the word was being performed.

// Let's say we decided to represent our frames as:
// 
//    double[] frame = { leftHandX, leftHandY, rightHandX, rightHandY }; // 4 dimensions
// 
// Since we captured words, this means we captured sequences of frames as we described 
// above. Let's write some of those as rough examples to explain how gesture recognition 
// can be done:

double[][] hello =
{
    new double[] { 1.0, 0.1, 0.0, 0.0 }, // let's say the word
    new double[] { 0.0, 1.0, 0.1, 0.1 }, // hello took 6 frames
    new double[] { 0.0, 1.0, 0.1, 0.1 }, // to be recorded.
    new double[] { 0.0, 0.0, 1.0, 0.0 },
    new double[] { 0.0, 0.0, 1.0, 0.0 },
    new double[] { 0.0, 0.0, 0.1, 1.1 },
};

double[][] car =
{
    new double[] { 0.0, 0.0, 0.0, 1.0 }, // the car word
    new double[] { 0.1, 0.0, 1.0, 0.1 }, // took only 4.
    new double[] { 0.0, 0.0, 0.1, 0.0 },
    new double[] { 1.0, 0.0, 0.0, 0.0 },
};

double[][] wardrobe =
{
    new double[] { 0.0, 0.0, 1.0, 0.0 }, // same for the
    new double[] { 0.1, 0.0, 1.0, 0.1 }, // wardrobe word.
    new double[] { 0.0, 0.1, 1.0, 0.0 },
    new double[] { 0.1, 0.0, 1.0, 0.1 },
};

// Please note that a real-world example would involve *lots* of samples for each word. 
// Here, we are considering just one from each class which is clearly sub-optimal and 
// should _never_ be done on practice. Please keep in mind that we are doing like this
// only to simplify this example on how to create and use HCRFs.

// These are the words we have in our vocabulary:
double[][][] words = { hello, car, wardrobe };

// Now, let's associate integer labels with them. This is needed
// for the case where there are multiple samples for each word.
int[] labels = { 0, 1, 2 };

// Create a new learning algorithm to train the hidden Markov model sequence classifier
var teacher = new HiddenMarkovClassifierLearning<Independent<NormalDistribution>, double[]>()
{
    // Train each model until the log-likelihood changes less than 0.001
    Learner = (i) => new BaumWelchLearning<Independent<NormalDistribution>, double[]>()
    {
        Topology = new Forward(5), // this value can be found by trial-and-error

        // We will create our classifiers assuming an independent Gaussian distribution 
        // for each component in our feature vectors (assuming a Naive Bayes assumption).
        Emissions = (s) => new Independent<NormalDistribution>(dimensions: 4), // 4 dimensions

        Tolerance = 0.001,
        Iterations = 100,

        // This is necessary so the code doesn't blow up when it realizes there is only one 
        // sample per word class. But this could also be needed in normal situations as well:
        FittingOptions = new IndependentOptions()
        {
            InnerOption = new NormalOptions() { Regularization = 1e-5 }
        }
    }
};

// PS: In case you find exceptions trying to configure your model, you might want 
//     to try disabling parallel processing to get more descriptive error messages:
// teacher.ParallelOptions.MaxDegreeOfParallelism = 1;

// Finally, we can run the learning algorithm!
var hmm = teacher.Learn(words, labels);
double logLikelihood = teacher.LogLikelihood;

// At this point, the classifier should be successfully 
// able to distinguish between our three word classes:
// 
int tc1 = hmm.Decide(hello);    // should be 0
int tc2 = hmm.Decide(car);      // should be 1
int tc3 = hmm.Decide(wardrobe); // should be 2

// Now, we can use the Markov classifier to initialize a HCRF
var baseline = HiddenConditionalRandomField.FromHiddenMarkov(hmm);

// We can check that both are equivalent, although they have
// formulations that can be learned with different methods:
int[] predictedLabels = baseline.Decide(words);

// Now we can learn the HCRF using one of the best learning
// algorithms available, Resilient Backpropagation learning:

// Create the Resilient Backpropagation learning algorithm
var rprop = new HiddenResilientGradientLearning<double[]>()
{
    Function = baseline.Function, // use the same HMM function

    Iterations = 50,
    Tolerance = 1e-5
};

// Run the algorithm and learn the models
var hcrf = rprop.Learn(words, labels);

// At this point, the HCRF should be successfully 
// able to distinguish between our three word classes:
// 
int hc1 = hcrf.Decide(hello);    // should be 0
int hc2 = hcrf.Decide(car);      // should be 1
int hc3 = hcrf.Decide(wardrobe); // should be 2