예제 #1
0
        /// <summary>
        ///   Creates the initial scatter plot graphs containing some random
        ///   data. This data is generated by sampling Gaussian distributions.
        /// </summary>
        /// 
        private void btnGenerateRandom_Click(object sender, EventArgs e)
        {
            k = (int)numClusters.Value;

            // Generate data with n Gaussian distributions
            double[][][] data = new double[k][][];

            for (int i = 0; i < k; i++)
            {
                // Create random centroid to place the Gaussian distribution
                double[] mean = Matrix.Random(2, -6.0, +6.0);

                // Create random covariance matrix for the distribution
                double[,] covariance = Accord.Statistics.Tools.RandomCovariance(2, -5, 5);

                // Create the Gaussian distribution
                var gaussian = new MultivariateNormalDistribution(mean, covariance);

                int samples = Accord.Math.Tools.Random.Next(150, 250);
                data[i] = gaussian.Generate(samples);
            }

            // Join the generated data
            mixture = Matrix.Stack(data);

            // Update the scatter plot
            CreateScatterplot(graph, mixture, k);

            // Forget previous initialization
            kmeans = null;
        }
예제 #2
0
        public static HiddenMarkovModel<MultivariateNormalDistribution> deserialize(string filename)
        {
            using (StreamReader r = new StreamReader(filename))
            {
                String data = r.ReadToEnd();
                String[] dataArr = data.Split('#');

                // probDelimitedStr dataArr[0]
                double[] prob = createSingleDimDoubleArray(dataArr[0], '|');

                // transDelimitedStr dataArr[1]
                double[,] trans = createDoubleDimDoubleArray(dataArr[1], '|', '*');

                // emissionsDelimitedStr dataArr[2]
                String[] emissions = dataArr[2].Split('$');

                MultivariateNormalDistribution[] e2 = new MultivariateNormalDistribution[emissions.Length];
                for (int i = 0; i < emissions.Length; i++)
                {
                    String[] meansNCovariance = emissions[i].Split('&');
                    String meansStr = meansNCovariance[0];
                    String covarianceStr = meansNCovariance[1];

                    double[] means = createSingleDimDoubleArray(meansStr, '|');
                    double[,] covariance = createDoubleDimDoubleArray(covarianceStr, '|', '*');
                    MultivariateNormalDistribution dist = new MultivariateNormalDistribution(means, covariance);
                    e2[i] = dist;
                }
                HiddenMarkovModel<MultivariateNormalDistribution> hmm = new HiddenMarkovModel<MultivariateNormalDistribution>(trans, e2, prob);
                return hmm;
            }
        }
        public void MultivariateNormalGenerateTest()
        {
            // mean vector
            double[] mu = { 2.0, 6.0 };

            // covariance
            double[,] cov = 
            {
                { 2, 1 },
                { 1, 5 } 
            };

            // Create a multivariate Normal distribution
            var normal = new MultivariateNormalDistribution(mu, cov);

            // Generate 1000000 samples from it
            double[][] samples = normal.Generate(1000000);

            // Try to estimate a new Normal distribution from
            // generated samples to check if they indeed match
            var actual = MultivariateNormalDistribution.Estimate(samples);

            Assert.IsTrue(mu.IsEqual(actual.Mean, 0.1));
            Assert.IsTrue(cov.IsEqual(actual.Covariance, 0.1));
        }
        public static HiddenMarkovClassifier<MultivariateNormalDistribution> CreateModel1()
        {
            // Create a Continuous density Hidden Markov Model Sequence Classifier
            // to detect a multivariate sequence and the same sequence backwards.
            double[][][] sequences = new double[][][]
            {
                new double[][] 
                { 
                    // This is the first  sequence with label = 0
                    new double[] { 0 },
                    new double[] { 1 },
                    new double[] { 2 },
                    new double[] { 3 },
                    new double[] { 4 },
                }, 

                new double[][]
                {
                     // This is the second sequence with label = 1
                    new double[] { 4 },
                    new double[] { 3 },
                    new double[] { 2 },
                    new double[] { 1 },
                    new double[] { 0 },
                }
            };

            // Labels for the sequences
            int[] labels = { 0, 1 };

            // Creates a sequence classifier containing 2 hidden Markov Models
            //  with 2 states and an underlying Normal distribution as density.
            MultivariateNormalDistribution density = new MultivariateNormalDistribution(1);
            var classifier = new HiddenMarkovClassifier<MultivariateNormalDistribution>(2, new Ergodic(2), density);

            // Configure the learning algorithms to train the sequence classifier
            var teacher = new HiddenMarkovClassifierLearning<MultivariateNormalDistribution>(classifier,

                // Train each model until the log-likelihood changes less than 0.001
                modelIndex => new BaumWelchLearning<MultivariateNormalDistribution>(classifier.Models[modelIndex])
                {
                    Tolerance = 0.0001,
                    Iterations = 0
                }
            );

            // Train the sequence classifier using the algorithm
            double logLikelihood = teacher.Run(sequences, labels);


            return classifier;
        }
        public void ConstructorTest1()
        {
            MultivariateNormalDistribution[] components = new MultivariateNormalDistribution[2];
            components[0] = new MultivariateNormalDistribution(new double[] { 2 }, new double[,] { { 1 } });
            components[1] = new MultivariateNormalDistribution(new double[] { 5 }, new double[,] { { 1 } });

            var mixture = new MultivariateMixture<MultivariateNormalDistribution>(components);

            double[] expected = { 0.5, 0.5 };

            Assert.IsTrue(expected.IsEqual(mixture.Coefficients));
            Assert.AreEqual(components, mixture.Components);
        }
        public void ConstructorTest4()
        {
            // Create a multivariate Gaussian distribution 
            var dist = new MultivariateNormalDistribution(

                // mean vector mu
                mean: new double[] 
                {
                    4, 2 
                },

                // covariance matrix sigma
                covariance: new double[,] 
                {
                    { 0.3, 0.1 },
                    { 0.1, 0.7 }
                }
            );

            // Common measures
            double[] mean = dist.Mean;     // { 4, 2 }
            double[] median = dist.Median; // { 4, 2 }
            double[] var = dist.Variance;  // { 0.3, 0.7 } (diagonal from cov)
            double[,] cov = dist.Covariance; // { { 0.3, 0.1 }, { 0.1, 0.7 } }

            // Probability mass functions
            double pdf1 = dist.ProbabilityDensityFunction(new double[] { 2, 5 }); // 0.000000018917884164743237
            double pdf2 = dist.ProbabilityDensityFunction(new double[] { 4, 2 }); // 0.35588127170858852
            double pdf3 = dist.ProbabilityDensityFunction(new double[] { 3, 7 }); // 0.000000000036520107734505265
            double lpdf = dist.LogProbabilityDensityFunction(new double[] { 3, 7 }); // -24.033158110192296

            // Cumulative distribution function (for up to two dimensions)
            double cdf = dist.DistributionFunction(new double[] { 3, 5 }); // 0.033944035782101548


            Assert.AreEqual(4, mean[0]);
            Assert.AreEqual(2, mean[1]);
            Assert.AreEqual(4, median[0]);
            Assert.AreEqual(2, median[1]);
            Assert.AreEqual(0.3, var[0]);
            Assert.AreEqual(0.7, var[1]);
            Assert.AreEqual(0.3, cov[0, 0]);
            Assert.AreEqual(0.1, cov[0, 1]);
            Assert.AreEqual(0.1, cov[1, 0]);
            Assert.AreEqual(0.7, cov[1, 1]);
            Assert.AreEqual(0.000000018917884164743237, pdf1);
            Assert.AreEqual(0.35588127170858852, pdf2);
            Assert.AreEqual(0.000000000036520107734505265, pdf3);
            Assert.AreEqual(-24.033158110192296, lpdf);
            Assert.AreEqual(0.033944035782101548, cdf);
        }
        public void ProbabilityDensityFunctionTest()
        {
            MultivariateNormalDistribution[] components = new MultivariateNormalDistribution[2];
            components[0] = new MultivariateNormalDistribution(new double[] { 2 }, new double[,] { { 1 } });
            components[1] = new MultivariateNormalDistribution(new double[] { 5 }, new double[,] { { 1 } });

            double[] coefficients = { 0.3, 0.7 };
            var mixture = new MultivariateMixture<MultivariateNormalDistribution>(coefficients, components);

            double[] x = { 1.2 };

            double expected =
                0.3 * components[0].ProbabilityDensityFunction(x) +
                0.7 * components[1].ProbabilityDensityFunction(x);

            double actual = mixture.ProbabilityDensityFunction(x);

            Assert.AreEqual(expected, actual);
        }
예제 #8
0
파일: Utils.cs 프로젝트: Wolfox/SIGame
        /*public static void SaveSequenceList(SequenceList seqList, string path)
        {
            Stream writeStream = new FileStream(path, FileMode.Create, FileAccess.Write, FileShare.None);
            seqList.Save(writeStream);
            writeStream.Close();
        }

        public static SequenceList LoadSequenceList(string path)
        {
            Stream readStream = new FileStream(path, FileMode.Open, FileAccess.Read, FileShare.Read);
            SequenceList seqList = SequenceList.Load(readStream);
            readStream.Close();
            return seqList;
        }*/
        public static HiddenMarkovModel<MultivariateNormalDistribution> CreateModelFromFrames(List<List<Frame>> frames)
        {
            SequenceList sequences = Utils.FramesToSequenceList(frames);

            HiddenMarkovModel<MultivariateNormalDistribution> hmm;
            MultivariateNormalDistribution mnd = new MultivariateNormalDistribution(sequences.GetDimensions());
            hmm = new HiddenMarkovModel<MultivariateNormalDistribution>(new Forward(5), mnd);

            var teacher = new BaumWelchLearning<MultivariateNormalDistribution>(hmm);
            teacher.Tolerance = 0.0001;
            teacher.Iterations = 0;
            teacher.FittingOptions = new NormalOptions()
            {
                Diagonal = true,      // only diagonal covariance matrices
                Regularization = 1e-5 // avoid non-positive definite errors
            };

            teacher.Run(sequences.GetArray());

            return hmm;
        }
        public void ConstructorTest1()
        {

            NormalDistribution normal = new NormalDistribution(4.2, 1.2);
            MultivariateNormalDistribution target = new MultivariateNormalDistribution(new[] { 4.2 }, new[,] { { 1.2 * 1.2 } });

            double[] mean = target.Mean;
            double[] median = target.Median;
            double[] var = target.Variance;
            double[,] cov = target.Covariance;

            double apdf1 = target.ProbabilityDensityFunction(new double[] { 2 });
            double apdf2 = target.ProbabilityDensityFunction(new double[] { 4 });
            double apdf3 = target.ProbabilityDensityFunction(new double[] { 3 });
            double alpdf = target.LogProbabilityDensityFunction(new double[] { 3 });
            double acdf = target.DistributionFunction(new double[] { 3 });
            double accdf = target.ComplementaryDistributionFunction(new double[] { 3 });

            double epdf1 = target.ProbabilityDensityFunction(new double[] { 2 });
            double epdf2 = target.ProbabilityDensityFunction(new double[] { 4 });
            double epdf3 = target.ProbabilityDensityFunction(new double[] { 3 });
            double elpdf = target.LogProbabilityDensityFunction(new double[] { 3 });
            double ecdf = target.DistributionFunction(new double[] { 3 });
            double eccdf = target.ComplementaryDistributionFunction(new double[] { 3 });


            Assert.AreEqual(normal.Mean, target.Mean[0]);
            Assert.AreEqual(normal.Median, target.Median[0]);
            Assert.AreEqual(normal.Variance, target.Variance[0]);
            Assert.AreEqual(normal.Variance, target.Covariance[0, 0]);

            Assert.AreEqual(epdf1, apdf1);
            Assert.AreEqual(epdf2, apdf2);
            Assert.AreEqual(epdf3, apdf3);
            Assert.AreEqual(elpdf, alpdf);
            Assert.AreEqual(ecdf, acdf);
            Assert.AreEqual(eccdf, accdf);
            Assert.AreEqual(1.0 - ecdf, eccdf);
        }
        public void MixtureWeightsFitTest()
        {
            // Randomly initialize some mixture components
            MultivariateNormalDistribution[] components = new MultivariateNormalDistribution[2];
            components[0] = new MultivariateNormalDistribution(new double[] { 2 }, new double[,] { { 1 } });
            components[1] = new MultivariateNormalDistribution(new double[] { 5 }, new double[,] { { 1 } });

            // Create an initial mixture
            var mixture = new MultivariateMixture<MultivariateNormalDistribution>(components);

            // Now, suppose we have a weighted data
            // set. Those will be the input points:

            double[][] points = new double[] { 0, 3, 1, 7, 3, 5, 1, 2, -1, 2, 7, 6, 8, 6 } // (14 points)
                .ToArray();

            // And those are their respective unormalized weights:
            double[] weights = { 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 3, 1, 1 }; // (14 weights)

            // Let's normalize the weights so they sum up to one:
            weights = weights.Divide(weights.Sum());

            // Now we can fit our model to the data:
            mixture.Fit(points, weights);   // done!

            // Our model will be:
            double mean1 = mixture.Components[0].Mean[0]; // 1.41126
            double mean2 = mixture.Components[1].Mean[0]; // 6.53301

            // If we need the GaussianMixtureModel functionality, we can
            // use the estimated mixture to initialize a new model:
            GaussianMixtureModel gmm = new GaussianMixtureModel(mixture);

            Assert.AreEqual(mean1, gmm.Gaussians[0].Mean[0]);
            Assert.AreEqual(mean2, gmm.Gaussians[1].Mean[0]);

            Assert.AreEqual(1.4112610766836404, mean1, 1e-10);
            Assert.AreEqual(6.5330177004151082, mean2, 1e-10);

            Assert.AreEqual(mixture.Coefficients[0], gmm.Gaussians[0].Proportion);
            Assert.AreEqual(mixture.Coefficients[1], gmm.Gaussians[1].Proportion);
        }
        public void FitTest2()
        {
            double[] coefficients = { 0.50, 0.50 };

            MultivariateNormalDistribution[] components = new MultivariateNormalDistribution[2];
            components[0] = new MultivariateNormalDistribution(new double[] { 2 }, new double[,] { { 1 } });
            components[1] = new MultivariateNormalDistribution(new double[] { 5 }, new double[,] { { 1 } });

            var target = new MultivariateMixture<MultivariateNormalDistribution>(coefficients, components);

            double[][] values = { new double[] { 2512512312 },
                                  new double[] { 1 }, 
                                  new double[] { 1 },
                                  new double[] { 0 },
                                  new double[] { 1 },
                                  new double[] { 6 },
                                  new double[] { 6 },
                                  new double[] { 5 },
                                  new double[] { 7 },
                                  new double[] { 5 } };

            double[] weights = { 0, 1, 1, 1, 1, 1, 1, 1, 1, 1 };
            weights = weights.Divide(weights.Sum());

            double[][] part1 = values.Submatrix(1, 4);
            double[][] part2 = values.Submatrix(5, 9);


            target.Fit(values, weights);

            var mean1 = Accord.Statistics.Tools.Mean(part1);
            var var1 = Accord.Statistics.Tools.Variance(part1);
            Assert.AreEqual(mean1[0], target.Components[0].Mean[0], 1e-5);
            Assert.AreEqual(var1[0], target.Components[0].Variance[0], 1e-5);

            var mean2 = Accord.Statistics.Tools.Mean(part2);
            var var2 = Accord.Statistics.Tools.Variance(part2);
            Assert.AreEqual(mean2[0], target.Components[1].Mean[0], 1e-5);
            Assert.AreEqual(var2[0], target.Components[1].Variance[0], 1e-5);


            var expectedMean = Accord.Statistics.Tools.WeightedMean(values, weights);
            var expectedVar = Accord.Statistics.Tools.WeightedCovariance(values, weights);

            var actualMean = target.Mean;
            var actualVar = target.Covariance;

            Assert.AreEqual(expectedMean[0], actualMean[0], 0.0000001);
            Assert.AreEqual(expectedVar[0, 0], actualVar[0, 0], 0.68);
        }
        public void ProbabilityDensityFunctionTest()
        {
            double[] mean = { 1, -1 };
            double[,] covariance = 
            {
                { 0.9, 0.4 },
                { 0.4, 0.3 },
            };

            var target = new MultivariateNormalDistribution(mean, covariance);

            double[] x = { 1.2, -0.8 };
            double expected = 0.446209421363460;
            double actual = target.ProbabilityDensityFunction(x);

            Assert.AreEqual(expected, actual, 0.00000001);
        }
        public void FitTest2()
        {
            double[][] observations = 
            {
                new double[] { 1, 2 },
                new double[] { 1, 2 },
                new double[] { 1, 2 },
                new double[] { 1, 2 }
            };


            var target = new MultivariateNormalDistribution(2);

            bool thrown = false;
            try { target.Fit(observations); }
            catch (NonPositiveDefiniteMatrixException) { thrown = true; }

            Assert.IsTrue(thrown);

            NormalOptions options = new NormalOptions() { Regularization = double.Epsilon };

            // No exception thrown
            target.Fit(observations, options);
        }
        public void FitTest()
        {
            double[][] observations = 
            {
                new double[] { 0.1000, -0.2000 },
                new double[] { 0.4000,  0.6000 },
                new double[] { 2.0000,  0.2000 },
                new double[] { 2.0000,  0.3000 }
            };

            double[] mean = Accord.Statistics.Tools.Mean(observations);
            double[,] cov = Accord.Statistics.Tools.Covariance(observations);

            var target = new MultivariateNormalDistribution(2);

            double[] weigths = { 0.25, 0.25, 0.25, 0.25 };

            target.Fit(observations, weigths);

            Assert.IsTrue(Matrix.IsEqual(mean, target.Mean));
            Assert.IsTrue(Matrix.IsEqual(cov, target.Covariance));
        }
        public void ConstructorTest()
        {
            double[] mean = { 1, -1 };
            double[,] covariance = 
            {
                { 2, 1 },
                { 1, 3 }
            };

            MultivariateNormalDistribution target = new MultivariateNormalDistribution(mean, covariance);

            Assert.AreEqual(covariance, target.Covariance);
            Assert.AreEqual(mean, target.Mean);
            Assert.AreEqual(2, target.Variance.Length);
            Assert.AreEqual(2, target.Variance[0]);
            Assert.AreEqual(3, target.Variance[1]);
            Assert.AreEqual(2, target.Dimension);
        }
예제 #16
0
        private static HiddenMarkovModel<MultivariateNormalDistribution> createModel()
        {
            double[][][] sequences =
            {
                new double[][] 
                {
                    new double[] { 1, 2 }, 
                    new double[] { 6, 7 }, 
                    new double[] { 2, 3 }, 
                },
                new double[][] 
                {
                    new double[] { 2, 2 }, 
                    new double[] { 9, 8 }, 
                    new double[] { 1, 0 }, 
                },
                new double[][] 
                {
                    new double[] { 1, 3 }, 
                    new double[] { 8, 9 }, 
                    new double[] { 3, 3 }, 
                },
            };

            var density = new MultivariateNormalDistribution(dimension: 2);

            var model = new HiddenMarkovModel<MultivariateNormalDistribution>(new Forward(2), density);

            var teacher = new BaumWelchLearning<MultivariateNormalDistribution>(model)
            {
                Tolerance = 0.0001,
                Iterations = 0,
            };

            double logLikelihood = teacher.Run(sequences);
            return model;
        }
        public void GenerateTest2()
        {
            Accord.Math.Tools.SetupGenerator(0);

            var normal = new MultivariateNormalDistribution(
                new double[] { 2, 6 },
                new double[,] { { 2, 1 }, { 1, 5 } });

            double[][] sample = new double[1000000][];
            for (int i = 0; i < sample.Length; i++)
                sample[i] = normal.Generate();

            double[] mean = sample.Mean();
            double[,] cov = sample.Covariance();

            Assert.AreEqual(2, mean[0], 1e-2);
            Assert.AreEqual(6, mean[1], 1e-2);

            Assert.AreEqual(2, cov[0, 0], 1e-2);
            Assert.AreEqual(1, cov[0, 1], 1e-2);
            Assert.AreEqual(1, cov[1, 0], 1e-2);
            Assert.AreEqual(5, cov[1, 1], 2e-2);
        }
예제 #18
0
        public void DecodeTest4()
        {
            var density = new MultivariateNormalDistribution(3);

            var hmm = new HiddenMarkovModel<MultivariateNormalDistribution>(2, density);

            bool thrown = false;
            try
            {
                double logLikelihood;
                int[] path = hmm.Decode(new double[] { 0, 1, 2 }, out logLikelihood);
            }
            catch
            {
                thrown = true;
            }

            Assert.IsTrue(thrown);
        }
        public void LogForwardTest3()
        {
            MultivariateNormalDistribution density = new MultivariateNormalDistribution(3);
            var hmm = new HiddenMarkovClassifier<MultivariateNormalDistribution>(2, new Ergodic(2), density);

            double[][][] inputs =
            {
                new [] { new double[] { 0, 1, 0 }, new double[] { 0, 1, 0 }, new double[] { 0, 1, 0 } },
                new [] { new double[] { 1, 6, 2 }, new double[] { 2, 1, 6 }, new double[] { 1, 1, 0 } },
                new [] { new double[] { 9, 1, 0 }, new double[] { 0, 1, 5 }, new double[] { 0, 0, 0 } },
            };

            int[] outputs = 
            {
                0, 0, 1
            };

            var function = new MarkovMultivariateFunction(hmm);

            var observations = inputs[0];

            double[,] expected = Matrix.Log(Accord.Statistics.Models.Fields.
                ForwardBackwardAlgorithm.Forward(function.Factors[0], observations, 0));

            double logLikelihood;
            double[,] actual = Accord.Statistics.Models.Fields.
                ForwardBackwardAlgorithm.LogForward(function.Factors[0], observations, 0, out logLikelihood);

            Assert.IsTrue(expected.IsEqual(actual, 1e-10));

            double p = 0;
            for (int i = 0; i < hmm[0].States; i++)
                p += Math.Exp(actual[observations.Length - 1, i]);

            Assert.AreEqual(Math.Exp(logLikelihood), p, 1e-8);
            Assert.IsFalse(double.IsNaN(p));
        }
예제 #20
0
        public void ConstructorTest2()
        {

            double[,] A = new double[,]
            {
                { 0.5, 0.5 },
                { 0.5, 0.5 }
            };

            double[] pi = new double[] { 1, 0 };

            var distribution = new MultivariateNormalDistribution(3);
            var hmm = new HiddenMarkovModel<MultivariateNormalDistribution>(2, distribution);

            for (int i = 0; i < hmm.Emissions.Length; i++)
            {
                IDistribution b = hmm.Emissions[i];

                Assert.AreNotSame(distribution, b);
                Assert.IsTrue(b is MultivariateNormalDistribution);

                MultivariateNormalDistribution n = b as MultivariateNormalDistribution;

                Assert.AreEqual(n.Dimension, hmm.Dimension);

                Assert.AreNotEqual(n.Covariance, distribution.Covariance);
                Assert.IsTrue(n.Covariance.IsEqual(distribution.Covariance));

                Assert.AreNotEqual(n.Mean, distribution.Mean);
                Assert.IsTrue(n.Mean.IsEqual(distribution.Mean));
            }

            Assert.AreEqual(2, hmm.States);
            Assert.AreEqual(3, hmm.Dimension);
            Assert.AreEqual(2, hmm.Emissions.Length);

            var logA = Matrix.Log(A);
            var logPi = Matrix.Log(pi);

            Assert.IsTrue(logA.IsEqual(hmm.Transitions));
            Assert.IsTrue(logPi.IsEqual(hmm.Probabilities));
        }
예제 #21
0
        public void FittingOptionsTest()
        {
            // Create a degenerate problem
            double[][] sequences = new double[][] 
            {
                new double[] { 1,1,1,1,1,0,1,1,1,1 },
                new double[] { 1,1,1,1,0,1,1,1,1,1 },
                new double[] { 1,1,1,1,1,1,1,1,1,1 },
                new double[] { 1,1,1,1,1,1         },
                new double[] { 1,1,1,1,1,1,1       },
                new double[] { 1,1,1,1,1,1,1,1,1,1 },
                new double[] { 1,1,1,1,1,1,1,1,1,1 },
            };

            // Creates a continuous hidden Markov Model with two states organized in a ergodic
            //  topology and an underlying multivariate Normal distribution as density.
            var density = new MultivariateNormalDistribution(1);

            var model = new HiddenMarkovModel<MultivariateNormalDistribution>(new Ergodic(2), density);

            // Configure the learning algorithms to train the sequence classifier
            var teacher = new BaumWelchLearning<MultivariateNormalDistribution>(model)
            {
                Tolerance = 0.0001,
                Iterations = 0,

                // Configure options for fitting the normal distribution
                FittingOptions = new NormalOptions() { Regularization = 0.0001, }
            };

            // Fit the model. No exceptions will be thrown
            double logLikelihood = teacher.Run(sequences);
            double likelihood = Math.Exp(logLikelihood);

            Assert.AreEqual(47.434837528491286, logLikelihood, 1e-15);
            Assert.IsFalse(double.IsNaN(logLikelihood));

            Assert.AreEqual(0.0001, (teacher.FittingOptions as NormalOptions).Regularization);



            // Try without a regularization constant to get an exception
            bool thrown;

            thrown = false;
            density = new MultivariateNormalDistribution(1);
            model = new HiddenMarkovModel<MultivariateNormalDistribution>(new Ergodic(2), density);
            teacher = new BaumWelchLearning<MultivariateNormalDistribution>(model) { Tolerance = 0.0001, Iterations = 0, };
            Assert.IsNull(teacher.FittingOptions);
            try { teacher.Run(sequences); }
            catch { thrown = true; }
            Assert.IsTrue(thrown);

            thrown = false;
            density = new Accord.Statistics.Distributions.Multivariate.MultivariateNormalDistribution(1);
            model = new HiddenMarkovModel<MultivariateNormalDistribution>(new Ergodic(2), density);
            teacher = new BaumWelchLearning<MultivariateNormalDistribution>(model)
            {
                Tolerance = 0.0001,
                Iterations = 0,
                FittingOptions = new NormalOptions() { Regularization = 0 }
            };
            Assert.IsNotNull(teacher.FittingOptions);
            try { teacher.Run(sequences); }
            catch { thrown = true; }
            Assert.IsTrue(thrown);
        }
예제 #22
0
        public void LearnTest10()
        {
            // Create sequences of vector-valued observations. In the
            // sequence below, a single observation is composed of two
            // coordinate values, such as (x, y). There seems to be two
            // states, one for (x,y) values less than (5,5) and another
            // for higher values. The states seems to be switched on
            // every observation.
            double[][][] sequences =
            {
                new double[][] // sequence 1
                {
                    new double[] { 1, 2 }, // observation 1 of sequence 1
                    new double[] { 6, 7 }, // observation 2 of sequence 1
                    new double[] { 2, 3 }, // observation 3 of sequence 1
                },
                new double[][] // sequence 2
                {
                    new double[] { 2, 2 }, // observation 1 of sequence 2
                    new double[] { 9, 8 }, // observation 2 of sequence 2
                    new double[] { 1, 0 }, // observation 3 of sequence 2
                },
                new double[][] // sequence 3
                {
                    new double[] { 1, 3 }, // observation 1 of sequence 3
                    new double[] { 8, 9 }, // observation 2 of sequence 3
                    new double[] { 3, 3 }, // observation 3 of sequence 3
                },
            };


            // Specify a initial normal distribution for the samples.
            var density = new MultivariateNormalDistribution(dimension: 2);

            // Creates a continuous hidden Markov Model with two states organized in a forward
            //  topology and an underlying univariate Normal distribution as probability density.
            var model = new HiddenMarkovModel<MultivariateNormalDistribution>(new Forward(2), density);

            // Configure the learning algorithms to train the sequence classifier until the
            // difference in the average log-likelihood changes only by as little as 0.0001
            var teacher = new BaumWelchLearning<MultivariateNormalDistribution>(model)
            {
                Tolerance = 0.0001,
                Iterations = 0,
            };

            // Fit the model
            double logLikelihood = teacher.Run(sequences);

            // See the likelihood of the sequences learned
            double a1 = Math.Exp(model.Evaluate(new[] { 
                new double[] { 1, 2 }, 
                new double[] { 6, 7 },
                new double[] { 2, 3 }})); // 0.000208

            double a2 = Math.Exp(model.Evaluate(new[] { 
                new double[] { 2, 2 }, 
                new double[] { 9, 8  },
                new double[] { 1, 0 }})); // 0.0000376

            // See the likelihood of an unrelated sequence
            double a3 = Math.Exp(model.Evaluate(new[] { 
                new double[] { 8, 7 }, 
                new double[] { 9, 8  },
                new double[] { 1, 0 }})); // 2.10 x 10^(-89)

            Assert.AreEqual(0.00020825319093038984, a1);
            Assert.AreEqual(0.000037671116792519834, a2);
            Assert.AreEqual(2.1031924118199194E-89, a3);
        }
        public void MixtureWeightsFitTest2()
        {
            MemoryStream stream = new MemoryStream(Resources.CircleWithWeights);

            ExcelReader reader = new ExcelReader(stream, xlsx: false);

            DataTable table = reader.GetWorksheet("Sheet1");

            double[,] matrix = table.ToMatrix();

            double[][] points = matrix.Submatrix(null, 0, 1).ToArray();
            double[] weights = matrix.GetColumn(2);

            // Randomly initialize some mixture components
            MultivariateNormalDistribution[] components = new MultivariateNormalDistribution[2];
            components[0] = new MultivariateNormalDistribution(new double[] { 0, 1 }, Matrix.Identity(2));
            components[1] = new MultivariateNormalDistribution(new double[] { 1, 0 }, Matrix.Identity(2));

            // Create an initial mixture
            var mixture = new MultivariateMixture<MultivariateNormalDistribution>(components);

            mixture.Fit(points, weights);

            // Our model will be:
            double mean00 = mixture.Components[0].Mean[0];
            double mean01 = mixture.Components[0].Mean[1];
            double mean10 = mixture.Components[1].Mean[0];
            double mean11 = mixture.Components[1].Mean[1];

            Assert.AreEqual(-0.11704994950834195, mean00, 1e-10);
            Assert.AreEqual(0.11603470123007256, mean01, 1e-10);
            Assert.AreEqual(0.11814483652855159, mean10, 1e-10);
            Assert.AreEqual(-0.12029275652994373, mean11, 1e-10);
        }
        public void ProbabilityDensityFunctionTest3()
        {
            double[] mean = new double[3];
            double[,] covariance = Matrix.Identity(3);

            var target = new MultivariateNormalDistribution(mean, covariance);

            double[] x = { 1.2, -0.8 };

            bool thrown = false;
            try
            {
                target.ProbabilityDensityFunction(x);
            }
            catch (DimensionMismatchException)
            {
                thrown = true;
            }

            Assert.IsTrue(thrown);
        }
예제 #25
0
        public void FittingOptionsTest()
        {
            // Create a degenerate problem
            double[][] sequences = new double[][]
            {
                new double[] { 1, 1, 1, 1, 1, 0, 1, 1, 1, 1 },
                new double[] { 1, 1, 1, 1, 0, 1, 1, 1, 1, 1 },
                new double[] { 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
                new double[] { 1, 1, 1, 1, 1, 1 },
                new double[] { 1, 1, 1, 1, 1, 1, 1 },
                new double[] { 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
                new double[] { 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
            };

            // Creates a continuous hidden Markov Model with two states organized in a ergodic
            //  topology and an underlying multivariate Normal distribution as density.
            var density = new MultivariateNormalDistribution(1);

            var model = new HiddenMarkovModel <MultivariateNormalDistribution>(new Ergodic(2), density);

            // Configure the learning algorithms to train the sequence classifier
            var teacher = new BaumWelchLearning <MultivariateNormalDistribution>(model)
            {
                Tolerance  = 0.0001,
                Iterations = 0,

                // Configure options for fitting the normal distribution
                FittingOptions = new NormalOptions()
                {
                    Regularization = 0.0001,
                }
            };

            // Fit the model. No exceptions will be thrown
            double logLikelihood = teacher.Run(sequences);
            double likelihood    = Math.Exp(logLikelihood);

            Assert.AreEqual(47.434837528491286, logLikelihood, 1e-15);
            Assert.IsFalse(double.IsNaN(logLikelihood));

            Assert.AreEqual(0.0001, (teacher.FittingOptions as NormalOptions).Regularization);



            // Try without a regularization constant to get an exception
            bool thrown;

            thrown  = false;
            density = new MultivariateNormalDistribution(1);
            model   = new HiddenMarkovModel <MultivariateNormalDistribution>(new Ergodic(2), density);
            teacher = new BaumWelchLearning <MultivariateNormalDistribution>(model)
            {
                Tolerance = 0.0001, Iterations = 0,
            };
            Assert.IsNull(teacher.FittingOptions);
            try { teacher.Run(sequences); }
            catch { thrown = true; }
            Assert.IsTrue(thrown);

            thrown  = false;
            density = new Accord.Statistics.Distributions.Multivariate.MultivariateNormalDistribution(1);
            model   = new HiddenMarkovModel <MultivariateNormalDistribution>(new Ergodic(2), density);
            teacher = new BaumWelchLearning <MultivariateNormalDistribution>(model)
            {
                Tolerance      = 0.0001,
                Iterations     = 0,
                FittingOptions = new NormalOptions()
                {
                    Regularization = 0
                }
            };
            Assert.IsNotNull(teacher.FittingOptions);
            try { teacher.Run(sequences); }
            catch { thrown = true; }
            Assert.IsTrue(thrown);
        }
        public void GradientTest()
        {
            // Creates a sequence classifier containing 2 hidden Markov Models
            //  with 2 states and an underlying Normal distribution as density.
            MultivariateNormalDistribution density = new MultivariateNormalDistribution(3);
            var hmm = new HiddenMarkovClassifier<MultivariateNormalDistribution>(2, new Ergodic(2), density);

            double[][][] inputs =
            {
                new [] { new double[] { 0, 1, 0 }, new double[] { 0, 1, 0 }, new double[] { 0, 1, 0 } },
                new [] { new double[] { 1, 6, 2 }, new double[] { 2, 1, 6 }, new double[] { 1, 1, 0 } },
                new [] { new double[] { 9, 1, 0 }, new double[] { 0, 1, 5 }, new double[] { 0, 0, 0 } },
            };

            int[] outputs = 
            {
                0, 0, 1
            };

            var function = new MarkovMultivariateFunction(hmm);

            var model = new HiddenConditionalRandomField<double[]>(function);
            var target = new ForwardBackwardGradient<double[]>(model);

            FiniteDifferences diff = new FiniteDifferences(function.Weights.Length);

            diff.Function = parameters => func(model, parameters, inputs, outputs);

            double[] expected = diff.Compute(function.Weights);
            double[] actual = target.Gradient(function.Weights, inputs, outputs);


            for (int i = 0; i < actual.Length; i++)
            {
                Assert.AreEqual(expected[i], actual[i], 0.05);
                Assert.IsFalse(double.IsNaN(actual[i]));
                Assert.IsFalse(double.IsNaN(expected[i]));
            }
        }
예제 #27
0
        public void DecodeTest5()
        {
            var density = new MultivariateNormalDistribution(3);

            var hmm = new HiddenMarkovModel<MultivariateNormalDistribution>(2, density);


            double logLikelihood;
            int[] path = hmm.Decode(new double[][]
                {
                    new double[] { 0, 1, 2 },
                    new double[] { 0, 1, 2 },
                }, out logLikelihood);

            Assert.AreEqual(-11.206778379787982, logLikelihood);
        }
        public void GenerateTest1()
        {
            Accord.Math.Tools.SetupGenerator(0);

            double[] mean = { 2, 6 };

            double[,] cov = 
            {
                { 2, 1 },
                { 1, 5 } 
            };

            var normal = new MultivariateNormalDistribution(mean, cov);
            double[][] source = normal.Generate(10000000);

            var target = new MultivariateEmpiricalDistribution(source);

            Assert.IsTrue(mean.IsEqual(target.Mean, 0.001));
            Assert.IsTrue(cov.IsEqual(target.Covariance, 0.003));

            double[][] samples = target.Generate(10000000);

            double[] sampleMean = samples.Mean();
            double[,] sampleCov = samples.Covariance();

            Assert.AreEqual(2, sampleMean[0], 1e-2);
            Assert.AreEqual(6, sampleMean[1], 1e-2);
            Assert.AreEqual(2, sampleCov[0, 0], 1e-2);
            Assert.AreEqual(1, sampleCov[0, 1], 1e-2);
            Assert.AreEqual(1, sampleCov[1, 0], 1e-2);
            Assert.AreEqual(5, sampleCov[1, 1], 2e-2);
        }
        /// <summary>
        ///   Generates a random vector of observations from a distribution with the given parameters.
        /// </summary>
        ///
        /// <param name="samples">The number of samples to generate.</param>
        /// <param name="mean">The mean vector μ (mu) for the distribution.</param>
        /// <param name="covariance">The covariance matrix Σ (sigma) for the distribution.</param>
        ///
        /// <returns>A random vector of observations drawn from this distribution.</returns>
        ///
        public static double[][] Generate(int samples, double[] mean, double[,] covariance)
        {
            var normal = new MultivariateNormalDistribution(mean, covariance);

            return(normal.Generate(samples));
        }
예제 #30
0
        public void LearnTest9()
        {
            // Include this example in the documentattion
            var observations = new double[][][]
            {
                #region example
                new double[][]
                {
                    new double[] {2.58825719356537, -6.10018078957452, -3.51826652951428,},
                    new double[] {1.5637531876564, -8.92844874836103, -9.09330631370717,},
                    new double[] {2.12242007255554, -14.8117769726059, -9.04211363915664,},
                    new double[] {0.39045587182045, -10.3548189544216, -7.69608701297759,},
                    new double[] {-0.553155690431595, -34.9185135663671, 14.6941023804174,},
                    new double[] {-0.923129916191101, -6.06337512248124, 8.28106954197084,},
                    new double[] {0.478342920541763, -4.93066650122859, 3.1120912556361,},
                },
                new double[][]
                {
                    new double[] {1.89824998378754, -8.21581113387553, -7.88790716806936,},
                    new double[] {2.24453508853912, -10.281886698766, -9.67846789539227,},
                    new double[] {0.946296751499176, -22.0276392511088, -6.52238763834787,},
                    new double[] {-0.251136720180511, -13.3010653290676, 8.47499524273859,},
                    new double[] {-2.35625505447388, -18.1542111199742, 6.25564428645639,},
                    new double[] {0.200483202934265, -5.48215328147925, 5.88811639894938,},
                },
                new double[][]
                {
                    new double[] {2.7240589261055, -3.71720542338046, -3.75092324997593,},
                    new double[] {2.19917744398117, -7.18434871865373, -4.92539999824263,},
                    new double[] {1.40723958611488, -11.5545592998714, -5.14780194932221,},
                    new double[] {1.61909088492393, -12.5262932665595, -6.34366687651826,},
                    new double[] {-2.54745036363602, -8.64924529565274, 4.15127988308386,},
                    new double[] {0.815489888191223, -33.8531051237431, 4.3954106953589,},
                    new double[] {-2.2090271115303, -7.17818258102413, 8.9117419130814,},
                    new double[] {-1.9000232219696, -2.4331659041997, 6.91224717766923,},
                },
                new double[][]
                {
                    new double[] {4.88746017217636, -4.36384651224969, -5.45526891285354,},
                    new double[] {1.07786506414413, -12.9399071692788, -5.88248026843442,},
                    new double[] {2.28888094425201, -15.4017823367163, -9.36490649113217,},
                    new double[] {-1.16468518972397, -35.4200913138333, 5.44735305966353,},
                    new double[] {-1.1483296751976, -13.5454911068913, 7.83577905727326,},
                    new double[] {-2.58188247680664, -1.10149600205281, 10.5928750605715,},
                    new double[] {-0.277529656887054, -6.96828661824016, 4.59381106840823,},
                },
                new double[][]
                {
                    new double[] {3.39118540287018, -2.9173207268871, -5.66795398530988,},
                    new double[] {1.44856870174408, -9.21319243840922, -5.74986260778932,},
                    new double[] {1.45215392112732, -10.3989582187704, -7.06932768129103,},
                    new double[] {0.640938431024551, -15.319525165245, -7.68866476960221,},
                    new double[] {-0.77500119805336, -20.8335910793105, -1.56702420087282,},
                    new double[] {-3.48337143659592, -18.0461677940976, 12.3393172987974,},
                    new double[] {-1.17014795541763, -5.59624373275155, 6.09176828712909,},
                },
                new double[][]
                {
                    new double[] {-3.984335064888, -6.2406475893692, -8.13815178201645,},
                    new double[] {-2.12110131978989, -5.60649378910647, -7.69551693188544,},
                    new double[] {-1.62762850522995, -24.1160212319193, -14.9683354815265,},
                    new double[] {-1.15231424570084, -17.1336790735458, -5.70731951079186,},
                    new double[] {0.00514835119247437, -35.4256585588532, 11.0357975880744,},
                    new double[] {0.247226655483246, -4.87705331087666, 8.47028869639136,},
                    new double[] {-1.28729045391083, -4.4684855254196, 4.45432778840328,},
                },
                new double[][]
                {
                    new double[] {-5.14926165342331, -14.4168633009146, -14.4808205022332,},
                    new double[] {-3.93681302666664, -13.6040611430423, -9.52852874304709,},
                    new double[] {-4.0200162678957, -17.9772444010218, -10.9145425003168,},
                    new double[] {2.99205146729946, -11.3995995445577, 10.0112700536762,},
                    new double[] {-1.80960297584534, -25.9626088707583, 3.84153700324761,},
                    new double[] {-0.47445073723793, -3.15995343875038, 3.81288679772555,},
                },
                new double[][]
                {
                    new double[] {-3.10730338096619, -4.90623566171983, -7.71155001801384,},
                    new double[] {-2.58265435695648, -12.8249488039327, -7.81701695282102,},
                    new double[] {-3.70455086231232, -10.9642675851383, -10.3474496036822,},
                    new double[] {2.34457105398178, -22.575668228196, -4.00681935468317,},
                    new double[] {-0.137023627758026, -22.8846781066673, 6.49448229892285,},
                    new double[] {-1.04487389326096, -10.8106353197974, 6.89123118904132,},
                    new double[] {-0.807777792215347, -6.72485967042486, 6.44026679233423,},
                    new double[] {-0.0864192843437195, -1.82784244477527, 5.21446167464657,},
                },
                new double[][]
                {
                    new double[] {-3.68375554680824, -8.91158395500054, -9.35894038244743,},
                    new double[] {-3.42774018645287, -8.90966793048099, -12.0502934183779,},
                    new double[] {-2.21796408295631, -20.1283824753482, -9.3404551995806,},
                    new double[] {0.275979936122894, -24.8898254667703, -1.95441472953041,},
                    new double[] {2.8757631778717, -25.5929744730134, 15.9213204397452,},
                    new double[] {-0.0532664358615875, -5.41014381829368, 7.0702071664098,},
                    new double[] {-0.523447245359421, -2.21351362388411, 5.47910029515575,},
                },
                new double[][]
                {
                    new double[] {-2.87790596485138, -4.67335526533981, -5.23215633615683,},
                    new double[] {-2.4156779050827, -3.99829080603495, -4.85576151355235,},
                    new double[] {-2.6987336575985, -7.76589206730162, -5.81054787011341,},
                    new double[] {-2.65482440590858, -10.5628263066491, -5.60468502395908,},
                    new double[] {-2.54620611667633, -13.0387387107748, -5.36223367466908,},
                    new double[] {-0.349991768598557, -6.54244110985515, -4.35843018634009,},
                    new double[] {1.43021196126938, -14.1423935327282, 11.3171592025544,},
                    new double[] {-0.248833745718002, -25.6880129237476, 3.6943247495434,},
                    new double[] {-0.191526114940643, -7.40986142342928, 5.01053017361167,},
                    new double[] {0.0262223184108734, -2.32355649224634, 5.02960958030255,},
                },
                new double[][]
                {
                    new double[] {-0.491838902235031, -6.14010393559236, 0.827477332024586,},
                    new double[] {-0.806065648794174, -7.15029676810841, -1.19623376104369,},
                    new double[] {-0.376655906438828, -8.79062775480082, -1.90518908829517,},
                    new double[] {0.0747844576835632, -8.78933441325732, -1.96265207353993,},
                    new double[] {-0.375023484230042, 3.89681155173501, 9.01643231817069,},
                    new double[] {-2.8106614947319, -11.460008093918, 2.27801912994775,},
                    new double[] {8.87353122234344, -36.8569805718597, 6.36432395690119,},
                    new double[] {2.17160433530808, -6.57312981892095, 6.99683358454453,},
                },
                new double[][]
                {
                    new double[] {-2.59969010949135, -3.67992698430228, 1.09594294144671,},
                    new double[] {-1.09673067927361, -5.84256216502719, -0.576662929456575,},
                    new double[] {-1.31642892956734, -7.75851355520771, -2.38379618379558,},
                    new double[] {-0.119869410991669, -8.5749576027529, -1.84393133510667,},
                    new double[] {1.6157403588295, -8.50491836461337, 1.75083250596366,},
                    new double[] {1.66225507855415, -26.4882911957686, 1.98153904369032,},
                    new double[] {2.55657434463501, -10.5098938623168, 11.632377227365,},
                    new double[] {1.91832333803177, -9.98753621777953, 7.38483383044985,},
                    new double[] {2.16058492660522, -2.7784029746222, 7.8378896386686,},
                },
#endregion
            };

            var density = new MultivariateNormalDistribution(3);
            var model = new HiddenMarkovModel<MultivariateNormalDistribution>(new Forward(5), density);

            var learning = new BaumWelchLearning<MultivariateNormalDistribution>(model)
            {
                Tolerance = 0.0001,
                Iterations = 0,
                FittingOptions = new NormalOptions() { Regularization = 0.0001 }
            };

            double logLikelihood = learning.Run(observations);

            Assert.IsFalse(Double.IsNaN(logLikelihood));

            foreach (double value in model.Transitions)
                Assert.IsFalse(Double.IsNaN(value));

            foreach (double value in model.Probabilities)
                Assert.IsFalse(Double.IsNaN(value));
        }
        public static HiddenMarkovClassifier<MultivariateNormalDistribution> CreateModel3(
            int states = 4, bool priors = true)
        {

            MultivariateNormalDistribution density = new MultivariateNormalDistribution(2);

            var classifier = new HiddenMarkovClassifier<MultivariateNormalDistribution>(6,
                new Forward(states), density);

            string[] labels = { "1", "2", "3", "4", "5", "6" };
            for (int i = 0; i < classifier.Models.Length; i++)
                classifier.Models[i].Tag = labels[i];

            // Create the learning algorithm for the ensemble classifier
            var teacher = new HiddenMarkovClassifierLearning<MultivariateNormalDistribution>(classifier,

                // Train each model using the selected convergence criteria
                i => new BaumWelchLearning<MultivariateNormalDistribution>(classifier.Models[i])
                {
                    Tolerance = 0.1,
                    Iterations = 0,

                    FittingOptions = new NormalOptions() { Diagonal = true, Regularization = 1e-10 }
                }
            );

            teacher.Empirical = priors;

            // Run the learning algorithm
            teacher.Run(inputTest, outputTest);

            return classifier;
        }
        public void ProbabilityDensityFunctionTest2()
        {
            double[] mean = new double[64];
            double[,] covariance = Accord.Tests.Math.CholeskyDecompositionTest.bigmatrix;

            var target = new MultivariateNormalDistribution(mean, covariance);

            double expected = 1.0;
            double actual = target.ProbabilityDensityFunction(mean);

            Assert.AreEqual(expected, actual, 0.00000001);

            double[] x = Matrix.Diagonal(covariance).Multiply(1.5945e7);

            expected = 4.781042576287362e-12;
            actual = target.ProbabilityDensityFunction(x);

            Assert.AreEqual(expected, actual, 1e-21);
        }