private static void naiveBayes(double[][] inputs, int[] outputs)
{
// In our problem, we have 2 classes (samples can be either
// positive or negative), and 2 inputs (x and y coordinates).
var nb = new NaiveBayes<NormalDistribution>(classes: 2,
inputs: 2, initial: new NormalDistribution());
// The Naive Bayes expects the class labels to
// range from 0 to k, so we convert -1 to be 0:
//
outputs = outputs.Apply(x => x < 0 ? 0 : x);
// Estimate the Naive Bayes
double error = nb.Estimate(inputs, outputs);
// Classify the samples using the model
int[] answers = inputs.Apply(nb.Compute);
// Plot the results
ScatterplotBox.Show("Expected results", inputs, outputs);
ScatterplotBox.Show("Naive Bayes results", inputs, answers)
.Hold();
}
public void ComputeTest2()
{
DataTable data = new DataTable("Mitchell's Tennis Example");
data.Columns.Add("Day", "Outlook", "Temperature", "Humidity", "Wind", "PlayTennis");
// We will set Temperature and Humidity to be continuous
data.Columns["Temperature"].DataType = typeof(double);
data.Columns["Humidity"].DataType = typeof(double);
data.Rows.Add("D1", "Sunny", 38.0, 96.0, "Weak", "No");
data.Rows.Add("D2", "Sunny", 39.0, 90.0, "Strong", "No");
data.Rows.Add("D3", "Overcast", 38.0, 75.0, "Weak", "Yes");
data.Rows.Add("D4", "Rain", 25.0, 87.0, "Weak", "Yes");
data.Rows.Add("D5", "Rain", 12.0, 30.0, "Weak", "Yes");
data.Rows.Add("D6", "Rain", 11.0, 35.0, "Strong", "No");
data.Rows.Add("D7", "Overcast", 10.0, 40.0, "Strong", "Yes");
data.Rows.Add("D8", "Sunny", 24.0, 90.0, "Weak", "No");
data.Rows.Add("D9", "Sunny", 12.0, 26.0, "Weak", "Yes");
data.Rows.Add("D10", "Rain", 25, 30.0, "Weak", "Yes");
data.Rows.Add("D11", "Sunny", 26.0, 40.0, "Strong", "Yes");
data.Rows.Add("D12", "Overcast", 27.0, 97.0, "Strong", "Yes");
data.Rows.Add("D13", "Overcast", 39.0, 41.0, "Weak", "Yes");
data.Rows.Add("D14", "Rain", 23.0, 98.0, "Strong", "No");
// Create a new codification codebook to
// convert strings into discrete symbols
Codification codebook = new Codification(data);
int classCount = codebook["PlayTennis"].Symbols; // 2 possible values (yes, no)
int inputCount = 4; // 4 variables (Outlook, Temperature, Humidity, Wind)
IUnivariateDistribution[] priors =
{
new GeneralDiscreteDistribution(codebook["Outlook"].Symbols), // 3 possible values (Sunny, overcast, rain)
new NormalDistribution(), // Continuous value (celsius)
new NormalDistribution(), // Continuous value (percentage)
new GeneralDiscreteDistribution(codebook["Wind"].Symbols) // 2 possible values (Weak, strong)
};
// Create a new Naive Bayes classifiers for the two classes
var target = new NaiveBayes<IUnivariateDistribution>(classCount, inputCount, priors);
// Extract symbols from data and train the classifier
DataTable symbols = codebook.Apply(data);
double[][] inputs = symbols.ToArray("Outlook", "Temperature", "Humidity", "Wind");
int[] outputs = symbols.ToArray<int>("PlayTennis");
// Compute the Naive Bayes model
target.Estimate(inputs, outputs);
double logLikelihood;
double[] responses;
// Compute the result for a sunny, cool, humid and windy day:
double[] instance = new double[]
{
codebook.Translate(columnName:"Outlook", value:"Sunny"),
12.0,
90.0,
codebook.Translate(columnName:"Wind", value:"Strong")
};
int c = target.Compute(instance, out logLikelihood, out responses);
string result = codebook.Translate("PlayTennis", c);
Assert.AreEqual("No", result);
Assert.AreEqual(0, c);
Assert.AreEqual(0.840, responses[0], 1e-3);
Assert.AreEqual(1, responses.Sum(), 1e-10);
Assert.IsFalse(double.IsNaN(responses[0]));
Assert.AreEqual(2, responses.Length);
}
private void btnCreate_Click(object sender, EventArgs e)
{
if (dgvLearningSource.DataSource == null)
{
MessageBox.Show("Please load some data first.");
return;
}
classNames = new string[] { "G1", "G2" };
// Finishes and save any pending changes to the given data
dgvLearningSource.EndEdit();
// Creates a matrix from the source data table
double[,] table = (dgvLearningSource.DataSource as DataTable).ToMatrix(out columnNames);
// Get only the input vector values
double[][] inputs = table.Submatrix(null, 0, 1).ToArray();
// Get only the label outputs
int[] outputs = table.GetColumn(2).ToInt32();
string[] colNames = columnNames.Submatrix(first: 2);
// Create the Bayes classifier and perform classification
bayes = new NaiveBayes<NormalDistribution>(2, 2, new NormalDistribution());
// Estimate the model parameters from the data
double error = bayes.Estimate(inputs, outputs);
// Show the estimated distributions and class probabilities
dataGridView1.DataSource = new ArrayDataView(bayes.Distributions, colNames, classNames);
// Generate samples for class 1
var x1 = bayes.Distributions[0, 0].Generate(1000);
var y1 = bayes.Distributions[0, 1].Generate(1000);
// Generate samples for class 2
var x2 = bayes.Distributions[1, 0].Generate(1000);
var y2 = bayes.Distributions[1, 1].Generate(1000);
// Combine in a single graph
var w1 = Matrix.Stack(x1, y1).Transpose();
var w2 = Matrix.Stack(x2, y2).Transpose();
var z = Matrix.Vector(2000, value: 1.0);
for (int i = 0; i < 1000; i++) z[i] = 0;
var graph = Matrix.Stack(w1, w2).Concatenate(z);
CreateScatterplot(zedGraphControl2, graph);
}
public void ComputeTest()
{
DataTable data = new DataTable("Mitchell's Tennis Example");
data.Columns.Add("Day", "Outlook", "Temperature", "Humidity", "Wind", "PlayTennis");
data.Rows.Add("D1", "Sunny", "Hot", "High", "Weak", "No");
data.Rows.Add("D2", "Sunny", "Hot", "High", "Strong", "No");
data.Rows.Add("D3", "Overcast", "Hot", "High", "Weak", "Yes");
data.Rows.Add("D4", "Rain", "Mild", "High", "Weak", "Yes");
data.Rows.Add("D5", "Rain", "Cool", "Normal", "Weak", "Yes");
data.Rows.Add("D6", "Rain", "Cool", "Normal", "Strong", "No");
data.Rows.Add("D7", "Overcast", "Cool", "Normal", "Strong", "Yes");
data.Rows.Add("D8", "Sunny", "Mild", "High", "Weak", "No");
data.Rows.Add("D9", "Sunny", "Cool", "Normal", "Weak", "Yes");
data.Rows.Add("D10", "Rain", "Mild", "Normal", "Weak", "Yes");
data.Rows.Add("D11", "Sunny", "Mild", "Normal", "Strong", "Yes");
data.Rows.Add("D12", "Overcast", "Mild", "High", "Strong", "Yes");
data.Rows.Add("D13", "Overcast", "Hot", "Normal", "Weak", "Yes");
data.Rows.Add("D14", "Rain", "Mild", "High", "Strong", "No");
// Create a new codification codebook to
// convert strings into discrete symbols
Codification codebook = new Codification(data);
int classCount = codebook["PlayTennis"].Symbols; // 2 possible values (yes, no)
int inputCount = 4; // 4 variables (Outlook, Temperature, Humidity, Wind)
GeneralDiscreteDistribution[] priors =
{
new GeneralDiscreteDistribution(codebook["Outlook"].Symbols), // 3 possible values (Sunny, overcast, rain)
new GeneralDiscreteDistribution(codebook["Temperature"].Symbols), // 3 possible values (Hot, mild, cool)
new GeneralDiscreteDistribution(codebook["Humidity"].Symbols), // 2 possible values (High, normal)
new GeneralDiscreteDistribution(codebook["Wind"].Symbols) // 2 possible values (Weak, strong)
};
// Create a new Naive Bayes classifiers for the two classes
var target = new NaiveBayes<GeneralDiscreteDistribution>(classCount, inputCount, priors);
// Extract symbols from data and train the classifier
DataTable symbols = codebook.Apply(data);
double[][] inputs = symbols.ToArray("Outlook", "Temperature", "Humidity", "Wind");
int[] outputs = symbols.ToArray<int>("PlayTennis");
// Compute the Naive Bayes model
target.Estimate(inputs, outputs);
double logLikelihood;
double[] responses;
// Compute the result for a sunny, cool, humid and windy day:
double[] instance = codebook.Translate("Sunny", "Cool", "High", "Strong").ToDouble();
int c = target.Compute(instance, out logLikelihood, out responses);
string result = codebook.Translate("PlayTennis", c);
Assert.AreEqual("No", result);
Assert.AreEqual(0, c);
Assert.AreEqual(0.795, responses[0], 1e-3);
Assert.AreEqual(1, responses.Sum(), 1e-10);
Assert.IsFalse(double.IsNaN(responses[0]));
Assert.AreEqual(2, responses.Length);
}
public void ComputeTest2()
{
// Some sample texts
string[] spamTokens = Tokenize(@"I decided to sign up for the Disney Half Marathon. Half of a marathon is 13.1 miles. A full marathon is 26.2 miles. You may wonder why the strange number of miles. “26.2” is certainly not an even number. And after running 26 miles who cares about the point two? You might think that 26.2 miles is a whole number of kilometers. It isn’t. In fact, it is even worse in kilometers – 42.1648128. I bet you don’t see many t-shirts in England with that number printed on the front.");
string[] loremTokens = Tokenize(@"Lorem ipsum dolor sit amet, Nulla nec tortor. Donec id elit quis purus consectetur consequat. Nam congue semper tellus. Sed erat dolor, dapibus sit amet, venenatis ornare, ultrices ut, nisi. Aliquam ante. Suspendisse scelerisque dui nec velit. Duis augue augue, gravida euismod, vulputate ac, facilisis id, sem. Morbi in orci. Nulla purus lacus, pulvinar vel, malesuada ac, mattis nec, quam. Nam molestie scelerisque quam. Nullam feugiat cursus lacus.orem ipsum dolor sit amet.");
// Their respective classes
string[] classes = { "spam", "lorem" };
// Create a new Bag-of-Words for the texts
BagOfWords bow = new BagOfWords(spamTokens, loremTokens)
{
// Limit the maximum number of occurrences in
// the feature vector to a single instance
MaximumOccurance = 1
};
// Define the symbols for the Naïve Bayes
int[] symbols = new int[bow.NumberOfWords];
for (int i = 0; i < symbols.Length; i++)
symbols[i] = bow.MaximumOccurance + 1;
// Create input and outputs for training
int[][] inputs =
{
bow.GetFeatureVector(spamTokens),
bow.GetFeatureVector(loremTokens)
};
int[] outputs =
{
0, // spam
1, // lorem
};
// Create the naïve Bayes model
NaiveBayes bayes = new NaiveBayes(2, symbols);
for (int i = 0; i < bayes.ClassCount; i++)
for (int j = 0; j < bayes.SymbolCount.Length; j++)
for (int k = 0; k < bayes.SymbolCount[j]; k++)
bayes.Distributions[i, j][k] = 1e-10;
// Estimate the model
bayes.Estimate(inputs, outputs);
// Initialize with prior probabilities
for (int i = 0; i < bayes.ClassCount; i++)
for (int j = 0; j < bayes.SymbolCount.Length; j++)
{
double sum = bayes.Distributions[i, j].Sum();
Assert.AreEqual(1, sum, 1e-5);
}
// Consume the model
{
// First an example to classify as lorem
int[] input = bow.GetFeatureVector(loremTokens);
int answer = bayes.Compute(input);
string result = classes[answer];
Assert.AreEqual("lorem", result);
}
{
// Then an example to classify as spam
int[] input = bow.GetFeatureVector(spamTokens);
int answer = bayes.Compute(input);
string result = classes[answer];
Assert.AreEqual("spam", result);
}
}
public void ComputeTest3_Obsolete()
{
// Let's say we have the following data to be classified
// into three possible classes. Those are the samples:
//
int[][] inputs =
{
// input output
new int[] { 0, 1, 1, 0 }, // 0
new int[] { 0, 1, 0, 0 }, // 0
new int[] { 0, 0, 1, 0 }, // 0
new int[] { 0, 1, 1, 0 }, // 0
new int[] { 0, 1, 0, 0 }, // 0
new int[] { 1, 0, 0, 0 }, // 1
new int[] { 1, 0, 0, 0 }, // 1
new int[] { 1, 0, 0, 1 }, // 1
new int[] { 0, 0, 0, 1 }, // 1
new int[] { 0, 0, 0, 1 }, // 1
new int[] { 1, 1, 1, 1 }, // 2
new int[] { 1, 0, 1, 1 }, // 2
new int[] { 1, 1, 0, 1 }, // 2
new int[] { 0, 1, 1, 1 }, // 2
new int[] { 1, 1, 1, 1 }, // 2
};
int[] outputs = // those are the class labels
{
0, 0, 0, 0, 0,
1, 1, 1, 1, 1,
2, 2, 2, 2, 2,
};
// Create a discrete naive Bayes model for 3 classes and 4 binary inputs
int[] symbols = new int[] { 2, 2, 2, 2 };
var bayes = new NaiveBayes(3, symbols);
// Teach the model. The error should be zero:
double error = bayes.Estimate(inputs, outputs);
// Now, let's test the model output for the first input sample:
int answer = bayes.Compute(new int[] { 0, 1, 1, 0 }); // should be 1
Assert.AreEqual(0, error);
for (int i = 0; i < inputs.Length; i++)
{
error = bayes.Compute(inputs[i]);
double expected = outputs[i];
Assert.AreEqual(expected, error);
}
}
private string bayes(DataTable tbl)
{
Codification codebook = new Codification(tbl,
"Clump Thickness", "Uniformity of Cell Size", "Uniformity of Cell Shape", "Marginal Adhesion", "Single Epithelial Cell Size", "Bare Nuclei", "Bland Chromatin", "Normal Nucleoli", "Mitoses", "Class");
// Translate our training data into integer symbols using our codebook:
DataTable symbols = codebook.Apply(tbl);
int[][] inputs = symbols.ToIntArray("Clump Thickness", "Uniformity of Cell Size", "Uniformity of Cell Shape", "Marginal Adhesion", "Single Epithelial Cell Size", "Bare Nuclei", "Bland Chromatin", "Normal Nucleoli", "Mitoses");
int[] outputs = symbols.ToIntArray("Class").GetColumn(0);
// Gather information about decision variables
int[] symbolCounts =
{
codebook["Clump Thickness"].Symbols, // 3 possible values (Sunny, overcast, rain)
codebook["Uniformity of Cell Size"].Symbols, // 3 possible values (Hot, mild, cool)
codebook["Uniformity of Cell Shape"].Symbols, // 2 possible values (High, normal)
codebook["Marginal Adhesion"].Symbols , // 2 possible values (Weak, strong)
codebook["Single Epithelial Cell Size"].Symbols ,
codebook["Bare Nuclei"].Symbols ,
codebook["Bland Chromatin"].Symbols ,
codebook["Normal Nucleoli"].Symbols ,
codebook["Mitoses"].Symbols
};
int classCount = codebook["Class"].Symbols; // 2 possible values (yes, no)
// Create a new Naive Bayes classifiers for the two classes
NaiveBayes target = new NaiveBayes(classCount, symbolCounts);
// Compute the Naive Bayes model
target.Estimate(inputs, outputs);
// We will be computing the label for a sunny, cool, humid and windy day:
int[] instance = codebook.Translate(inputlar[0], inputlar[1], inputlar[2], inputlar[3],
inputlar[4], inputlar[5], inputlar[6], inputlar[7], inputlar[8]);
// Now, we can feed this instance to our model
int output = target.Compute(instance);
// Finally, the result can be translated back to one of the codewords using
string result = codebook.Translate("Class", output); // result is "No"
return result;
}
public void ComputeTest3()
{
// Let's say we have the following data to be classified
// into three possible classes. Those are the samples:
//
double[][] inputs =
{
// input output
new double[] { 0, 1, 1, 0 }, // 0
new double[] { 0, 1, 0, 0 }, // 0
new double[] { 0, 0, 1, 0 }, // 0
new double[] { 0, 1, 1, 0 }, // 0
new double[] { 0, 1, 0, 0 }, // 0
new double[] { 1, 0, 0, 0 }, // 1
new double[] { 1, 0, 0, 0 }, // 1
new double[] { 1, 0, 0, 1 }, // 1
new double[] { 0, 0, 0, 1 }, // 1
new double[] { 0, 0, 0, 1 }, // 1
new double[] { 1, 1, 1, 1 }, // 2
new double[] { 1, 0, 1, 1 }, // 2
new double[] { 1, 1, 0, 1 }, // 2
new double[] { 0, 1, 1, 1 }, // 2
new double[] { 1, 1, 1, 1 }, // 2
};
int[] outputs = // those are the class labels
{
0, 0, 0, 0, 0,
1, 1, 1, 1, 1,
2, 2, 2, 2, 2,
};
// Create a new continuous naive Bayes model for 3 classes using 4-dimensional Gaussian distributions
var bayes = new NaiveBayes<NormalDistribution>(inputs: 4, classes: 3, initial: NormalDistribution.Standard);
// Teach the Naive Bayes model. The error should be zero:
double error = bayes.Estimate(inputs, outputs, options: new NormalOptions
{
Regularization = 1e-5 // to avoid zero variances
});
// Now, let's test the model output for the first input sample:
int answer = bayes.Compute(new double[] { 0, 1, 1, 0 }); // should be 1
Assert.AreEqual(0, error);
for (int i = 0; i < inputs.Length; i++)
{
double actual = bayes.Compute(inputs[i]);
double expected = outputs[i];
Assert.AreEqual(expected, actual);
}
}