ID3Learning Class

[SerializableAttribute]
public class ID3Learning : DecisionTreeLearningBase, 
	ISupervisedLearning<DecisionTree, int[], int>

<SerializableAttribute>
Public Class ID3Learning
	Inherits DecisionTreeLearningBase
	Implements ISupervisedLearning(Of DecisionTree, Integer(), Integer)

// In this example, we will learn a decision tree directly from integer
// matrices that define the inputs and outputs of our learning problem.

int[][] inputs =
{
    new int[] { 0, 0 },
    new int[] { 0, 1 },
    new int[] { 1, 0 },
    new int[] { 1, 1 },
};

int[] outputs = // xor between inputs[0] and inputs[1]
{
    0, 1, 1, 0
};

// Create an ID3 learning algorithm
ID3Learning teacher = new ID3Learning();

// Learn a decision tree for the XOR problem
var tree = teacher.Learn(inputs, outputs);

// Compute the error in the learning
double error = new ZeroOneLoss(outputs).Loss(tree.Decide(inputs));

// The tree can now be queried for new examples:
int[] predicted = tree.Decide(inputs); // should be { 0, 1, 1, 0 }

// In this example, we will be using the famous Play Tennis example by Tom Mitchell (1998).
// In Mitchell's example, one would like to infer if a person would play tennis or not
// based solely on four input variables. Those variables are all categorical, meaning that
// there is no order between the possible values for the variable (i.e. there is no order
// relationship between Sunny and Rain, one is not bigger nor smaller than the other, but are 
// just distinct). Moreover, the rows, or instances presented above represent days on which the
// behavior of the person has been registered and annotated, pretty much building our set of 
// observation instances for learning:

// Note: this example uses DataTables to represent the input data , but this is not required.
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");

// In order to try to learn a decision tree, we will first convert this problem to a more simpler
// representation. Since all variables are categories, it does not matter if they are represented
// as strings, or numbers, since both are just symbols for the event they represent. Since numbers
// are more easily representable than text string, we will convert the problem to use a discrete 
// alphabet through the use of a Accord.Statistics.Filters.Codification codebook.</para>

// A codebook effectively transforms any distinct possible value for a variable into an integer 
// symbol. For example, “Sunny” could as well be represented by the integer label 0, “Overcast” 
// by “1”, Rain by “2”, and the same goes by for the other variables. So:</para>

// Create a new codification codebook to 
// convert strings into integer symbols
var codebook = new Codification(data);

// Translate our training data into integer symbols using our codebook:
DataTable symbols = codebook.Apply(data);
int[][] inputs = symbols.ToArray<int>("Outlook", "Temperature", "Humidity", "Wind");
int[] outputs = symbols.ToArray<int>("PlayTennis");

// For this task, in which we have only categorical variables, the simplest choice 
// to induce a decision tree is to use the ID3 algorithm by Quinlan. Let’s do it:

// Create a teacher ID3 algorithm
var id3learning = new ID3Learning()
{
    // Now that we already have our learning input/ouput pairs, we should specify our
    // decision tree. We will be trying to build a tree to predict the last column, entitled
    // “PlayTennis”. For this, we will be using the “Outlook”, “Temperature”, “Humidity” and
    // “Wind” as predictors (variables which will we will use for our decision). Since those
    // are categorical, we must specify, at the moment of creation of our tree, the
    // characteristics of each of those variables. So:

    new DecisionVariable("Outlook",     3), // 3 possible values (Sunny, overcast, rain)
    new DecisionVariable("Temperature", 3), // 3 possible values (Hot, mild, cool)  
    new DecisionVariable("Humidity",    2), // 2 possible values (High, normal)    
    new DecisionVariable("Wind",        2)  // 2 possible values (Weak, strong) 

    // Note: It is also possible to create a DecisionVariable[] from a codebook:
    // DecisionVariable[] attributes = DecisionVariable.FromCodebook(codebook);
};

// Learn the training instances!
DecisionTree tree = id3learning.Learn(inputs, outputs);

// Compute the training error when predicting training instances
double error = new ZeroOneLoss(outputs).Loss(tree.Decide(inputs));

// The tree can now be queried for new examples through 
// its decide method. For example, we can create a query

int[] query = codebook.Transform(new[,]
{
    { "Outlook",     "Sunny"  },
    { "Temperature", "Hot"    },
    { "Humidity",    "High"   },
    { "Wind",        "Strong" }
});

// And then predict the label using
int predicted = tree.Decide(query);  // result will be 0

// We can translate it back to strings using
string answer = codebook.Revert("PlayTennis", predicted); // Answer will be: "No"