/// <summary>
/// Method responsible for select the best attribute, based on information gain
/// </summary>
/// <param name="attributeList">Array of attributes</param>
/// <param name="categoricalAttribute">The categorical attribute</param>
/// <param name="data">Array of training data</param>
/// <returns>Best attribute</returns>
private static shared.Attribute GetAttributeLargestGain(shared.Attribute[] attributeList,
shared.Attribute categoricalAttribute,
string[][] data)
{
// creates a list that stores the attribute and its information gain
List<Tuple<shared.Attribute, double>> listInformationGain = new List<Tuple<shared.Attribute, double>>();
// for each attribute
foreach (shared.Attribute attribute in attributeList)
{
List<double> entropyList = new List<double>();
// if the attribute has a domain
if (attribute.Type == typeof(string))
{
// for each value to the attribute
foreach(string value in attribute.Values)
{
// gets entropy and it is proportion
double proportion = 0;
double entropy = GetEntropy(attribute, categoricalAttribute, value, data, out proportion);
// add the entropy to entropyList
entropyList.Add(entropy * proportion);
}
// the information gain is 1.0 minus the sum of all entropies
listInformationGain.Add(new Tuple<shared.Attribute, double>(attribute, 1D - entropyList.Sum()));
}
else
{
// clear all possible values
attribute.Values = new List<string>();
// gets a distinct ordered list from data
double[] orderedValues = data.ToList().OrderBy(m => double.Parse(m[attribute.Index]))
.ToList().ConvertAll<double>(m => double.Parse(m[attribute.Index])).Distinct().ToArray();
List<double> continousEntropyList = new List<double>();
List<Tuple<string, double>> continousGainList = new List<Tuple<string, double>>();
// for each distinct value in data
foreach (double item in orderedValues)
{
// for each value to that specific partition (first partition)
foreach (double line in orderedValues.Where(m => m < item).ToArray())
{
// gets entropy and it is proportion
double proportion = 0;
double entropy = GetEntropy(attribute, categoricalAttribute, line.ToString(), data,
out proportion);
// add the entropy to entropyList
continousEntropyList.Add(entropy * proportion);
}
// the information gain is 1.0 minus the sum of all entropies
if (continousEntropyList.Sum() > 0)
continousGainList.Add(
new Tuple<string, double>("<" + item, 1D - continousEntropyList.Sum()));
continousEntropyList.Clear();
// for each value to that specific partition (last partition)
foreach (double line in orderedValues.Where(m => m >= item).ToArray())
{
// gets entropy and it is proportion
double proportion = 0;
double entropy = GetEntropy(attribute, categoricalAttribute, line.ToString(), data,
out proportion);
// add the entropy to entropyList
continousEntropyList.Add(entropy * proportion);
}
// the information gain is 1.0 minus the sum of all entropies
if (continousEntropyList.Sum() > 0)
continousGainList.Add(
new Tuple<string, double>("=>" + item, 1D - continousEntropyList.Sum()));
}
// if there is any item in gain list
if (continousGainList.Count() > 0)
{
// gets the maximum gain
var maxGainContinuous = continousGainList.OrderByDescending(m => m.Item2).First();
// add value to the current attribute
attribute.Values.Add(maxGainContinuous.Item1);
// add the another partition to values as well
if (maxGainContinuous.Item1.IndexOf("=>") > -1)
attribute.Values.Add(maxGainContinuous.Item1.Replace("=>", "<"));
else
attribute.Values.Add(maxGainContinuous.Item1.Replace("<", "=>"));
// the information gain is 1.0 minus the sum of all entropies
listInformationGain.Add(
new Tuple<shared.Attribute, double>(attribute, maxGainContinuous.Item2));
}
}
}
// gets the max information gain element
if (listInformationGain.Count() > 0)
return listInformationGain.OrderByDescending(m => m.Item2).First().Item1;
else
return attributeList.First();
}