机器学习 -- 决策树根节点的选择过程

测试数据：

//############################### data table ##########################
// Outlook		Temp		Humidity		Windy		Play Golf
// Rainy		Hot		High			False		No
// Overoast		Hot		High			True		No
// Sunny		Mild		High			False		Yes
// Sunny		Cool		Normal			False		Yes
// Sunny		Cool		Normal			True		No
// Overoast		Cool		Normal			True		Yes
// Rainy		Mild		High			False		No
// Rainy		Cool		Normal			False		Yes
// Sunny		Mild		Normal			False		Yes
// Rainy		Mild		Normal			True		Yes
// Overoast		Mild		High			True		Yes
// Overoast		Hot		Normal			False		Yes
// Sunny		Mild		High			True		No
//######################################################################

测试代码：

void Main()
{
	




	var e_total = E(5,9);
	var e_Outlook = E2(new []
					{
						new []{3,2},
						new []{4,0},
						new []{2,3}
					},
					14.0
					);


	Console.WriteLine("gain of outlook:" + (e_total-(e_Outlook)));
	
	var e_Temp = E2(new []
					{
						new []{2,2},
						new []{4,2},
						new []{3,1}
					},
					14.0
					);
	Console.WriteLine("gain of temperature:"+ (e_total-e_Temp));
	
	var e_Humidity = E2(new []
					{
						new []{3,4},
						new []{6,1}
					},
					14.0
					);
	Console.WriteLine("gain of humidity:"+ (e_total-e_Humidity));
	
	var e_windy = E2(new []
					{
						new []{3,3},
						new []{6,2}
					},
					14.0
					);
	Console.WriteLine("gain of windy:"+ (e_total-e_windy));
	
	//Max Gaining wins
}
static double E2(dynamic pairs, double total){
	var r = 0.0;
	for(var i =0 ;i < pairs.Length; i++){
		var p_i = (pairs[i][0] + pairs[i][1])/total;
		var e_i = E(pairs[i][0] ,pairs[i][1]);
		r += p_i * e_i;
	}
	return r;
}
static double E(int x1, int x2){
	if(x1 == 0 || x2 ==0){return 0;}
	
	var p1 = x1 * 1.0/(x1+x2);
	var p2 = x2 * 1.0/(x1+x2);
	
	return -p1*Math.Log(p1,2) - p2*Math.Log(p2,2);
}

参考链接：
http://www.saedsayad.com/decision_tree.htm