机器学习 --KNN的介绍与实现

具体思路为：

1.初始化学习样本，即向量集合
2.指定每个向量集合所属的分类，例如a,b,c
3.对于新来的向量v，指定邻居数K，找到距离v最近的K个邻居，设为集合s
4.对于s中的每个向量，找出分类数最大的那个（例如K=5，3向量分在了a，1个在b，1个在c），则v的分类为a。

图例



实现（c#）

1.安装 accord framework 的nuget



2.实例代码 
  

public class Vector
{
public double[] Features { get; set; }

public Vector(double[] features)
{
Features = features;
}

public override string ToString()
{
return "(" + string.Join(",", Features) + ")";
}
}

public class KNNDemo
{
private static double[][] Inputs;
private static int[] Outputs;

private static void Training()
{
Inputs = new[]
{
// The first two are from class 0
new double[] { -5, -2, -1 },
new double[] { -5, -5, -6 },

// The next four are from class 1
new double[] {  2,  1,  1 },
new double[] {  1,  1,  2 },
new double[] {  1,  2,  2 },
new double[] {  3,  1,  2 },

// The last three are from class 2
new double[] { 11,  5,  4 },
new double[] { 15,  5,  6 },
new double[] { 10,  5,  6 },
};

Outputs = new[]
{
0, 0,        // First two from class 0
1, 1, 1, 1,  // Next four from class 1
2, 2, 2      // Last three from class 2
};
}

private const int K = 3;
private const int TotalClasses = 3;

public static void SortDistancesThenShow(Vector v)
{
var results = new List<dynamic>();

for (int i = 0; i < Inputs.Length; i++)
{
var dist = DistanceBetween(Inputs[i], v.Features);
results.Add(new
{
InputStr = Stringify(Inputs[i]),
Dist = dist,
Class =Outputs[i]
});
}

results = results.OrderBy(x=>x.Dist).ToList();
foreach (var result in results)
{
dynamic r = result;
Console.WriteLine("input : {0}, class : {1} , distance : {2}", r.InputStr, r.Class, r.Dist);
}

}

private static string Stringify(double[] values)
{
return "(" + string.Join(",", values) + ")";
}

private static double DistanceBetween(double[] v1, double[] v2)
{
if (v1.Length != v2.Length)
{
throw new ArgumentException("vectors should be in same dimension.");
}

var distance = 0.0;
for (int i = 0; i < v1.Length; i++)
{
distance += Math.Pow(v1[i] - v2[i], 2);
}

return Math.Sqrt(distance);
}

public static int Execute(Vector v)
{
Training();

var knn = new KNearestNeighbors(K, TotalClasses, Inputs, Outputs);
return knn.Compute(v.Features);
}

}

class Program
{
static void Main(string[] args)
{
var v = new Vector(new double[] {11, 5, 4});

var result = KNNDemo.Execute(v);
Console.WriteLine("Classification for input '{0}' result is '{1}'", v, result);

KNNDemo.SortDistancesThenShow(v);

Console.ReadLine();
}
}

运行结果



从运行的打印结果中可以看出（已按距离排序），预测的分类为2，以及新向量到每个测试数据的距离是多少。