KNN算法基本实例

　　KNN算法是机器学习领域中一个最基本的经典算法。它属于无监督学习领域的算法并且在模式识别，数据挖掘和特征提取领域有着广泛的应用。

给定一些预处理数据，通过一个属性把这些分类坐标分成不同的组。这就是KNN的思路。

　　下面，举个例子来说明一下。图中的数据点包含两个特征：

　　现在，给出数据点的另外一个节点，通过分析训练节点来把这些节点分类。没有分来的及诶但我们标记为白色，如下所示：

　　直观来讲，如果我们把那些节点花道一个图片上，我们可能就能确定一些特征，或组。现在，给一个没有分类的点，我们可以通过观察它距离那个组位置最近来确定它属于哪个组。意思就是，假如一个点距离红色的组最近，我们就可以把这个点归为红色的组。简而言之，我们可以把第一个点（2.5,7）归类为绿色，把第二个点（5.5,4.5）归类为红色。

　　算法流程：

　　假设m是训练样本的数量，p是一个未知的节点。

　　1 把所有训练的样本放到也数组arr[]中。这个意思就是这个数组中每个元素就可以使用元组（x,y）表示。

　　2 伪码

for i= to m:
  Calculate Euclidean distance d(arr[i], p).

　　3 标记设置S为K的最小距离。这里每个距离都和一个已经分类的数据点相关。

　　4 返回在S之间的大多数标签。

　　实际程序C代码：

　

// C++ program to find groups of unknown
// Points using K nearest neighbour algorithm.
#include <bits/stdc++.h>
using namespace std;

struct Point
{
    int val;     // Group of point
    double x, y;     // Co-ordinate of point
    double distance; // Distance from test point
};

// Used to sort an array of points by increasing
// order of distance
bool comparison(Point a, Point b)
{
    return (a.distance < b.distance);
}

// This function finds classification of point p using
// k nearest neighbour algorithm. It assumes only two
// groups and returns 0 if p belongs to group 0, else
// 1 (belongs to group 1).
int classifyAPoint(Point arr[], int n, int k, Point p)
{
    // Fill distances of all points from p
    for (int i = ; i < n; i++)
        arr[i].distance =
            sqrt((arr[i].x - p.x) * (arr[i].x - p.x) +
                 (arr[i].y - p.y) * (arr[i].y - p.y));

    // Sort the Points by distance from p
    sort(arr, arr+n, comparison);

    // Now consider the first k elements and only
    // two groups
    int freq1 = ;     // Frequency of group 0
    int freq2 = ;     // Frequency of group 1
    for (int i = ; i < k; i++)
    {
        if (arr[i].val == )
            freq1++;
        else if (arr[i].val == )
            freq2++;
    }

    return (freq1 > freq2 ?  : );
}

// Driver code
int main()
{
    int n = ; // Number of data points
    Point arr[n];

    arr[].x = ;
    arr[].y = ;
    arr[].val = ;

    arr[].x = ;
    arr[].y = ;
    arr[].val = ;

    arr[].x = ;
    arr[].y = ;
    arr[].val = ;

    arr[].x = ;
    arr[].y = ;
    arr[].val = ;

    arr[].x = ;
    arr[].y = ;
    arr[].val = ;

    arr[].x = 1.5;
    arr[].y = ;
    arr[].val = ;

    arr[].x = ;
    arr[].y = ;
    arr[].val = ;

    arr[].x = ;
    arr[].y = ;
    arr[].val = ;

    arr[].x = 3.8;
    arr[].y = ;
    arr[].val = ;

    arr[].x = ;
    arr[].y = ;
    arr[].val = ;

    arr[].x = 5.6;
    arr[].y = ;
    arr[].val = ;

    arr[].x = ;
    arr[].y = ;
    arr[].val = ;

    arr[].x = 3.5;
    arr[].y = ;
    arr[].val = ;

    arr[].x = ;
    arr[].y = ;
    arr[].val = ;

    arr[].x = ;
    arr[].y = ;
    arr[].val = ;

    arr[].x = ;
    arr[].y = ;
    arr[].val = ;

    arr[].x = ;
    arr[].y = ;
    arr[].val = ;

    /*Testing Point*/
    Point p;
    p.x = 2.5;
    p.y = ;

    // Parameter to decide groupr of the testing point
    int k = ;
    printf ("The value classified to unknown point"
            " is %d.\n", classifyAPoint(arr, n, k, p));
    return ;
}

　　实际程序python代码：

　　

 # Python3 program to find groups of unknown
 # Points using K nearest neighbour algorithm.

 import math

 def classifyAPoint(points,p,k=):
     '''
      This function finds classification of p using
      k nearest neighbour algorithm. It assumes only two
      groups and returns  if p belongs to group , else
        (belongs to group ).

       Parameters -
           points : Dictionary of training points having two keys -  and
                    Each key have a list of training data points belong to that 

           p : A touple ,test data point of form (x,y)

           k : number of nearest neighbour to consider, default is
     '''

     distance=[]
     for group in points:
         for feature in points[group]:

             #calculate the euclidean distance of p from training points
             euclidean_distance = math.sqrt((feature[]-p[])** +(feature[]-p[])**)

             # Add a touple of form (distance,group) in the distance list
             distance.append((euclidean_distance,group))

     # sort the distance list in ascending order
     # and select first k distances
     distance = sorted(distance)[:k]

     freq1 =  #frequency of group
     freq2 =  #frequency og group 

     for d in distance:
         if d[] == :
             freq1 +=
         elif d[] == :
             freq2 += 

     return  if freq1>freq2 else 

 # driver function
 def main():

     # Dictionary of training points having two keys -  and
     # key  have points belong to class
     # key  have points belong to class 

     points = {:[(,),(,),(,),(,),(3.5,),(,),(,),(,)],
               :[(,),(,),(1.5,),(,),(,),(3.8,),(5.6,),(,),(,)]}

     # testing point p(x,y)
     p = (2.5,)

     # Number of neighbours
     k = 

     print("The value classified to unknown point is: {}".\
           format(classifyAPoint(points,p,k)))

 if __name__ == '__main__':
     main()

 # This code is contributed by Atul Kumar (www.fb.com/atul.kr.)