KNN算法-k近邻算法（k-Nearest Neighbors）前言

KNN优点：

1.思想极度简单；
2、应用数学知识少（近乎为零）；
3、效果好；
4、可以解释机器算法使用过程中的很多细节问题；
5、更完整的刻画机器学习应用的流程；

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一、普通knn算法是什么？

解析：

如图，就是一个肿瘤病人相关的数据，横轴代表发现肿瘤病人肿块的大小，纵轴代表发现肿瘤块的时间，每一个病人肿瘤发现时间及大小就构成图上一个点，恶性肿瘤用蓝色点表示，良性用红色。这就是初始信息，如果现状新来一个病人（绿点），那么分析他最有可能是良性肿瘤患者还是恶性肿瘤患者？我们采用K近邻算法来算。首先取一个k值，k=3；
在所有的点中寻找离绿点最近的三个点，之后这三个点用自己的属性进行投票，如图，蓝色：红色=3：0，因此就说这个绿点有很高的概率也是蓝色的点，即这个新的病人很有可能是一个恶性肿瘤患者；
这就是k近邻算法；
在这里插入图片描述

二、普通knn算法基础

1.分布解析

在这里插入图片描述

2.使用pycharm函数封装的形式运行KNN算法

使用pycharm函数封装的形式运行KNN算法：
import numpy as np
from math import sqrt
from collections import Counter
def kNN_classify(k,x_train,y_train,x):
assert 1<=k<=x_train.shape[0],“k must be valid”
assert x_train.shape[0]==y_train.shape[0],
“the size of x_train must equal to the size of y_train”
assert x_train.shape[1]==x.shape[0],
“the feature number of x must bu equal to x_train”
distances=[sqrt(np.sum((X_train-x)**2)) for X_train in x_train]
nearest = np.argsort(distances)
topK_y = [y_train[i] for i in nearest[:k]]
votes = Counter(topK_y)
return votes.most_common(1)[0][0]

import numpy as np
from math import sqrt
from collections import Counter
def kNN_classify(k,x_train,y_train,x):assert 1<=k<=x_train.shape[0],"k must be valid"assert x_train.shape[0]==y_train.shape[0],\"the size of x_train must equal to the size of y_train"assert x_train.shape[1]==x.shape[0],\"the feature number of x must bu equal to x_train"distances=[sqrt(np.sum((X_train-x)**2)) for X_train in x_train]nearest = np.argsort(distances)topK_y = [y_train[i] for i in nearest[:k]]votes = Counter(topK_y)return votes.most_common(1)[0][0]

在这里插入图片描述

3.使用scikit-learn中的knn

使用scikit-learn中的knn：
import numpy as np
from math import sqrt
from collections import Counter
class KNNClassifier:
# 初始化KNN分类器
def init(self,k):
assert k>=1,“k must be valid”
self.k=k
self._x_train=None
self._y_train = None
def fit(self,x_train,y_train):
“”“根据训练数据集训练knn分类器”“”
assert x_train.shape[0] == y_train.shape[0],
“the size of x_train must equal to the size of y_train”
assert self.k<=x_train.shape[0],
“the size of x_train must be at least k.”
self._x_train = x_train
self._y_train = y_train
return self
def predict(self,x_predict):
assert self._x_train is not None and self._y_train is not None,
“must fit before predict!”
assert x_predict.shape[1]==self._x_train.shape[1],
“the feature number of x_predict must be equal to x_train”
y_predict=[self._predict(x) for x in x_predict]
return np.array(y_predict)
def _predict(self,x):
“”“给一个单个预测数据x,返回x的预测结果”“”
assert x.shape[0] ==self._x_train.shape[1],
“the feature number of x must be equal to x_train”
distances = [sqrt(np.sum((X_train - x) ** 2)) for X_train in self._x_train]
nearest = np.argsort(distances)
topK_y = [self._y_train[i] for i in nearest[:self.k]]
votes = Counter(topK_y)
return votes.most_common(1)[0][0]

import numpy as np
from math import sqrt
from collections import Counter
class KNNClassifier:# 初始化KNN分类器def __init__(self,k):assert k>=1,"k must be valid"self.k=kself._x_train=Noneself._y_train = Nonedef fit(self,x_train,y_train):"""根据训练数据集训练knn分类器"""assert x_train.shape[0] == y_train.shape[0], \"the size of x_train must equal to the size of y_train"assert self.k<=x_train.shape[0],\"the size of x_train must be at least k."self._x_train = x_trainself._y_train = y_trainreturn selfdef predict(self,x_predict):assert self._x_train is not None and self._y_train is not None,\"must fit before predict!"assert x_predict.shape[1]==self._x_train.shape[1],\"the feature number of x_predict must be equal to x_train"y_predict=[self._predict(x) for x in x_predict]return np.array(y_predict)def _predict(self,x):"""给一个单个预测数据x,返回x的预测结果"""assert x.shape[0] ==self._x_train.shape[1],\"the feature number of x must be equal to x_train"distances = [sqrt(np.sum((X_train - x) ** 2)) for X_train in self._x_train]nearest = np.argsort(distances)topK_y = [self._y_train[i] for i in nearest[:self.k]]votes = Counter(topK_y)return votes.most_common(1)[0][0]

在这里插入图片描述